project_ report
TRANSCRIPT
Topology Optimization
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ME 59700
Topology Optimization
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.