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ISSN 2167-1273 Volume 4, Issue 01, January 2015 FEA Information Engineering Journal SIMULATION

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ISSN 2167-1273 Volume 4, Issue 01, January 2015

FEA Information Engineering Journal

SIMULATION

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FEA Information Engineering Journal

Aim and Scope FEA Information Engineering Journal (FEAIEJ™) is a monthly published online journal to cover the latest Finite Element Analysis Technologies. The journal aims to cover previous noteworthy published papers and original papers. All published papers are peer reviewed in the respective FEA engineering fields. Consideration is given to all aspects of technically excellent written information without limitation on length. All submissions must follow guidelines for publishing a paper, or periodical. If a paper has been previously published, FEAIEJ requires written permission to reprint, with the proper acknowledgement give to the publisher of the published work. Reproduction in whole, or part, without the express written permissio of FEA Information Engineering Journal, or the owner of of the copyright work, is strictly prohibited. FEAIJ welcomes unsolicited topics, ideas, and articles. Monthly publication is limited to no more then five papers, either reprint, or original. Papers will be archived on www.feaiej.com For information on publishing a paper original or reprint contact [email protected] Subject line: Journal Publication

Cover Sound Radiation Analysis of a Tire with LS-DYNA®

Zhe Cui - Yun Huang Livermore Software Technology Corporation

Figure 5: Reflecting surface was modeled as rigid

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FEA Information Engineering Journal

TABLE OF CONTENTS Publications are © to 13th LS-DYNA International Users Conference, 2014

All contents are copyright © to the publishing company, author or respective company. All rights reserved. Sound Radiation Analysis of a Tire with LS-DYNA®

Zhe Cui - Yun Huang Livermore Software Technology Corporation

ATV and MATV Techniques for BEM Acoustics in LS-DYNA®

Zhe Cui - Yun Livermore Software Technology Corporation

Benchmark of Frequency Domain Methods for Composite Materials with Damage using LS-DYNA®

THEME Engineering, Inc. Numerical Investigation of Landslide Mobility and Debris-Resistant Flexible Barrier with LS-DYNA®

Yuli Huang, Jack Yiu, Jack Pappin, and Richard Sturt Arup

Julian S. H. Kwan and Ken K. S. Ho Geotechnical Engineering Office, Civil Engineering & Development

Application of LS-DYNAÒ for Auto NVH Problems Yun Huang, Zhe Cui

Livermore Software Technology Corporation

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Sound Radiation Analysis of a Tire with LS-DYNAÒ

Zhe Cui

Livermore Software Technology Corporation 7374 Las Positas Rd., Livermore, CA, United States 94551

[email protected] 925-245-4582

Yun Huang Livermore Software Technology Corporation

7374 Las Positas Rd., Livermore, CA, United States 94551 [email protected]

925-245-4521

Abstract

In vibro-acoustic problems, which are assumed to be weak acoustic-structure interactions, the vibration of structural response is computed first. The obtained result is taken as boundary condition for the acoustic part of the vibro-acoustic problem. Consequently, the radiated noise at any point into space can be calculated. This paper presents a case study of applying the steady state dynamics (SSD) coupling with boundary element method (BEM) in LS-DYNA for calculating sound radiation of a tire.

Introduction

LS-DYNA is a widely used finite element code, intended to solve complex mechanical problems. One of the recent developments of the code is the addition of a vibro-acoustic solver [1], which enables users to perform a variety of vibro-acoustic simulations in the frequency domain.

Steady State Dynamics

The steady state dynamics (SSD) in LS-DYNA[2] calculates the steady state response of a structure subjected to known harmonic excitations. The excitation spectrum can be given as nodal force, pressure or base accelerations. The excitation spectrum takes complex variable input. In other words, both the amplitude and the phase angle of the excitation are considered. The frequency domain dynamic features: SSD are based on the results of modal analysis of the structures, e.g. the natural frequencies and modal shapes. They use either mode superposition method, or mode acceleration method or some other modal combination methods. Thus one needs to run implicit eigenvalue analysis preceding the frequency domain dynamic analysis. The SSD feature can be activated by the keyword *FREQUENCY_DOMAIN_SSD. The results are also complex and have either real and imaginary parts, or amplitude / phase angle pairs. The amplitudes of the response are given in a binary plot file d3ssd, which is accessible by LS-PrePost®. A complete results including the amplitude and phase angle can be found in ASCII

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database NODOUT_SSD for nodes specified in keyword *DATABASE_HISTORY_NODE, and database ELOUT_SSD for elements specified in the following keywords *DATABASE_HISTORY_SOLID *DATABASE_HISTORY_BEAM *DATABASE_HISTORY_SHELL *DATABASE_HISTORY_TSHELL.

BEM Model for Acoustic System

In frequency domain, the acoustic wave propagation in an ideal fluid in absence of any volume acoustic source is governed by Helmholtz equation [3] given as follows:

02 =+D pkp (1) Where ck /w= denotes the wave number, c is the sound velocity, fpw 2= is the pulsation frequency and p is the pressure at any field point. Equation (1) can be transformed into an integral equation by using Green's theorem. In this case, the pressure at any point in the fluid medium can be expressed as an integral of both pressure and velocity over a surface as given by the following equation:

G¶¶

-¶¶

= òGd

nGp

npGPCp )()( (2)

where r

eGikr

p4

-

= is the Green's function, n is the normal on the surface Γ , C is the jump term

resulting from the treatment of the singular integral involving Green's function, and r is the distance between the field point P and surface integration point. The normal derivative of the

pressure is related to the normal velocity by npvinp w-=

¶¶ .

The knowledge of pressure and velocity on the surface allows calculating the pressure of any field points. This constitutes the main idea of the integral equation theory. In practical cases, the problems are Neumann, Dirichlet or Robin ones. In Neumann problem, the velocity is prescribed on the surface while in Dirichlet case the pressure is imposed on the surface. Finally, for robin problems the acoustic impedance, which is a combination of velocity and pressure, is given on the surface. Hence, generally only half of the variables are known on the surface. By using the variational indirect method or the collocation method, a linear equation system can be established, which provides solution for the other half of the variables on the surface. Then the integral equation (2) can be used to calculate the acoustic pressure at any field points. The BEM acoustic solver has been coupled with the FEM dynamic analysis capability of LS-DYNA to provide an integrated solution for vibro-acoustic problems. Two options are available to couple the BEM acoustic solver with the FEM dynamic analysis. For the first one, the traditional time domain FEM is performed and the time domain dynamic response of the structure is converted to frequency domain by using Fast Fourier Transform (FFT); for the second one, frequency domain steady state dynamics is performed (using *FREQUENCY_DOMAIN_SSD) and it gives response in frequency domain directly. The obtained boundary velocities (accelerations) provide boundary condition for the subsequent

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BEM acoustic computation. Both the variational indirect BEM and collocation direct BEM are available in LS-DYNA.

Sound radiation prediction of a tire Tire noise is one of main sources in automotive noise, especially pass-by noise. In this paper, we consider only radiation noise caused by structural vibration. The tire model is shown in figure1.

Figure 1: Tire Model

The harmonic point force is applied to the nodes which are in contact with ground. Tire surface velocity can be obtained from SSD analysis in figure 2.

Figure 2: Surface velocities at different frequency

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Figure 3: the setup for a pass-by noise test form the ISO 362 Standard.

Figure 4: R7.5 hemi sphere field point used for pass-by noise test

To calculate the sound radiation, a hemisphere field points (radius= 7.5m) are used for pass-by noise test [4], which is shown in figures 3 and 4. Considering tire on road are reflecting surface radiation case, reflecting surface was modeled as rigid shown in figure 5. The keyword *FREQENCY_DOMAIN_ACOUSTIC_BEM_HALF_SPACE can be used for reflecting surface case. Figure 6 shows the sound pressure level of different frequency at field points.

Figure 5: Reflecting surface was modeled as rigid

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Figure 6: Sound pressure level contours of field points

In the classical approach, the acoustic response is calculated by solving the system of equations for each loading conditions. For a multi-load case solution such as tire vibration due to different road condition, Modal acoustic transfer vectors (MATVs) approach can be used. The modal acoustic transfer vectors (MATVs) are the modal counter part of the ATVs: they express the acoustic transfer function in modal coordinates from a radiating structure to a field point, and, therefore, list the acoustic contribution from each individual structural mode. The acoustic response in the field point is obtained by recombination of the MATV with the corresponding structural modal responses. Working in modal coordinates results in an important data reduction. However, MATVs are no longer independent from the structural model as they are linked to the structural modal basis. Whenever the structural modal basis changes, e.g. due to structural modifications, the set of MATVs need to be re-evaluated. In general, the ATVs are known as [5], the acoustic pressure ( )wp at a field point is computed by a rapid vector-vector product of ATV and normal vibration shape on the surface ( ){ }wnv , which requires very little calculation time:

( ) ( ){ } ( ){ }www nT vATVp = (3)

The process for computing the structural response frequently relies on modal superposition, so that:

( ){ } [ ] ( ){ }www mrspjv nn F= (4) Where [ ]nF is the matrix of modal vectors, projected on the local normal direction of the radiating surface, and ( ){ }wmrsp is the modal response (vector of modal participation factors). The structural analysis in LS-DYNA can provide the participation factors of the modes, at each frequency, for each load case. Considering again Equation (3), we can use the mode shape vectors (for the radiating surface only) as surface vibration shapes, thus deriving Modal Acoustic Transfer Vectors iMATV as:

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( ){ } { }niT

i ATVjMATV fww= (5) Where { }nif is the (projected) shape vector of the thi mode shape. Then, the final acoustic result is determined by multiplying the MATVs by the modal participations:

( ) ( ){ } ( ){ }ww mrspMATVwp T= (6)

To run MATV, we use the keyword * FREQENCY_DOMAIN_ACOUSTIC_BEM_MATV. Figure 7 shows sound pressure level of node 2839929 from hemi sphere field point (Figure 4)

Figure 7: Sound pressure level at field point

Conclusions

This paper introduces briefly steady state dynamics and acoustics boundary element method of LS-DYNA for solving frequency domain vibration and acoustic problems. The BEM coupled with SSD analysis in LS-DYNA are used to predict the sound radiation of tire. The objective of implementing these features is to provide users the capabilities to deal with frequency domain vibration and acoustic problems, which are very common in auto industries.

References

1. Y. Huang, M. Souli, C. Ashcraft, R. grimes, J. Wang, Development of Frequency Domain Dynamic and Acoustic Capabilities in LS-DYNA. 8th European LS-DYNA Users Conference, Strasbourg, May 2011.

2. Huang Y., Wang B., Mode-based frequency response function and steady state dynamics in LS-DYNA. Proceedings of the 11th International LS-DYNA®

Users’ Conference, June 6-8, 2010, Dearborn, Michigan. 3. T.W. Wu (Editor), Boundary Element Acoustics: Fundamentals and Computer Codes, Advances in

Boundary Elements, WIT Press, Boston, 2000. 4. ISO IS 362-1:2007, Measurement of noise emitted by accelerating road vehicles – Engineering method -

Part 1: M and N categories, International Organization for Standardization, Geneva, Switzerland (2007). 5. R. Citarella, L.Federico, A. Cicatiello, Modal acoustic transfer vector approach in a FEM-BEM vibro-

acoustic analysis. Engineering Analysis with Boundary Element 31, 248-258 2007.

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ATV and MATV Techniques for BEM Acoustics in LS-DYNAÒ

Yun Huang, Zhe Cui

Livermore Software Technology Corporation 7374 Las Positas Road, Livermore CA 94551

Abstract This paper presents the new ATV (Acoustic Transfer Vector) and MATV (Modal Acoustic Transfer Vector) techniques for BEM acoustics in LS-DYNA, which were implemented recently. Acoustic Transfer Vector provides the transfer function between the normal nodal velocity on structural surface and the acoustic response at selected field points; Modal Acoustic Transfer Vector provides similar transfer function, but is based on the excitation from modal shape vibrations. ATV and MATV reveal the inherent properties of structures and acoustic volume, and can be used to predict radiated noise from vibrating structures when combined with vibration boundary conditions. Particularly they are useful for the acoustic analysis of structures subjected to multiple load cases. Some examples are given to illustrate the application of the ATV and MATV techniques. For ATV, post-processing of the results in the form of binary plot database is also presented.

Introduction

Recently a bunch of acoustic boundary element methods (BEM) have been implemented to LS-DYNA [1]. These acoustic BEM can be used to predict the noise from a vibrating structure. They have wide application in auto NVH analysis, and other vibro-acoustic analysis.

To facilitate the acoustic analysis for the situation where multiple load cases are present, two new techniques ATV (Acoustic Transfer Vector) and MATV (Modal Acoustic Transfer Vector) have been implemented to the acoustic BEM.

ATV is defined as the transfer function between the normal nodal (elemental) velocity and the acoustic pressure at field points. Once all the ATV are obtained, the total acoustic pressure at field points can be computed by simple matrix – vector multiplication, as in equation (1)

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In equation (1), ip is the acoustic pressure at field point i and jv is the actual normal velocity at node j. m is the number of field points and n is the number of nodes in boundary elements. ji,W represents the acoustic pressure at field point i, due to unit normal velocity at node j. Please note that all the variables in equations (1) and (2) are dependent on frequency w=2p f. Besides, the variables in both equations are complex.

As indicated by equation (2), for a given frequency and given geometry, the ATV matrix is constant and is not dependent on the loading condition. Once the ATV matrix is obtained, for any given normal velocity vector { }nv , a simple matrix-vector multiplication can provide the total pressure { }mP quickly. That is why this method is very efficient and provides huge saving in CPU times if multiple load cases have to be considered.

To get the velocity vector { }nv , one can run lab testing, road testing, or numerical vibration analysis such like using the keyword *FREQUCNY_DOMAIN_SSD in LS-DYNA. The *FREQUCNY_DOMAIN_SSD keyword provides the solution for harmonic steady state vibration based on mode superposition method. For each vibration frequency, the structural response is composed of contribution from all the involved eigen modes. This suggests that one can first run acoustic computation for each eigen mode, to get acoustic contribution from each mode, and then do a modal superposition to get the total acoustic pressure, using the same modal coordinates obtained in SSD calculation. This brings us to the concept of modal ATV, or MATV, as illustrated by equation (3)

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Or equation (4) in short form

{ } [ ] { }llmm qMATVP ´= (4)

Where, ji,Y represents the acoustic pressure at field point i, due to the normal velocity boundary condition for eigen mode j. Once again ip is the acoustic pressure at field point i. jq is the modal coordinates for mode j. jq is obtained from SSD (Steady State Dynamics) analysis. m is the number of field points and l is the number of modes involved in the mode superposition procedure. Once again all the variables in equation (1) are dependent on frequency w=2p f and they are all complex. Please note that ATV and MATV can be related by the following equation

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Where i is the imaginary unit ( 1-=i ) and { }nu is the displacement vector. The matrix [ ] ln´f is the modal shape matrix, provided by implicit eigenvalue analysis. { }lq is the modal coordinate vector.

One can see, for each load case, only the modal coordinates vector { }lq need to be updated and once it is ready, a simple matrix-vector multiplication can be performed and it provides the solution for acoustic pressure vector at the field points.

For a real practical problem, the number of eigen modes involved is usually much less than the number of nodes in the boundary elements ( ln << ), so the MATV approach represented by equation (3) or (4) is more efficient than the ATV approach, if the vibration simulation can be accomplished by SSD.

For ATV, a binary plot database d3atv is provided in LS-DYNA, to visualize the acoustic pressure due to unit normal velocity at each surface node. This helps to study the contribution to acoustic pressure from each surface node. To get d3atv database, the keyword *DATABASE_FREQUENCY_BINARY_D3ATV is needed in LS-DYNA keyword input deck. For more details about this keyword, please refer to LS-DYNA Keyword Users’ Manual [2].

Several examples are given below to demonstrate the ATV and MATV capabilities.

ATV for a simplified engine model

Figure 1 shows a simplified engine model and the location of two field points. To run ATV analysis for this model, the keyword *FREQUENCY_DOMAIN_ACOUSTIC_BEM_{ATV} is employed. In this keyword, we set up the range of frequencies to compute, the number of excitation frequencies, the location of field points, and some other parameters for BEM Acoustic analysis. More details about this keyword can be found in reference [2].

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Field point 2Field point 1

Figure 1: A simplified engine model for ATV computation

In LS-DYNA computation, we run BEM analysis for unit normal velocity from each of the surface nodes, and compute the acoustic pressure at the two field points. Please note that for each frequency, one does not need to reform the complex influence matrix for each surface node under consideration --- it is formed only once. We only need to update the R.H.S. of the equation system (see equation (6) below).

( )[ ] ( ){ } ( ){ }www yxC = (6)

The results of the ATV computation are given in 1) ASCII files

ATV_FIELD_PT_ID ATV_DB_FIELD_PT_ID And 2) BINARY database d3atv.

In ATV_FIELD_PT_ID, the complex pressure for one field point (indicated by ID) for user specified excitation frequencies is given for each surface node. When multiple field points are present, LS-DYNA will generate multiple ATV_FIELD_PT_ID, with different ID.

In ATV_DB_FIELD_PT_ID, the SPL (Sound Pressure Level, or dB) for the field point ID for user specified excitation frequencies is given for each surface node.

D3atv is a binary plot database, and it is written in the same format as d3plot and other binary plot databases in LS-DYNA. It is accessible to LS-PrePostÒ. It shows the real part, imaginary part and dB values of the acoustic pressure, at each field point, at each frequency, due to unit normal velocity at each surface node. For this example, some of the results are given in Figure 2,

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Figure 2: Real part of pressure ATV at field point 1

and Figure 3.

Figure 3: Imaginary part of pressure ATV at point 2

From d3atv, such as Figures 2 and 3, people can see easily that which part of the surface gives more contribution to the final acoustic pressure at field points.

MATV for a simplified engine model

Figure 4 shows a simplified door model. It is fixed at the upper edge and the 4 holes near the lower edge. It is subjected to 10 load cases. For each of the load case, a nodal force spectrum is given at one node on the door. The range of frequency is same for the 10 load cases. So this provides a good example for using the MATV technique in LS-DYNA.

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Figure 4: A door model for MATV computation

To using the MATV technique, the first thing to do is to generate the MATV matrices. The excitation frequency is 100-500 Hz, with 101 equally spaced frequencies. So for running implicit eigenvalue analysis, modes up to 600 Hz (which is 20% higher than the highest excitation frequency) is needed. Keyword *FREQUENCY_DOMAIN_ACOUSTIC_BEM_{MATV} is used, without specifying any loading or excitation conditions for acoustic computation. Keywords *CONTROL_IMPLICIT_GENERAL, *CONTROL_IMPLICIT_EIGENVALUE are set, to perform the implicit eigenvalue analysis, and generate d3eigv binary plot database. LS-DYNA will extract the eigen vectors { }jf from d3eigv. For each excitation frequency f, LS-DYNA will generate the psedo-velocity boundary condition { }ji fw ( fpw 2= ) and run BEM acoustic computation to get the MATV matrix.

For the second step, the keyword *FREQUENCY_DOMAIN_SSD is adopted, to run steady state dynamic computation for given nodal force loading. SSD will generate the modal coordinates { }lq for each excitation frequency. The keyword *FREQUENCY_DOMAIN_ACOUSTIC_BEM_{MATV} is also needed and we set IREST=1, which means that we are running restart BEM acoustic computation based on existing MATV.

To check the accuracy of the method, we run this problem also in the traditional way (SSD + BEM Acoustic computation) without using MATV. The results for one load case by the two different methods are plotted in Figure 5, and one can see that the two curves match very well.

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Figure 5: SPL at field point

The total CPU time for running 1 load case and 10 load cases is listed in Table 1. The computation is performed on Intel Xeron CPU E5504 @2.00 GHz (CPU MHz: 1596.00 cache size 4096 KB). Three different methods are used: 1) Direct SSD + traditional BEM, which means that we go through the whole procedures (Modal analysis, SSD and tradition BEM) for each load case; 2) Restart SSD + traditional BEM, which means that starting from the 2nd load case, we skip the modal analysis part, and run a restart SSD using existing d3eigv, and then the traditional BEM; and 3) Restart SSD + MATV BEM, which means that we skip the modal analysis part starting from the 2nd load case, and run a restart SSD and then use the MATV based BEM to get the acoustic pressure for all the load cases.

For 1) Direct SSD + traditional BEM method, the total CPU time for 10 load cases is simply 10 times of the CPU time for one load case. For 2) Restart SSD + traditional BEM, starting from the 2nd load case, LS-DYNA can make use of the existing d3eigv database, and run modal superposition to get SSD response directly. This way we can skip the time-consuming modal analysis step, and gain some CPU saving. The most CPU saving is observed in 3) Restart SSD + MATV BEM. For 3), the step 1 (generating the MATV matrices) is needed only once and the step2 (BEM acoustic calculation based on MATV) is repeated 10 times if 10 load cases are present. Since the CPU time for step 2 is so small one can expect that when more load cases are present, more CPU saving can be achieved by the MATV BEM, comparing to the traditional BEM.

Cases 1) Direct SSD + traditional BEM

2) Restart SSD + traditional BEM

3) Restart SSD + MATV BEM

1 load case 2 h 39 m 50 s 2 h 39 m 50 s 4 h 40 m 56 s

10 load cases 26 h 38 m 18 s 25 h 53 m 13 s 4 h 41 m 10 s

Table 1: CPU time for different methods (h: hour; m: minute; s: second)

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For the “1 load case”, one always has to start from modal analysis and generate d3eigv binary database. So the CPU time for methods 1) and method 2) is same for the “1 load case”. Method 3) takes longer time to run for the “1 load case” but the extra time is well compensated by the huge saving in computation for additional load cases.

Conclusion

For BEM Acoustic solver in LS-DYNA, ATV and MATV techniques have been implemented. ATV provides the transfer function between the normal nodal velocity on structural surface and the acoustic response at selected field points; Modal Acoustic Transfer Vector provides similar transfer function, but is based on the excitation from modal shape vibrations. ATV and MATV are properties of the structure and they are not dependent on the loading conditions. Once computed, they can be used for many load cases. That is why they are useful and provide efficient tools when one needs to run acoustic computation for multiple load cases.

Another possible application of ATV and MATV is the inverse acoustic analysis. Based on the measured acoustic environment, and using the ATV / MATV techniques, one is able to locate the source of vibration excitation. This can be useful to solve the auto BSR (Buzz, Squeak and Rattle) problems.

References 1. Huang Y., Souli M., Development of acoustic and vibro acoustic solvers in LS-DYNA®. Proceedings of

the 10th International LS-DYNA® Users’ Conference, June 8-10, 2008, Dearborn, Michigan.

2. LS-DYNA Keyword User's Manual, Livermore Software Technology Corporation, January 14, 2014 (revision: 4571).

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Benchmark of Frequency Domain Methods for Composite Materials with Damage using LS-DYNA®

Myeong-Gyu Bae*, Seonwoo Lee

THEME Engineering, Inc.

Abstract The composite material is widely used in the structures as aircrafts, satellites, ships,

automobiles, and so on which demand light weight and high performance. A various type of damage could occur through low-speed impacts and fatigue loads. It is generally known that the assessment of the natural frequency by vibration testing is a very attractive method as a Non-Destructive Test (NDT) and the vibration response of a composite structure can be utilized as an indicator of damage. In this paper, a desirable FE modeling technique regarding composite types

(Laminated/Sandwich) and laminate methods of composite material were investigated using LS-DYNA. Firstly, according to the laminated properties of composite material (number of layers,

anisotropy, shape, etc.), frequency responses were compared between the latest theories and the latest version of LS-DYNA. Secondly, various types of damage in cantilever beam with composite material were represented and estimated in FE model and those frequency responses were compared among experiments, LS-DYNA, and other FE code. Finally, delamination phenomenon in rectangular plate with composite material was represented and estimated in FE model and those frequency responses were compared between experiment and LS-DYNA. It was evaluated and verified that the prediction for the tendency of natural frequency using the

frequency domain method in LS-DYNA could be appropriate for composite materials with or without damage.

1. Introduction The applications of composite materials have become common in various fields of industries.

These materials have higher stiffness and strength to weight ratio and also offer many advantages in the designing and manufacturing of structures. The application of woven fabric composites in engineering structures has been significantly

increased due to attractive characteristics such as flexible processing options, low fabrication cost while also possessing adequate mechanical properties. The laminated composite plates are basic structural components used in a variety of engineering

structures. Composite plate structures often operate in complex environmental conditions and are frequently exposed to a variety of dynamic excitations. A measurement of the natural frequency by vibration testing is a very attractive method as Non-Destructive Test (NDT). The vibration test would not require access to the whole surface and the time taken to perform the test can be very small. Thus the vibration response of a composite plate can be utilized as an indicator of damage estimation.

This paper deals with the evaluation and verification on the frequency responses of composite structure with damage and those results by modal and frequency domain analysis using the latest version of LS-DYNA are compared among the latest theories, experiment, and other FE code.

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2. Analysis solutions of theories and responses of LS-DYNA 2.1 Theories The Classical Laminate Plate Theory (CLPT) which ignores the effect of transverse shear

deformation becomes inadequate for the analysis of multilayer composites. In general the CLPT often underpredicts deflections and overpredicts natural frequencies and bucking loads. And the first-order theories (FSDTs) assume linear in-plane stresses and displacements respectively through the laminate thickness. Since the FSDT accounts for layerwise constant states of transverse shear stress, shear correction coefficients are needed to rectify the unrealistic variation of the shear strain/stress through the thickness and which ultimately define the shear strain energy. In order to overcome the limitations of FSDT, higher-order shear deformation theories (HSDTs) have been developed through many other previous studies [1, 2, 3, 4, 5]. In displacement model, in order to approximate the three-dimensional elasticity problem to a

two-dimensional plate problem, the displacement components

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Model (4) – Senthilnathan et al.

TYPICAL LAMINA

1 2

3, z

(1,2,3) – LAMINA REFERENCE AXES

z, 3

w0

v0

y

a

b u0

x

L = 1 L = 2

zL zL+1

L = NL

( x,y,z ) – LAMINATE REFERENCE AXES

LAMINATE MID-PLANE

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At edges

layers of equal thickness

Laminated Composite

Sandwich Composite

Core

Face

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Table.2 Nondimensionalized fundamental frequency

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Face sheets (Graphite-Epoxy T300/934)

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Table.6 Nondimensionalized fundamental frequency

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Fig.5 Nondimensionalized first and fifth mode natural frequency (

) versus aspect ratio (a/b) of a simply supported five-layer sandwich plate with antisymmetric cross-ply face sheets. 3. Damage detection in composite materials using frequency response methods 3.1 Experimental setup The full explanations on the experimental setup for damage detection in composite materials can be found in the reference [7] and are summarized as below:

Four graphite/epoxy panels were manufactured according to standard in-house procedure using AS4/3501-6. A [90/±45/0]s quasi-isotropic laminate was selected for these experiments, and the specimens were cut to (250 x 50 x 1)

using a continuous diamond grit cutting wheel. Next, various types of damage were introduced to the specimens. In the first group, 6.4 mm diameter holes were drilled into the center of each specimen using a silicon-carbide core drill to minimize damage during the drilling process. The second group was cyclically loaded in the same fixture for 2000 cycles at 80% of this load with an R ratio of -1. In the next group, the center mid-plane of the laminate was delaminated using a thin utility blade to cut a

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3.3 Damage Modeling in LS-DYNA Several types of damage were also simulated in various models, as represented in Figure 6.

First, one simple variation of the control model had a hole modeled into it. Second, the laminate modulus was affected more by fatigue-induced cracks for the same crack density, achieving about 80% of its original value. Third, two separate cantilever parts with half of original thickness in each had same nodal positions at mid surface and were distinguished as lower part and upper part via defining the location of reference surface (NLOC) and then the delamination area of interest was modeled by untied nodes using *CONTACT_TIED_NODES_TO_SUR FACE in LS-DYNA.

Fig.6 X-Radiographs(left) and FE(right) of damage models 3.4 Results and discussion It shows that very similar mode shapes regarding each frequency are observed between

experiments of control specimen and responses of LS-DYNA as shown in Figure 7. In natural frequency responses at Table 7, the error of values for each bending modes and torsional mode in LS-DYNA is about 3% and 10% in maximum as compared with experiment. It is appeared that the range of error values is larger in torsional mode compared to bending mode for both LS-DYNA and other FE code. A further study needs to be followed for this low accuracy of frequencies in torsional modes of laminated composites with damage. The velocity response magnitude according to the frequencies is given as Figure 8 and it shows that the amplitude of response and the mode shape between LS-DYNA and other FE code are in good agreement.

Fig.7 First to fourth mode shapes of control specimen plotted using laser vibrometer data (left) and LS-DYNA results (right)

First bending

Second bending

First torsion

Third bending

First bending

Second bending

First torsion

Third bending

A

B

C

D

A

B

C

D

Control Hole Damage Delamination Control Hole Damage Delamination

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Table.7 Natural frequencies and mode shapes as determined from scanning laser vibrometer data, FEM in I-DEAS and LS-DYNA

(All Hz) Mode Shape Source Control Hole Damage Delamination Mode 1 1st Bending Experiment 12.5 12.5 12.5 12.5

I-DEAS 12.5 12.4 12.1 12.1 LS-DYNA 12.4 12.4 12.3 12.3

Mode 2 2nd Bending Experiment 78.1 78.1 75.0 78.1 I-DEAS 77.8 77.2 73.7 75.5 LS-DYNA 77.5 77.4 76.3 76.6

Mode 3 1st Torsion Experiment 157 148 146 137 I-DEAS 157 155 150 149 LS-DYNA 156 156 154 151

Mode 4 3rd Bending Experiment 218 217 209 215 I-DEAS 218 217 213 211 LS-DYNA 217 217 215 212

Mode 5 4th Bending Experiment 423 423 413 428 I-DEAS 428 425 413 412 LS-DYNA 427 426 423 420

Mode 6 2nd Torsion Experiment 461 453 428 451 I-DEAS 476 473 466 465 LS-DYNA 475 474 469 462

1. Results from experiment and I-DEAS are found in reference [7].

Fig.8 Frequency response function plot from I-DEAS(left) and LS-DYNA(right), range of 0-500 Hz

4. Delamination detection of composite laminates using natural frequency

vibration method 4.1 Experimental setup The full explanations on the experimental setup for delamination detection in composite

materials can be found in the reference [7] and are summarized as below: The composite plate specimens used in this experiment are made from woven eight plies (0/90)

with (

= 3.75 kg/m2) composite of E-glass fiber and epoxy matrix with hardener (Epolam,

2017). After the curing process at room temperature, four test specimens of size (200 x 200 x 2.5)mm

3 are cut from a plate of 8 plies laminate by using cutting machine, with different area of

mid plane artificial delamination (50x50, 100x100, 150x150)mm2 as shown in Figure 9.

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4.2 Healthy& Delamination FE Model in LS-DYNA Finite element analyses were performed in LS-DYNA to determine the frequency responses of

8-layered woven fiber glass/epoxy specimens. 4-node quadrilateral shell elements were used to model the (200 x 200 x 2.5)mm3 specimen. It consisted of 8-layers (0/90) quasi-isotropic laminate of Epolam 2017 (E1 = 26GPa, E2 = 13GPa, G12= 1GPa, v12= 0.25), which were entered into a material property card (*MAT_COMPOSITE_DAMAGE, *MAT_022) in LS-DYNA. Additionally, the new keyword card *FREQUENCY_DOMAIN_FRF was defined in order for the computation of frequency responses. In order to represent delamination (50 x 50, 100 x 100, 150 x 150)mm2 in FE model, the

procedure introduced in the previous damage FE modeling was utilized in the same way; two separate cantilever parts with half of original thickness in each had same nodal positions at mid surface and were distinguished as lower part and upper part via defining the location of reference surface (NLOC) and then the delamination area of interest was modeled by untied nodes using *CONTACT_TIED_NODES_TO_SUR FACE in LS-DYNA.

Fig.9 Test Specimens (left) and LS-DYNA FE Model (right) of Delamination of Composite Laminates models 4.3 Vibration test The full explanations on this vibration test with composite materials can be found in the

reference [7] and are summarized as below: Vibration tests are conducted on 8-layers (0/90) woven E glass fiber/epoxy composite plates,

with and without artificial delamination to detect the effect of delamination area on plate natural frequencies. The natural frequencies are measured for all specimens with four edges simply supported boundary condition. Locally manufactured, two square frames with side element diameter of 5 mm, Figure 10, are used to simulate four edges simply supporting conditions. An impact hammer was used to hit the plate five times at the marked point and the data averaged for each test as shown in Figure 11.

A. Healthy Plate (No Delamination) B. Delamination (50

C. Delamination (100

D. Delamination (150

B. Delamination (50

C. Delamination (100

D. Delamination (150

A. Healthy Plate (No Delamination)

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Fig.10 Simple supported fixture apparatus of Square Laminate Specimen

Fig.11 Vibration test system

4.4 Results and discussion The 1st to 4th mode shapes of healthy plate in LS-DYNA are depicted in Figure 12. The results

indicate that the frequency responses between LS-DYNA and experiment are in good agreement because the error in average is about within 4% as shown in Table 8. It also apparently shows that the tendency on decreasing of natural frequency while the delamination area increases is predicted well in LS-DYNA as shown in Figure 13. The accelerance response according to the frequencies for the laminated composites with delamination is given as Figure 14.

Fig.12 First to fourth mode shapes of healthy plate plotted using LS-DYNA results

200 mm

200 mm

Fixing Fiber glass/epoxy square plate 2.5mm hi k Delamination

5mm diameter square frame

Hammer Exciter

Accelerometer

Plate Amplifier

Channel 1

Channel 2

Dual channel signal analyzer

First mode Second mode Third mode Fourth mode

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Table.8: Experimental measured Natural Frequency (Hz) of square laminate plates with different central mid plane delamination area

(All Hz) Source Healthy Plate Mid Plane Delamination Area 50

100

150

Mode 1 Experiment 172.2 170.3 (1.10%) 169.2 (1.74%) 159.4 (7.43%) LS-DYNA 173.4 173.4 (0.00%) 171.3 (1.21%) 157.1 (9.40%)

Mode 2 Experiment 459.5 420.8 (8.42%) 314.5 (31.55%) 258.2 (43.80%) LS-DYNA 473.2 454.7 (3.90%) 350.9 (25.84%) 274.5 (41.99%)

Mode 3 Experiment 466.3 432.5 (7.24%) 337.4 (27.64%) 271.2 (41.84%) LS-DYNA 473.2 454.7 (3.90%) 350.9 (25.84%) 274.5 (41.99%)

Mode 4 Experiment 686.4 637.3 (7.15%) 549.2 (19.98%) 293.3 (57.26%) LS-DYNA 688.0 683.8 (0.61%) 582.7 (15.30%) 288.0(58.13%)

( - ): Percentage reduction of Natural Frequencies compare with healthy plate due to different delamination area

Fig.13 Response of Natural Frequency with Normalized Delamination Area (left) and Relative Delamination Area (right)

Fig.14 Frequency response function plot from LS-DYNA

5. Conclusions

Firstly, in compared with analytical solutions of 5 theories (4 HSDTs and 1 FSDT) for frequency responses with various types of composites, a desirable FE modeling technique regarding composite types (Laminated/Sandwich) was studied and validated in diverse manners using the latest version of LS-DYNA. In laminated composite models, the frequencies among all theories and LS-DYNA were in good agreement. In sandwich composite models, the frequencies between LS-DYNA and FSDT were in good agreement but were higher while giving stiffer responses than all other 4 HSDTs. Consequently, it can be concluded that a consideration of the

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higher-order shear deformation mode needs to be implemented in LS-DYNA to enhance the accuracy of frequency responses in sandwich composites with higher thickness of the core to thickness of the flange. Secondly, in the frequency response study for evaluating the effects of damage and

delamination for the laminated cantilever beam and rectangular plate models, various types of damage were represented in FE models and delamination were also modeled particularly via *CONTACT_TIED card. As a result, a good correlation between experiment and LS-DYNA can be observed as below:

▪ Laminated cantilever beam model: about 2.6% error (in average) ▪ Laminated rectangular plate model: about 4.0% error (in average) Finally, through the frequency domain analyses supported by *FREQUENCY_DOMAIN_FRF

in LS-DYNA, it was verified that the frequency responses between vibration experiment and LS-DYNA are fully comparable and in good agreement.

References 1. T. Kant, K.Swaminathan, “Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory”, Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai – 400 076, India, 2001. 2. Kant T, Manjunatha BS. An unsymmetric FRC laminate C finite element model with 12 degrees of freedom per node. EngComput 1988. 3. Pandya BN, Kant T. Finite element stress analysis of laminated composite plates using higher order displacement model.ComposSciTechnol 1988. 4. Reddy JN. A simple higher order theory for laminated composite plates. ASME J ApplMech 1984. 5. Senthilnathan NR, Lim KH, Lee KH, Chow ST. Buckling of shear deformable plates. AIAA J 1987. 6. Whitney JM, Pagano NJ. Shear deformation in heterogeneous anisotropic plates. ASME J ApplMech 1970. 7. Seth S. Kessler, S. Mark Spearing, Mauro J. Atalla, and Carlos E. S. Cesnik, “DAMAGE DETECTION IN COMPOSITE MATERIALS USING FREQUENCY RESPONSE METHODS”, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139,USA. 8. Yun Huang, “Frequency domain dynamic and acoustic analysis with LS-DYNA”, Livermore Software Technology Corporation, Livermore, CA, USA, November 2010. 9. Yun Huang, Bor-Tsuen Wang, “Implementation and Validation of Frequency Response Function in LS-DYNA”, Livermore Software Technology Corporation, Livermore, CA, USA, November 2010. 10. R Sultan, S Guirguis, M Younes, “DELAMINATION DETECTION OF COMPOSITE LAMINATES USING NATURAL FREQUENCY VIBRATION METHOD”, International Journal of Mechanical Engineering and Robotics Research, Vol 1, No. 2, July 2012. 11. John O. Hallquist, “LS-DYNA KEYWORD USER’S MANUAL”, Livermore Software Technology Corporation, Livermore, CA, USA, June 2013.

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Numerical Investigation of Landslide Mobility and Debris-Resistant Flexible Barrier with LS-DYNA®

Yuli Huang, Jack Yiu, Jack Pappin, and Richard Sturt

Arup

Julian S. H. Kwan and Ken K. S. Ho Geotechnical Engineering Office, Civil Engineering & Development Department,

Hong Kong SAR Government

Abstract Driven by the initiative of the Geotechnical Engineering Office, Civil Engineering and Development Department of Hong Kong, Arup is undertaking a pilot numerical investigation of the landslide dynamics and the interaction of landslide debris flow and flexible barriers. Such modeling work is technically challenging as it calls for both sophisticated debris mobility analysis and structural assessment of flexible barriers. The multi-purpose finite element program, LS-DYNA, has therefore been used to carry out the numerical analysis. This paper presents the modeling methodology for landslide mobility and flexible barriers, and assessments with the USGS laboratory flume tests, the full-scale rockfall tests, the 2008 Yu Tung Road debris flow event in Hong Kong, and Illgraben flexible barrier field test in Switzerland. The excellent correlation suggests that the proposed methodology is promising for numerical investigation on landslide mobility and its interaction with flexible barriers.

Introduction

Hong Kong has a high proportion of land area that consists of relatively steep natural terrain. This land area is susceptible to landslides that can travel long distances and can pose a significant hazard to the development in the vicinity of the natural hillsides. Flexible barriers could be a feasible option for mitigating the natural landslide risk. Proprietary flexible rockfall protection barriers with or without modifications have recently been proposed to resist debris flows and open hillside landslides. Existing studies suggest that these flexible barriers are capable of stopping and retaining a certain amount of landslide debris. Debris-resistant flexible barrier is attractive because that its construction involves relatively lightweight plant and materials, which can greatly facilitate construction in hilly terrain, and that it is less obstructive environmentally and visually. An example of such barrier installed in Hong Kong is shown in Figure 1.

Figure 1: A flexible barrier setup at the Hong Kong University of Science and Technology

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Despite the merits mentioned above, a comprehensive and recognized design standard for flexible debris-resistant barriers is unavailable. The development of such a design standard and appropriate design methodology for flexible barriers requires an understanding of both landslide dynamics and the interaction of landslide debris and flexible barriers. Driven by the initiative of the Geotechnical Engineering Office (GEO), Civil Engineering and Development Department of Hong Kong, Arup is undertaking a pilot numerical investigation of the landslide debris-barrier interaction. The work is technically challenging as it calls for coupling of landslide mobility analysis and flexible barrier assessment. The multi-purpose finite element program, LS-DYNA, has been used to carry out the numerical analysis and provide input to the investigation.

Numerical Investigation Program

Although the simulation of debris mobility and the structural modeling of flexible barriers have been successfully carried out separately by various researcher and practitioners in the past, the coupled modeling remains a great challenge. In order to achieve a comprehensive modeling of debris flow impacting on a flexible barrier, it is necessary to identify an appropriate computer program with the advanced modeling capabilities. LS-DYNA is a multi-purpose finite element program for linear and non-linear mechanics. Its automated contact algorithm and wide range of material models support the solution of complex real world problems such as automotive crash analysis, metal forming, drop testing, seismic engineering, blast simulation, etc. It has the capability to analyze multi-physics problems such as fluid-structure interaction, and thermal-structure coupling. LS-DYNA has also been used extensively in civil engineering related design and analysis, including rail, offshore, structural, wind and vibration engineering. Based on the capability assessment, it has been chosen for the numerical investigation. The numerical investigation is divided into different stages including the methodology development for assessment of flexible barrier behavior, landslide debris mobility, and interaction between them, followed by a parametric study of different sizes and velocities of debris flow impacting on a flexible barrier and their design implications, and ultimately the development of a design methodology. At the time of preparing this paper, the stages of parametric study and beyond are in progress and not presented in the paper.

Structural Behavior of Flexible Barriers

Because of the highly flexible nature of the barrier, it is crucial that the numerical simulation methodology adopted would be able to handle material and geometrical nonlinearities of individual structural components. A benchmarking exercise has been carried out based on the rockfall field tests conducted by the Swiss Institute for Snow and Avalanche Research (SLF Davos) on flexible barriers (Grassl, 2002; Volkwein, 2004). Among different test set-ups reported by Volkwein (2004), it was decided that tests on the movable positioned ring net (Figure 2) be adopted for the benchmarking exercise. This flexible net was made of 300-mm diameter rings which were formed by 7 nos. winding of steel wires. These rings were able to slide freely against each other. The flexible ring net was connected to pre-stressed steel cables via shackles. These shackles allowed the edge rings to move along the

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cable direction. The steel cables were supported by the beams of the steel rigs and are anchored to a concrete block on the ground at the ends. To simulate the rockfall scenarios, an 820-mm diameter ball made of steel-fiber-reinforced concrete was adopted as the weight. The total mass of the weight was 825 kg. Tests were performed with the concrete ball dropping at different heights (16 m & 32 m). The performance and the non-linear behavior of different structural components of the flexible barrier were studied in the numerical simulation.

Figure 2: The specifically-built test rig for rock fall tests (after Volkwein, 2004)

In the LS-DYNA simulation, all structural components were modeled explicitly using beam elements, whereas the concrete ball was modeled as a rigid sphere. Inelastic material models were assigned for some of the structural components such as the steel rings where plasticity may develop under large deformation demand. The rings of the barrier, shackles and cables are not connected by sharing nodes because they may slide against each other as observed in the experiment. Their connectivity was simulated with beam-to-beam contact algorithm. Material and sectional properties were assigned consistently with those reported in Grassl (2002) and Volkwein (2004). The model was initialized with gravity. The concrete ball was then released to fall freely and impact on the flexible barrier. The elevation and velocity of the concrete ball were recorded. The potential and kinetic energy were derived from the elevation and velocity respectively.

a) Elevation versus Time b) Energy versus Time

Figure 3: Comparison for the 16m and 32m drop cases

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The elevation and total (potential and kinetic) energy histories of the ball were compared between the LS-DYNA simulation and the experiment (Figure 3). Time t = 0s represents the moment when the ball reached the elevation of the test rig beams. It is demonstrated that the simulation accurately predicts the movement of concrete ball decelerated by the flexible barrier, and the energy dissipation during the interaction. Explicit modeling of the structural components and contact algorithm for their interaction (Figure 4) provides a straightforward approach and eliminates any high level phenomenological assumptions and calibrations. Figure 5 shows that the predicted sideways movement of the steel cables is very similar to the actual tested barrier, among many other features of the interaction that were observed in the experiment. Excellent agreement between the simulation and experiment suggests that the methodology is able to model the structural behavior of the flexible barrier and its interaction with an impacting object.

a) t = 0.00s b) t = 0.10s c) t = 0.20s d) t = 0.35s

e) t = 0.40s f) t = 0.80s g) t = 1.00s h) t = 1.20s

Figure 4: Simulated behavior of the flexible barrier for the 16 m drop case

(steel frame of the test rig not shown for clarity)

a) Experiment (after Volkwein, 2004) b) Simulation

Figure 5: Comparison of flexible barrier configuration at equilibrium for the 16 m drop case

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Landslide Debris Mobility

Whilst the flexible barrier provides structural resistance, the load is primarily determined by the sizes and velocity of the landslide debris flow, which necessitates an accurate representation of the debris flow that involves rapid downslope motion on irregular surfaces. To this end, the general multi-material arbitrary Lagrangian-Eulerian (MMALE) solver is selected to accommodate the large displacement and deformation of the debris flow. In order to justify the appropriateness of the methodology and identify the suitable constitutive models and rheological parameters, the proposed methodology is benchmarked against instrumented tests on granular avalanches across irregular three-dimensional terrains (referred to as the USGS laboratory flume tests in this paper) reported by Iverson et al. (2004), and then the 2008 Yu Tung Road debris flow event in Hong Kong (AECOM, 2012). The 1999 Sham Tseng San Tsuen and 2005 Kwun Yam Shan debris flow events, both in Hong Kong, were also assessed and good agreements were observed. The USGS laboratory flume tests (Iverson et al., 2004) The USGS laboratory flume tests reported by Iverson et al. (2004) consisted of two experiments, viz. Experiment A and Experiment B, carried out in a bench top flume of 0.2m wide and approximately 1.0m long (Figure 5). The steep part of the flume was fitted with a urethane insert to form an irregular basal surface as the 'topography'. Two types of dry sand materials, one angular and the other rounded, were used for the flume tests. A head gate was installed at the upslope section for storage of the static dry sand, which enabled an instantaneous release of the static granular mass. A summary of experiment conditions and sand properties is given in Table 1. Digital photography and laser cartography were adopted for capturing the movement of the avalanches during the experiments.

a) Experiment (after Iverson et al., 2004) b) Simulation

Figure 6: Flume bed topography for Experiment and Simulation B

In the LS-DYNA simulation, the flume bed topography is modeled as rigid shell structure fixed in space. The structure was then treated as Lagrangian and fluid-structure interaction (FSI) was used for coupling with the MMALE domain (CONSTRAINED_LAGRANGE_IN_SOLID). The friction coefficients in FSI were specified to be consistent with experiment. The sand debris flow was modeled with frictional material model (MAT_SOIL_AND_FOAM) and the material properties were calibrated against the friction angle in pure shear reported in the experiment.

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Table 1: Summary of experiment conditions and sand properties (Iverson et al., 2004)

Experiment Internal Friction Angle

of Sand Basal Friction Angle

Sand on Irregular Topology Basal Friction Angle Sand on Elsewhere

A 43.99° 19.85° 23.47° B 39.39° 22.46° 25.60°

The model was initialized with gravity. The head gate was opened at t = 0 and simulated by instantaneous removal of shell element representing the gate. Timestamps expressed the time elapsed since the opening of the head gate. The MMALE material fraction field was recorded. The location and displacement of the granular avalanche front were then derived from the material fraction field. The frontal displacement versus time curves from experiement and simualtion are compared in Figure 7. The more intuitve vertical ortho-photography time lapse comparison is showed in Figure 8. The LS-DYNA simulation generally matched the experimental results very in terms of the movement and the deposition extent. In addition the simulations were able to predict the development of the sand prisms behind the head gate after some of the granular avalanches had been released through the opening and run down the slope. The predicted frontal displacement and experiment measurement match reasonably well for both Experiments A and B. The simulation produced a slightly shorter displacement of the granular avalanches at about 0.5s in Experiment B. This was probably because the phenomenon of spreading of a thin layer of the granular avalanche at the front was more pronounced in this case. It was likely to be a consequence of using spherical sand which has a relatively strong tendency to spread out as noted by Iverson et al. (2004). The sand was much diffused at the front and therefore was not perfectly picked up by the LS-DYNA simulation conducted. The result could be improved if the ALE domain is further refined.

Figure 7: Comparison of frontal displacement versus time between experiment and simulation

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Experiment A (after Iverson et al., 2004) Simulation A

0.30s

0.51s

0.93s

1.97s

2.81s

Experiment B (after Iverson et al., 2004) Simulation B

0.27s

0.48s

0.69s

1.32s

8.00s

Figure 8: Comparison of the flume test vertical ortho-photography time lapse

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2008 Yu Tung Road debris flow The Yu Tung Road landslide on Lantau Island, Hong Kong was triggered by an estimated 1 in 600 year return period rainstorm on 7 June 2008. Details of the incident are available in AECOM (2012). The landslide was located in Tung Chung, Lantau and was referenced as Landslide LS08-241 in the database. Figure 9 shows the aerial photographs of the site after the landslide incident. The crown of the landslide was situated above 200mPD. Over 3000m3 of debris ran down the hillside as channelized flow down to Yu Tung Road which was approximately at 17mPD. The landslide travelled a total distance of over 600m at an apparent travel angle of 17°.

a) Aerial photograph b) Simulation Figure 9: Yu Tung Road site after the 2008 landslide

The analysis methodology similar to the flume test simulation was adopted. The topography was modeled as rigid shell structure fixed in space. Fluid-structure interaction (FSI) is incorporated. The debris flow was modeled with frictional and rheological material model and the material properties were calibrated against the observed flow characteristics (e.g. thickness). Entrainment and some secondary slides were not modeled.

Figure 10 Comparison of debris frontal movement

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Figure 10 compares the debris frontal movement against observation, in particular that the debris front travelled from chainage 320m to 530m in approximately 20 to 21 seconds. This was accurately reproduced by the simulation. The distance between the front and tail of the debris mass when it reached chainage 540m was also measured. It was noted that the simulations predicted a distance of within 200m (Figure 11) that is consistent with observation too. This suggests that the proposed methodology for simulating landslide debris mobility is promising for further investigation on debris mobility and its interaction with flexible barrier structures.

Figure 11 Simulated results of debris flow extent at the crest of cut slope, overlapping site layout

Interaction between Debris Flow and Flexible Barrier

With methodologies for flexible barrier behavior and landslide debris mobility assessed in previous sections, the main purpose of this stage is to investigate the interaction between them through numerical analyses and from its findings facilitate the development of a design standard for debris-resistant flexible barriers. The full-scale field tests conducted in Illgraben, Canton Valais of Switzerland was identifies as a good source of data. The Illgraben was reported to be one of the most active debris-flow rivers in Swiss Alps. Since 2000, the site has been monitored by Swiss Federal Institute for Forest, Snow and Landscape Research (WSL). Monitoring instrumentations such as geophones, laser, weight systems as well as video cameras were installed to record and measure the debris flow events. From 2005 onward, test barriers have been constructed in the Illgraben river bed so that the behavior of the flexible barrier under the impact of debris flow could be investigated. Load cells were installed to the test barriers in order to measure the force induced on the support ropes during the debris flow event. The test flexible barrier was installed at the end of the Illgraben channel next to the river Rhone. The details of Illgraben flexible barrier field test in particular during the debris flow events in 2006 was discussed in details in Wendeler et al. (2006), Wendeler et al. (2008), Wendeler (2008), and Bartelt et al. (2009). Figure 12 shows the elevation view of the installed test barrier. The debris flow in the event on May 18, 2006 recorded a volume of about 15,000m3 with front velocity of 2.9m/s (Wendeler et al., 2008).

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The LS-DYNA simulation was setup following the proposed methodologies discussed in previous sections. The flexible barrier was modeled as beam elements with beam-to-beam contact and the debris flow was modeled in the MMALE domain interacting with the ground topology as rigid shell. In addition, to account for the interaction between the debris flow and the flexible barrier, a null membrane with no stiffness or strength was included to cover/connect the flexible barrier. It transferred the interacting force from the debris flow to the flexible barrier. The debris flow in the MMALE domain interacted with the null membrane in the same manner that it interacted with the rigid ground topology. The model was initialized with gravity. Then an MMALE source boundary started to provide a debris flow at the velocity consistent with the reported one. Table 2 summarizes the pressure of debris mass acting on the flexible barrier and the axial force induced on the top and bottom ropes suggested by LS-DYNA simulation, as well as those reported in Wendeler et al. (2008) and Bartelt et al. (2009) back analysis. Good agreement between simulation and field measurement is observed. Figure 12 compares flexible barrier configuration before and after the debris flow impact, between the LS-DYNA simulated results and the photographs taken at the field test. Figure 13 illustrates the interaction between the debris flow and the flexible barrier at the moments before and after overtopping happens. It is showed that many salient features observed in field tests have been captured by the simulation. The LS-DYNA simulation analysis results demonstrated that the modeling methodology adopted can successfully simulate the interaction between the flexible barrier and the landslide debris. The simulation enables tracking of forces and developed in individual structural components, which would contribute helpful input to the development of flexible barrier design philosophy. The LS-DYNA simulation is able to estimate the debris pressure exerting on the flexible barrier during the impact. With parametric study in progress, the LS-DYNA simulations would be able to provide the insight on the relationship of the debris pressure with the debris volume, speed, condition (e.g. granular vs. watery), as well as the behavior of the flexible barriers.

Table 2: Comparison of simulation results and field measurements

Simulation Wendeler et al. (2008) Bartelt et al. (2009)

Max debris pressure (kPa) ~69 ~60 (estimated from rope force measurement) N/A

Max bottom ropes force (kN) 261 248 (measurement) 240

Max top ropes force (kN) 200 150 (measurement) 170

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Field Photograph (after Wendeler et al. 2006) Simulation

before debris flow impact

after debris flow impact

Figure 12: Comparision of flexible barrier configuration

Field Photograph (after Wendeler et al. 2006) Simulation

before overtopping

after overtopping

Figure 13: Interaction between the debris flow and the flexible barrier

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Concluding Remarks

The present study has explored the appropriate numerical analysis methodologies to investigate the interaction of landslide debris flow and flexible barriers. The work indicates that a multi-purpose 3D finite element program, such as LS-DYNA, is capable of modeling the highly non-linear behavior of the structural components of the flexible barrier structures as well as the large deformation of debris mass. It highlights the potential of using such computer programs to obtain a better understanding of the mechanics of the landslide debris as well as its interaction with flexible barrier. It is believed that further findings obtained from the numerical investigation would provide useful insights for the design practice of flexible debris-resistant barriers.

Acknowledgements

This paper is published with the permission of the Head of the Geotechnical Engineering Office and the Director of the Civil Engineering and Development, Government of the Hong Kong Special Administrative Region.

References

AECOM Asia Company Limited (2012). "Detailed Study of the 7 June 2008 Landslides on the Hillside about Yu Tung Road, Tung Chung." Report 271, Geotechnical Engineering Office, Civil Engineering and Development Department, The Government of the Hong Kong SAR. Bartelt, P., Volkwein, A., Wendeler, C., (2009). “Full-scale Testing and Dimensioning of Flexible Debris Flow Barriers.” Summary Report CTI Debris Flows, Swiss Federal Institute of Forest, Snow and Landscape Research. Grassl, H. G. (2002). “Experimentelle und numerische Modellierung des dynamischen Trag- und Verformungsverhaltens von hochflexiblen Schutzsystemen gegen Steinschlag.” Doktorarbeit, Eidgenössische Technische Hochschule Zürich. Iverson, R. M., Logan, M. and Denlinger R. P. (2004). “Granular Avalanches across Irregular Three-Dimensional Terrain: 2. Experimental Tests.” Journal of Geophysical Research, 109, F01015. Volkwein, A. K. H. (2004), “Numerische Simulation von flexiblen Steinschlagschutzsystemen.” Doktorarbeit, Eidgenössische Technische Hochschule Zürich. Wendeler, C. (2008). “Murgangrückhalt in Wildbächen – Grundlagen zu Planung und Berechnung von flexiblen Barrieren.” Doktorarbeit, Eidgenössische Technische Hochschule Zürich. Wendeler, C., McArdell, B. W., Rickenmann, D., Volkwein, A., Roth, A., Denk, M. (2006). “Field Testing and Numerical Modeling of Flexible Debris Flow Barriers.” Proceedings of International Conference on Physical Modelling in Geotechnics, Hong Kong. Wendeler, C., McArdell B.W., Volkwein A., Denk, M. and Groener, E. (2008). “Debris Flow Mitigation with Flexible Ring Net Barriers – Field Tests and Case Studies.” Proceedings of Second International Conference on Monitoring, Simulation, Prevention and Remediation of Dense and Debris Flows, Wessex Institute of Technology, United Kingdom, 21-31

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Application of LS-DYNAÒ for Auto NVH Problems

Yun Huang, Zhe Cui

Livermore Software Technology Corporation 7374 Las Positas Road, Livermore CA 94551

Abstract

NVH (Noise, Vibration and Harshness) is an important topic for the design and research of automotives. Increasing demands for improved NVH performance in automotives have motivated the development of frequency domain vibration and acoustic solvers in LS-DYNA. This paper presents a brief introduction of the recently developed frequency domain vibration and acoustic solvers in LS-DYNA, and the application of these solvers in auto NVH problems. Some examples are given to illustrate the applications.

Introduction

Originally LS-DYNA is a nonlinear, transient dynamic finite element analysis software, and is mainly used in crashworthiness, impact analysis. With many new features added to LS-DYNA in recent years, the application of LS-DYNA has been extended to many new areas. One of such areas is automotive NVH analysis.

NVH stands for noise, vibration and harshness. They are important properties of automotives. To improve customers’ comfort and make the new vehicles more competitive, all the auto makers are doing intensive research and testing to improve the NVH performance of their new vehicles. The lab testing, which is the traditional way to perform NVH study, is usually expensive and time consuming. Thus the numerical simulation with CAE models, which is relatively cheaper and faster, gain more and more attention. Due to the fact that vibration and noise are essentially related to driving frequencies, the NVH problems are usually studies in frequency domain. To perform NVH analysis with CAE models, the capabilities to run modal analysis, vibration analysis and acoustic computation are needed for a software. Besides, a massive parallel computing capability is a must since the auto models are usually very complicated and they may involve millions of nodes and elements sometimes.

In LS-DYNA, the modal analysis capability has been made available, by the keywords *CONTROL_IMPLICIT_GENERAL, and *CONTROL_IMPLICIT_EIGENVALUE, and some other optional keywords, for example, *CONTROL_IMPLICIT_SOLUTION, *CONTROL_IMPLICIT_STABILIZATION, etc.

Recently a series of frequency domain features were introduced to LS-DYNA, in addition to the existing implicit eigenvalue analysis keywords. They aimed to solve a variety of vibration and acoustic problems. The corresponding keywords are listed below:

* FREQUENCY_DOMAIN_ACOUSTIC_BEM_{OPTION} * FREQUENCY_DOMAIN_ACOUSTIC_FEM * FREQUENCY_DOMAIN_FRF * FREQUENCY_DOMAIN_RANDOM_VIBRATION_{OPTION}

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* FREQUENCY_DOMAIN_RESPONSE_SPECTRUM * FREQUENCY_DOMAIN_SSD

These keywords are used to activate the acoustic simulation (by FEM or FEM), or FRF (Frequency response function) analysis, or random vibration analysis, or response spectrum analysis, or steady state dynamic analysis. The acoustic solvers include indirect and direct BEM, approximate Rayleigh method and Kirchhoff method, as well as FEM. More detailed introduction of the BEM and FEM acoustic methods in LS-DYNA can be found in references [1] and [2]. The results of acoustic computation are given in the form of ASCII files Press_Pa and Press_dB, which are accessible to LS-PrePostÒ, and binary plot databases d3atv and d3acs. D3atv shows the acoustic transfer vector, which is the acoustic pressure due to unit normal nodal velocity for each surface node. D3acs is generated by FEM acoustic computation and it shows the contour plot of acoustic pressure for an internal problem. The Finite element mesh is used to model the acoustic domain inside the cabin or compartment. The vibration analysis solvers include FRF (frequency response function), SSD (steady state dynamics) and random vibration. FRF provides a transfer function between excitations and response, and it can be used to locate the energy transfer path, or some important dynamic properties of structures [3]. The result of FRF analysis is written in ASCII files frf_amplitude and frf_angle. Frf_amplitude / frf_angle shows the amplitude / phase angle of FRF analysis respectively. They can be accessed by LS-PrePost, as xyplot files. For auto NVH analysis, FRF can be given in many different forms, as given in Table 1.

Input Output FRF Force Acceleration Accelerance, Inertance

Acceleration Force Effective mass

Force Velocity Mobility

Velocity Force Impedance

Force Displacement Dynamic compliance

Displacement Force Dynamic stiffness

Table 1: FRF formulations

SSD provides the steady state dynamic response of structures, subject to harmonic excitation [3]. The result of SSD analysis is given in binary plot database d3ssd, which is accessible to LS-PrePost. Random vibration provides PSD response of structures under random PSD loading and it gives the distribution of energy in a range of vibration frequencies [4,5]. RMS value of the nodal and

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elemental variables can also be provided. The RMS plot can be used to identify the hot-spot of auto bodies in all kinds of operation conditions. The results of random vibration analysis are given in binary plot database d3psd and d3rms, which are accessible to LS-PrePost. It is worthy to note that the vibration analysis solvers are all based on the results of modal analysis. In other words, the computation of FRF, SSD and random vibration relies on the eigen-modes (natural frequencies and modal shape vectors, provided in binary plot database d3eigv). So the modal analysis is the basis for these new frequency domain vibration solvers. With both the vibration and the acoustic solvers ready, and with the implicit eigenvalue analysis capability, LS-DYNA is well prepared to perform NVH analysis for automotives. Several other assistant keywords are also provided in LS-DYNA, such as *FREQUENCY_DOMAIN_MODE, *FREQUENCY_DOMAIN_PATH, etc. These keywords can be used to set up simulation environment for frequency domain analysis.

In this paper, a few examples are given to illustrate the application of LS-DYNA in auto NVH problems. They include a FRF example for a car model, a random vibration example for the same car model, and internal acoustic evaluation by finite element and boundary element methods in LS-DYNA.

FRF analysis on a BIW model

A BIW model is employed to demonstrate the FRF analysis procedure with LS-DYNA. The keyword *FREQUENCY_DOMAIN_FRF is used for this example, as well as *CONTROL_IMPLICIT_GENERAL and *CONTROL_IMPLICIT_EIGENVALUE for modal analysis. The model has 137 parts, including 176598 nodes and 165573 elements. For frf analysis, unit nodal force is applied at point A (user node ID 1), and response in form of acceleration is calculated at point B (user node ID 928300). The load is given in z direction and the response is also computed in z-direction.

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Figure 1: BIW model for FRF analysis (model provided by JSOL Corporation) The accelerance result at point B (user node ID 928300) for the range of 1-200 Hz is plotted in Figure 2. Only amplitude of the FRF result is given.

Figure 2: FRF result (amplitude) at point B

SSD analysis on a side frame model

In this example, a side frame model is subjected to harmonic vibration. It is constrained to shaker table via three holes. The model is depicted in Figure 3. The model has only 1 part, with 18551 nodes and 18082 shell elements. Keyword *FREQUENCY_DOMAIN_SSD and *DATABASE_FREQUENCY_BINARY_D3SSD are used in this example.

Figure 3: Side frame model of an automotive (model from NCAC)

The excitation is given in the range of 10-140 Hz, in the form of unit nodal force in y direction (vertical to the frame). The results are given in binary plot database d3ssd. For 4 excitation frequencies, the distribution of the acceleration is given in Figure 4.

The frame is constrained via the 3 holes

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Figure 4: Acceleration SSD for auto frame

Random vibration analysis on a BIW model

Random vibration analysis for the same model in Figure 1 is also performed, to study the dynamic behavior of the BIW under base acceleration PSD excitation. The acceleration is specified in x-direction (see Figure 1). The PSD curve is given as white noise (1g^2/Hz) for the range of 1-200 Hz as follows.

Freq (Hz)

Acc

eler

atio

n P

SD

(g2 /h

z)

1 200

1

0

Figure 5: Acceleration PSD for random vibration analysis

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The keywords

*FREQUENCY_DOMAIN_RANDOM_VIBRATION, and *DATABASE_FREQUENCY_BINARY_D3PSD, and *DATABASE_FREQUENCY_BINARY_D3RMS are used in this example.

The whole structure is constrained to a shaker table through a set of nodes. For response, binary plot database d3psd, and d3rms are provided. D3psd provides the PSD (power spectral density) values of nodal and elemental results, such as displacement, velocity and acceleration and stress components as well as Von-Mises stress. D3rms provides the RMS (root mean square) values of the same variables.

In Figure 6, the RMS value of the x-displacement is provided.

Figure 6: The RMS of x-displacement (unit: mm)

In Figure 7, the RMS value of Von-Mises stress is provided. This figure can help to locate the zones with high stress.

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Figure 7: The RMS of Von-Mises stress (unit: MPa)

Compartment acoustic analysis

In this example, a series of numerical methods are adopted to study the acoustic behavior of a simplified cabin model. The interior noise of the cabin is computed in this example. The methods employed include finite element method (*FREQUENCY_DOMAIN_ACOUSTIC_FEM), and boundary element method (*FREQUENCY_DOMAIN_ACOUSTIC_BEM).

The model can be found in Figure 8.

Figure 8: A simplified cabin model (mesh and profile)

The model is excited by unit normal velocity (1mm/s) given at the base panel, the excitation is given in the frequency range of 10-300 Hz. The other surfaces of the model are assumed to be rigid.

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Figure 9: base panel subjected to uniform normal velocity

Results given by LS-DYNA (BEM and FEM) and Nastran results are plotted together in Figure 10. As one can see that the results given by NASTRAN and LS-DYNA (FEM) have better match. This is because that NASTRAN also uses FEM for its acoustic computation.

Figure 10: SPL at field point

Conclusion

A family of new keywords have been introduced in LS-DYNA to perform frequency domain analysis. They can be used to perform vibration and acoustic computation and have important applications in auto NVH analysis. A series of binary databases are also implemented to facilitate post-processing the computational results. These new frequency domain features,

Base panel with velocity b.c.

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combined with the existing implicit eigenvalue analysis capability, and time domain dynamic analysis capability, establish LS-DYNA as an attractive tool for auto NVH analysis problems.

References

1. Huang Y., Souli M., Liu R., New developments of frequency domain acoustic methods in LS-DYNA. Presented at the 11th International LS-DYNA Users Conference, June 6-8, 2010, Dearborn, Michigan, USA.

2. Cui Z., Huang Y., Boundary Element Analysis of Muffler Transmission Loss with LS-DYNA, presented at the 12th

International LS-DYNA Users Conference, June 3-5, 2012, Dearborn, Michigan, USA.

3. Huang Y., Wang B., Mode-based frequency response function and steady state dynamics in LS-DYNA. Presented at the 11th International LS-DYNA Users Conference, June 6-8, 2010, Dearborn, Michigan, USA.

4. Rassaian M., Huang Y., Lee J., Arakawa T., Structural analysis with vibro-acoustic loads in LS-DYNA. Presented at the 10th International LS-DYNA Users Conference, June 8-10, 2008, Dearborn, Michigan, USA.

5. Shor O., Lev Y., Huang Y., Simulation of a thin walled aluminum tube subjected to base acceleration using LS-DYNA's vibro-acoustic solver. Presented at the 11th International LS-DYNA Users Conference, June 6-8, 2010, Dearborn, Michigan, USA.