Optimal Design of Complex Mechanical Systems Project Report

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ME 59700

Optimal Design of Complex Mechanical Systems

Project report

On

The Optimal Design of Thin Walled Structures for

Maximum Specific Energy Absorption Using LS-OPT

Date: 05/08/2016

Submitted by:

Prasad Tapkir, Prasad Mehta

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1. Introduction:

In this age of high speed vehicles, 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. This whole process assures the decreasing rate of human suffering and financial

penalties. Energy absorption systems include reversible absorber and collapsible absorber [2] [3].

Our project puts emphasis on collapsible energy absorber, which absorbs the energy by plastic

deformation of a thin-walled structure. The thin-walled structures have number of sections such as

circular, square, tapered, honeycomb, and octagonal section [2]. For instance, circular or square

thin-walled tubes play their role in energy absorption process. However, for further improvement

in safety, the proposed work includes optimal design of thin-walled tube with square cross section.

In current practices, to address the design optimization of the thin-walled structures, the optimal

dimensions are determined using optimization toolbox of MATLAB. The global approximation

techniques such as Artificial Neural Networks (ANN), Inverse distance weighing (IDW), and the

Kriging sequential approximation method are used to determine the population of design variables

[1] [4]. The usage of these approximation method determines the accuracy of the optimal solution.

For a record, kriging method and corresponding meta-model are the most accurate among these

approximations. In many cases, considering the linearity or non- linearity of the objective functions

and subjective constraints, global optimal is found using different optimization tools such as genetic

algorithm (GA), constrained nonlinear minimization (FMINCON), unconstrained nonlinear

minimization, and multi-objective genetic algorithm (MOGA). However, in our case, the objective

function and corresponding constraints are obtained by using LS-DYNA, while the different steps

of optimization mentioned above are performed using the architecture provided in LS-OPT.

In order to find optimal solution, crash analysis in LS-DYNA serves the basis to determine the

specific energy absorption and crushing force, which are the factor to be focused. Thus, for making

the car safer, the objective of our proposed method is to maximize the specific energy absorption

and to minimize crushing force. The mass of the thin-walled structure subjective constraints on the

dimensions of the thin-walled structures. The optimization procedure is performed using LS-OPT,

where LS-OPT extract objective functions and subjective constraints from LS-DYNA. As there are

numerous sampling methods, Latin hypercube sampling is used to distribute the desired number of

samples with utmost effectiveness. As mentioned earlier, kriging meta-model is used to fit these

sample points in corresponding approximation. In the last phase of the project, using the fit of

kriging meta-model and genetic algorithm, the optimal dimensions of thin-walled structures and

corresponding specific energy absorption is determined.

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2. Theoretical Background:

This section of the report provides a theoretical background for concept such as crashworthiness of

the vehicle, importance of LS-DYNA, interface of LS OPT, and methodology to link LS OPT and

LS DYNA.

The crashworthiness is the ability of the system (vehicle) to protect the occupants in the event of

crashing. The consequences of crashing mainly depend on two factors, first is the type and the

intensity of the impact, and the second is the methodology by which the crashworthiness of the

vehicle is determined. Thus, in the event of crashing, designer is not able to control the type or the

intensity of impact, but designer may emphasize on the crashworthiness of the vehicle to protect

the occupants. Considering the different methods to determine the crashworthiness, designer is

supposed to evaluate important factors such as internal energy, crushing force, and the mass of the

vehicle. After determining these factors, the design is able to understand the concept of specific

energy absorption, which is a function of internal energy generated while crashing and the mass of

the component being crushed. The effective crashworthiness provides us the maximum specific

energy absorption and least peak crushing force. Therefore, the designer is supposed to obtain these

important parameters of crashworthiness by using analysis package, while the task of maximizing

the specific energy absorption is done by using optimization package. In our proposed work, we

have used LS-DYNA for obtaining the important parameters, whereas the optimization is

performed using LS-OPT.

In LS-DYNA, the CAD model of component to be crashed is called from solid modeling package.

Usually, the component under testing is crashed against the rigid wall structure. Some of the times,

component is kept stationary and wall is hit against the component. In both cases, due to material

and modelling properties, the component is deformed or collapsed. The results of crash analysis is

determined by the type of deformation of the component. For instance, after crashing, if the

deformation is in the form of progressive folding or collapsing then the results are obtained are

more effective and reliable for optimization purposes. The variables for optimization, for instance

thickness, is set as a parameter in LS-DYNA. Lastly, the important parameters of the crash analysis,

which are mentioned earlier in the report are obtained from standard output database of LS-DYNA

package. The number of outputs depend on the requirement of optimization methodology.

Focusing on optimization methodology, designer is supposed to use different optimization tools in

MATLAB. In contrast, we preferred to use LS-OPT, as this package is highly compatible with LS-

DYNA and corresponding output database. Unlike MATLAB, LS-OPT does not demand actual

equations of objectives to be achieved. It directly extracts the output database and parameters of

LS-DYNA and put them as inputs to the optimization loop for the desires number of iterations. For

creating a Meta model, LS-OPT provides number of options such as radial based meat model,

kriging method, polynomial based meta model, and artificial neural network. While the sampling

method is chosen based on the accuracy demanded by optimization process. The designer decides

stores the LS-DYNA outputs as histories and responses in LS-OPT database. In latter stage of the

optimization, designer use these histories and responses to set objective functions and constraints

of the optimization. Based on the desired number of iterations, LS-OPT achieves the objective

functions by keeping the constraints within their bounds and optimizes the parameters, which are

set in LS-DYNA database.

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3. Methodology:

This section explains the analysis and optimization methodologies. The analysis methodology

includes the preset parameters and procedure to perform crash analysis, whereas, optimization

methodology describes the flow of optimization process from sampling to the final result.

3.1. Crash analysis:

a) Basic model of tube was developed using Solidworks. Tube dimensions taken were

50x50x500mm.

b) This model was imported in LS-Dyna and meshed uniformly.

c) Rigid wall was created to crash the tube and velocity of 15 m/s was given to the tube.

d) The keywords used were, boundary conditions, control, contact, database, mat, parts, elements

and parameter (thickness).

e) In database from ASCII, GLSTAT, MATSUM, RCforce were selected. Also, D3plot and

Histories- Shell database were selected to extract outputs.

f) The termination for crash was assigned as 0.02 seconds.

3.2. Optimization Methodology:

a) Extraction of important parameters:

The first step of the optimization process is to provide a path of LS-DYNA solver to LS-

OPT interface. With the help of this path, output of LS-DYNA is called in LS-OPT stage

block to establish histories and responses. We extracted reaction forces, internal energy,

and mass from LS DYNA database.

b) Setup:

For setting up the parameter to be optimize, in our case shell thickness (t), we provided

upper bound (2 mm), lower bound (0.5 mm), and initial guess (2 mm) for shell thickness.

c) Sampling:

As mentioned, the accuracy of the final output depends on distribution of the sampling, we

preferred Latin hypercube sampling (LHS) to sample the variable values with 5 samples

points.

d) Building a Meta model:

As accuracy of the optimal thickness depends on type of sampling and corresponding Meta

model, we preferred kriging meta- model as during the course we have observed that

kriging method provides the best approximation for the given optimization problem.

e) Building a composite:

The purpose of composite is to set an expression for mean crushing force and specific

energy absorption. In composite, we used histories and responses of stage block and set

expressions for specific energy absorption (SEA) and mean rushing force as,

SEA= (Internal energy/Mass) and Pmean= (Internal energy/0.5)

f) Optimization:

In optimization step, we have used genetic algorithm to optimize the thickness and set our

objective function and constrains as,

To Maximize f = SEA (t)

Subject to Pmax (t) ≤ Panalysis

tLB ≤ t ≤ tUB

Where, Panalysis= 1.38e5 N

g) Termination:

In termination step, we set out iteration limit up to 10 iteration to get final output.

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4. Results and Discussions: This section of the report provides the estimate of internal energy, peak crushing force, and specific

energy absorption with respect to time frame of crash analysis and sampled values of thickness.

4.1. Internal energy Vs time Vs thickness:

Fig 1

4.2. Peak crushing force VS time Vs thickness:

Fig 2

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4.3. The overall statistics at peak crushing force:

Fig 3

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5. Conclusions:

a) As we can observe that for thickness value between 1.93 mm and 2 mm, the computed value

of specific energy absorption is greater than predicted value.

b) In the same thickness range the maximum crushing force is 9.2e4 N, which is less than the

constraint we set for optimization (1.38e5 N). c) As optimization process was terminated only after two iterations, the LS-OPT did not converge

the value of thickness to optimal value.

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6. References:

1) M. Mirzaei, M. Shakeri, M. Sadighi, and H. Akbarshahi, Crashworthiness Design for Cylindrical

Tube using Neural Network and Genetic Algorithm, Procedia Engineering 14 (2011) 3346–3353.

2) 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.

3) 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.

4) Mastinu, G., M. Gobbi, and C. Miano, Optimal Design of Complex Mechanical Systems, 2010:

Springer, 359.

5) LS-OPT User’s Manual.

6) LS-DYNA User’s Manual.