Application of the Mathematical Theory of Homogenization in Topology Optimization Problems

2009 ◽  
Author(s):  
Y. Wang ◽  
D. Tran
Keyword(s):  
Topology Optimization ◽  
Mathematical Theory ◽  
Optimization Problems

Finding Better Local Optima in Topology Optimization via Tunneling

2018 ◽  
Author(s):  
Shanglong Zhang ◽  
Julián A. Norato
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Structural Response ◽  
Free Form ◽  
Local Optima ◽  
Design Representation ◽  
Tunneling Method ◽  
Optimization Parameters ◽  
Gradient Based ◽  
Geometric Primitives

Topology optimization problems are typically non-convex, and as such, multiple local minima exist. Depending on the initial design, the type of optimization algorithm and the optimization parameters, gradient-based optimizers converge to one of those minima. Unfortunately, these minima can be highly suboptimal, particularly when the structural response is very non-linear or when multiple constraints are present. This issue is more pronounced in the topology optimization of geometric primitives, because the design representation is more compact and restricted than in free-form topology optimization. In this paper, we investigate the use of tunneling in topology optimization to move from a poor local minimum to a better one. The tunneling method used in this work is a gradient-based deterministic method that finds a better minimum than the previous one in a sequential manner. We demonstrate this approach via numerical examples and show that the coupling of the tunneling method with topology optimization leads to better designs.

Topology Optimization Considering Gravitational and Centrifugal Forces

2006 ◽  
Author(s):  
Bin Zheng ◽  
Hae Chang Gea
Keyword(s):  
Topology Optimization ◽  
Kinetic Energy ◽  
Structural Design ◽  
Gravitational Force ◽  
Body Force ◽  
Optimization Problems ◽  
Sensitivity Analyses ◽  
Centrifugal Forces ◽  
Gravitational Forces ◽  
Mean Compliance

In this paper, topology optimization problems with two types of body force are considered: gravitational force and centrifugal force. For structural design under both external and gravitational forces, a total mean compliance formulation is used to produce the stiffest structure. For rotational structural design with high angular velocity, one additional design criteria, kinetic energy, is included in the formulation. Sensitivity analyses of the total mean compliance and kinetic energy are derived. Finally, design examples are presented and compared to show the effects of body forces on the optimized results.

Solving Topology Optimization Problems Using Wavelet Approximations

1998 ◽  
Author(s):  
Giuseppe C. A. DeRose ◽  
Alejandro R. Díaz
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Finite Element Methods ◽  
Condition Number ◽  
Optimization Problems ◽  
Mesh Size ◽  
Elasticity Problem ◽  
New Method ◽  
Galerkin Scheme

Abstract A new method to solve topology optimization problems is discussed. This method is based on the use of a Wavelet-Galerkin scheme to solve the elasticity problem associated with each iteration of the topology optimization sequence. Typically, finite element methods are used for this analysis. However, as the mesh size grows, the computational requirements necessary to solve the finite element equations increase beyond the capacity of current desk top computers. This problem is inherent to finite element methods, as the condition number of finite element matrices increases with mesh size. Wavelet-Galerkin techniques are used to replace standard finite element methods in an attempt to alleviate this problem. Examples demonstrating the performance of the new methodology are presented.

A NEW ELEMENT-BASED METHOD FOR SOLVING STRUCTURAL TOPOLOGY OPTIMIZATION PROBLEMS WITH NON-UNIFORM MESHES

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Kuang-Wu Chou ◽  
Chang-Wei Huang
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Optimization Method ◽  
Optimal Topology ◽  
Evolutionary Stage ◽  
Structural Topology Optimization ◽  
Volume Constraint ◽  
Structural Topology ◽  
Exchange Method ◽  
Python Scripting

This study proposes a new element-based method to solve structural topology optimization problems with non-uniform meshes. The objective function is to minimize the compliance of a structure, subject to a volume constraint. For a structure of a fixed volume, the method is intended to find a topology that could almost conform to the compliance minimum. The method is refined from the evolutionary switching method, whose policy of exchanging elements is improved by replacing some empirical decisions with ones according to optimization theories. The method has the evolutionary stage and the element exchange stage to conduct topology optimization. The evolutionary stage uses the evolutionary structural optimization method to remove inefficient elements until the volume constraint is satisfied. The element exchange stage performs a procedure refined from the element exchange method. Notably, the procedures of both stages are refined to conduct non-uniform finite element meshes. The proposed method was implemented to use the Abaqus Python scripting interface to call the services of Abaqus such as running analysis and retrieving the output database of an analysis. Numerical examples demonstrate that the proposed optimization method could determine the optimal topology of a structure that is subject to a volume constraint and whose mesh is non-uniform.

Mixed-integer second-order cone optimization for composite discrete ply-angle and thickness topology optimization problems

2020 ◽  
Author(s):  
Sicheng He ◽  
Mohammad Shahabsafa ◽  
Weiming Lei ◽  
Ali Mohammad-Nezhad ◽  
Tamás Terlaky ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Mixed Integer ◽  
Second Order Cone

scholarly journals Fast Nondominated Sorting Genetic Algorithm II with Lévy Distribution for Network Topology Optimization

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Maoqing Zhang ◽  
Lei Wang ◽  
Zhihua Cui ◽  
Jiangshan Liu ◽  
Dong Du ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Topology Optimization ◽  
Network Topology ◽  
Optimization Problems ◽  
Selection Strategy ◽  
Nsga Ii ◽  
Comparison Results ◽  
Practical Engineering ◽  
Network Topology Optimization ◽  
Nondominated Sorting

Fast nondominated sorting genetic algorithm II (NSGA-II) is a classical method for multiobjective optimization problems and has exhibited outstanding performance in many practical engineering problems. However, the tournament selection strategy used for the reproduction in NSGA-II may generate a large amount of repetitive individuals, resulting in the decrease of population diversity. To alleviate this issue, Lévy distribution, which is famous for excellent search ability in the cuckoo search algorithm, is incorporated into NSGA-II. To verify the proposed algorithm, this paper employs three different test sets, including ZDT, DTLZ, and MaF test suits. Experimental results demonstrate that the proposed algorithm is more promising compared with the state-of-the-art algorithms. Parameter sensitivity analysis further confirms the robustness of the proposed algorithm. In addition, a two-objective network topology optimization model is then used to further verify the proposed algorithm. The practical comparison results demonstrate that the proposed algorithm is more effective in dealing with practical engineering optimization problems.

Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2013 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Wei Song
Keyword(s):  
Topology Optimization ◽  
External Load ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Convex Model ◽  
Structure Response ◽  
Gradient Based ◽  
Bounded Convex ◽  
Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

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