Project_ Report

Topology Optimization

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ME 59700


Project Report

On

Topology Optimization of Front Rail for the Improvement of

Crashworthiness

Submitted By:

Prasad Tapkir

Date: 08/10/2016


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1. Introduction:

The topology optimization has been formulated to improve the crashworthiness of the

vehicle. Basically, the project uses two main research papers. One is based on design

optimization of front rail and second is based on topology optimization of the front rail.

The project work depicts combination of these two methods to enhance the crashworthiness

of the vehicle. As we proceed in the report, the literature review is explained in the first

section. Second section mainly contains the verification of some of the literature review

using LS-DYNA package. The third section mainly deals with problem formulation and

methodology for topology optimization of front rail. The fourth section depicts the result

obtained from topology optimization technique. The tool which has been used for

optimization is Hyper works- OPTISTRUCT. The report is concluded with further

improvement of the optimization technique.

2. Literature Review:

As far as crashworthiness of the vehicle is concerned, the implementation of energy

absorbing systems in automobile designs is an important aspect to be considered. This

system acts as a transformation medium, which receives kinetic energy which may take

place due to crashing and converts this energy into another form [4]. This whole process

assures the decreasing rate of human suffering and financial penalties. As previous research

depicts, there are several ways to improve the crashworthiness. A special emphasis has

been put on reversible absorber and collapsible absorber [3]. For instance, optimal design

of thin-walled tube with different cross section such as circular, square can be optimized

using meta-model based approach. This method comes under thickness optimization or

purely design optimization techniques. The literature review of the project passed through

two main phases, which are mentioned as follows

a) Phase 1:

One of the main research papers project utilizes is optimal design of S- rail for

improvement in crashworthiness. This paper uses design of experiments to get number

of results for internal energy and peak crushing force in terms of width (w) and the

height (h) of the front rail cross section. With the help of this data set, the explicit

relation between internal energy and cross sectional dimensions (h and w) as well as

between peak crushing force and cross sectional dimensions (h and w). Finally, with

the help of genetic algorithm technique, researchers reached to the optimal design of

the s-rail [2]. The methodology is shown graphically as follows


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b) Phase 2:

The method mentioned above is quite convincing for design optimization field.

However it is difficult to get a proper vehicle design which can optimize the

crashworthiness due to the large nonlinear deformation in a complex vehicle model and

many uncertainties in the modeling and simulation process, including determining

loading and boundary conditions in the design process. Thus, the project preferred to

refer topology optimization technique introduced by researchers of University of

Michigan in 2009. In this approach, the researcher have used so called “Magic Cube

Approach” [1]. The name of the approach is magical cube is just because the researcher

developed a cube which has number of important factors on the each side of the cube.

The cube is shown below.

However, in this approach, the researcher used time and space decomposition method

to simply the design of the vehicle chassis.

A) Space Decomposition:

Based on the initial crash analysis, the researchers reached to the conclusion that

the front rail is one of the most important component as far as crashworthiness is

concerned. This is because, the major share of internal energy is absorbed by front

rail of the vehicle chassis. Thus, to simplify the design, the researchers only

considered the front rail as a design domain and rest of the chassis as non-design

domain.


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B) Time Decomposition:

Using time decomposition, researchers observed that, the front part of the s-rail

faces the maximum crushing force while curvature and back part faces global

bending. Thus, the front part is considered for topology optimization problem

formulation. This helps in getting progressive collapse, which in turns improves the

specific energy absorption of the vehicle.

3. Verification of literature review:

This section emphasizes on the verification of the phase 1 of the literature review. To verify

the result of optimal design of the s-rail, the initial and optimized design has been crashed

against the rigid wall. The rigid wall forces (crushing forces) and internal energies has been

obtained and plotted to get clear idea about the difference between initial and optimal

design. The basic dimensions of the s-rail is shown in the following figure.

The verification is done as follows:

A) Initial design:

W=100 mm

H= 160 mm

Curvature angle (α)= 300

1) Deformed shape:


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2) Internal Energy plot with respect to time:

Maximum internal energy: 3.71e3 KN/mm

3) Crushing force plot with respect to time:

Peak Crushing Force: 61.5 KN


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B) Optimized Design:

H=160 mm

W=40 mm

Curvature angle (α)=150

1) Deformed Shape:

2) Internal Energy plot with respect to time:

Maximum internal energy: 4.35e3 KN/mm


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3) Crushing force plot with respect to time:

Peak Crushing Force: 67.5 KN

Thus, in this way, the verification of literature review is performed. The results shows that there is

a drastic change in the internal energy absorption is noticed. Now, with the help of this section,

project proceeds into the topology optimization phase.

4. Problem formulation and Methodology for topology optimization problem:

4.1.Problem Formulation:

With conventional notations, the problem is formulated as follows

Min f (x)

Subject to V (low (i)) < V(x (i)) < V (up (i))

Where i=1, 2,…, m (i= number of subdomain)

f (x) is overall compliance of s-rail

V is volume fraction


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4.2.Methodology:

As mentioned in the literature review section, the researcher have used to the

composition method, so they can consider only front section of the s-rail as a design

domain as curvature and back section is considered as non-design domain. Then,

this design domain can be divided into number of subdomains. The number of

subdomains depends on the designer. In this case, the front section has been divided

into five sub domains, which are graphically shown as follows:

Out of five domain, the last domain is kept as no design domain, this is because of

as we move backwards, and we need stiffer section. Thus, at the section number

five, the volume fraction becomes 1 itself.

Now, without conventional notation, the problem is formulated as follows:


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The next step in the methodology is to apply boundary conditions to get topology optimized

geometry of the front section. In this method, for every section or subdomain, the boundary

conditions are applied separately, which implies that the topology of the each section is

optimized separately. The following figure shows us the boundary conditions applied for

the first sub domain

For this particular section, the crash force is applied according to the crushing force

obtained in the LS DYNA as shown in the section 3 (Verification of literature). For other

sections, the forces are applied according to the section forces generated in the previous

domain. In other words, when first section totally collapses, the end forces are applied to

obtain topology optimization of the second domain

For every section, the rest of the geometry is kept as non-design domain and corresponding

support and forces are applied.

NOTE: The simulation steps are included and submitted in the code section.


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5. Results:

This section gives us the results of all the sub domains as shown in the previous section of

the report (sub domain 1, 2, 3, and 4) and the convergence step

a) Sub domain 1:

Other colors: Intermediate densities

b) Sub domain 2:


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c) Sub domain 3:

d) Sub domain 4:


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Convergence step:

The following figure explains the convergence of the optimization problem


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6. Conclusions:

a) Literature review is completed and verified

b) Outputs of LS Dyna successfully applied to static optimization in OPTISTRUCT

c) Topology optimization problem formulated to minimize compliance

d) Section wise topology optimization is performed with variable volume constraints

7. References:

1) Sibo Hu, Ping Hu, Magic Cube Approach Application on Crashworthiness Design of

Front Rail in Front Angle Impact, International Conference on Mechatronics and

Automation, 2009

2) Hequan Wu, Yong Xi, Optimal Design of S-rail for crashworthiness Analysis, 2009

International Joint Conference on Computational Sciences and Optimization

3) M. Mirzaei, M. Shakeri, M. Sadighi, and S. Seyedi, Using of neural network and

genetic algorithm in multiobjective optimization of collapsible energy absorbers,

International Conference on Engineering Optimization.

4) S. Salehghaffari, M. Rais-Rohani, and A. Najafi, Analysis and Optimization of

Externally Stiffened Crush Tubes, 51st AIAA/ASME/ASCE/AHS/ASC Structures,

Structural Dynamics, and Materials Conference.

Project_ Report

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