An Efficient Topology Optimization Method for Structures with Uniform Stress

2018 ◽  
Vol 15 (08) ◽  
pp. 1850073 ◽  
Author(s):  
Sheng Chu ◽  
Liang Gao ◽  
Mi Xiao
Keyword(s):  
Topology Optimization ◽  
Decision Problem ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Bisection Method ◽  
Uniform Stress ◽  
Topology Optimization Problem ◽  
Self Organized ◽  
Volume Minimization ◽  
Single Objective

This paper focuses on two kinds of bi-objective topology optimization problems with uniform-stress constraints: compliance-volume minimization and local frequency response–volume minimization problems. An adaptive volume constraint (AVC) algorithm based on an improved bisection method is proposed. Using this algorithm, the bi-objective uniform-stress-constrained topology optimization problem is transformed into a single-objective topology optimization problem and a volume-decision problem. The parametric level set method based on the compactly supported radial basis functions is employed to solve the single-objective problem, in which a self-organized acceleration scheme based on shape derivative and topological sensitivity is proposed to adaptively adjust the derivative of the objective function and the step length during the optimization. To solve the volume-decision problem, an improved bisection method is proposed. Numerical examples are tested to illustrate the feasibility and effectiveness of the self-organized acceleration scheme and the AVC algorithm based on the improved bisection method. An extended application to the bi-objective stress-constrained topology optimization of a structure with stress concentration is also presented.

Topology Optimization Design of Bars Structure Based on SKO Method

2013 ◽  
Vol 394 ◽  
pp. 515-520 ◽  
Author(s):  
Wen Jun Li ◽  
Qi Cai Zhou ◽  
Xu Hui Zhang ◽  
Xiao Lei Xiong ◽  
Jiong Zhao
Keyword(s):  
Global Optimization ◽  
Topology Optimization ◽  
Optimization Design ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Topology Optimization Problem ◽  
Proposed Model ◽  
Continuum Structure ◽  
The Impact

There are less topology optimization methods for bars structure than those for continuum structure. Bionic intelligent method is a powerful way to solve the topology optimization problems of bars structure since it is of good global optimization capacity and convenient for numerical calculation. This article presents a SKO topology optimization model for bars structure based on SKO (Soft Kill Option) method derived from adaptive growth rules of trees, bones, etc. The model has been applied to solve the topology optimization problem of a space frame. It uses three optimization strategies, which are constant, decreasing and increasing material removed rate. The impact on the optimization processes and results of different strategies are discussed, and the validity of the proposed model is proved.

A Framework of Multi-Fidelity Topology Design and its Application to Optimum Design of Flow Fields in Battery Systems

2019 ◽  
Author(s):  
Kentaro Yaji ◽  
Shintaro Yamasaki ◽  
Shohji Tsushima ◽  
Kikuo Fujita
Keyword(s):  
Topology Optimization ◽  
Design Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Flow Fields ◽  
Design Solution ◽  
Design Parameters ◽  
High Fidelity ◽  
Topology Optimization Problem ◽  
Battery Systems

Abstract We propose a novel framework based on multi-fidelity design optimization for indirectly solving computationally hard topology optimization problems. The primary concept of the proposed framework is to divide an original topology optimization problem into two subproblems, i.e., low- and high-fidelity design optimization problems. Hence, artificial design parameters, referred to as seeding parameters, are incorporated into the low-fidelity design optimization problem that is formulated on the basis of a pseudo-topology optimization problem. Meanwhile, the role of high-fidelity design optimization is to obtain a promising initial guess from a dataset comprising topology-optimized design candidates, and subsequently solve a surrogate optimization problem under a restricted design solution space. We apply the proposed framework to a topology optimization problem for the design of flow fields in battery systems, and confirm the efficacy through numerical investigations.

Optimal Layout of Shell Stiffeners With Frequency Design Considerations

1995 ◽  
Author(s):  
Yong Fu ◽  
Hae Chang Gea
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Layout ◽  
Two Phase ◽  
New Approach ◽  
Topology Optimization Problem ◽  
Design Considerations ◽  
Programming Tools ◽  
Effective Material Properties

Abstract In this paper, a new method to design the layout of shell stiffeners is introduced. This new approach has been derived from a two-phase spherical micro-inclusions model and resulted in very simple closed-form expressions for the effective material properties. The “relaxed” topology optimization problem can then be solved by general mathematical programming tools. It is very common to experience the eigenvalue switchover when solving topology optimization problems with frequency design considerations. An incremental objective function formulation with two strategies were studied to reduce the oscillation of optimization solutions. Design Examples are presented and compared.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Topology Optimization for the Single Phase Flow Using Two Point Flux Approximation Model

2013 ◽  
Author(s):  
Guang Dong ◽  
Yulan Song
Keyword(s):  
Porous Media ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Approximation Model ◽  
Single Phase Flow ◽  
Topology Optimization Problem ◽  
Flux Approximation

The topology optimization method is extended to solve a single phase flow in porous media optimization problem based on the Two Point Flux Approximation model. In particular, this paper discusses both strong form and matrix form equations for the flow in porous media. The design variables and design objective are well defined for this topology optimization problem, which is based on the Solid Isotropic Material with Penalization approach. The optimization problem is solved by the Generalized Sequential Approximate Optimization algorithm iteratively. To show the effectiveness of the topology optimization in solving the single phase flow in porous media, the examples of two-dimensional grid cell TPFA model with impermeable regions as constrains are presented in the numerical example section.

An Interactive Neural Network for Constrained Multi-Objective Optimization with Application to the Design of Digital Filters

2012 ◽  
Vol 433-440 ◽  
pp. 2808-2816
Author(s):  
Jian Jin Zheng ◽  
You Shen Xia
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Computational Complexity ◽  
Digital Filters ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

This paper presents a new interactive neural network for solving constrained multi-objective optimization problems. The constrained multi-objective optimization problem is reformulated into two constrained single objective optimization problems and two neural networks are designed to obtain the optimal weight and the optimal solution of the two optimization problems respectively. The proposed algorithm has a low computational complexity and is easy to be implemented. Moreover, the proposed algorithm is well applied to the design of digital filters. Computed results illustrate the good performance of the proposed algorithm.

Topology Optimization Under Independent Multi-Load With Uncertainty

2016 ◽  
Author(s):  
Hae Chang Gea ◽  
Xing Liu ◽  
Euihark Lee ◽  
Limei Xu
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Engineering Practice ◽  
Worst Case ◽  
Load Uncertainty ◽  
Topology Optimization Problem ◽  
Level Problem ◽  
Upper Level ◽  
Mean Compliance

In this paper, topology optimization under multiple independent loadings with uncertainty is presented. In engineering practice, load uncertainty can be found in many applications. From the literature, researchers have focused mainly on problems containing only a single uncertain external load. However, such idealistic problems may not be very useful in engineering practice. Problems involving multi-loadings with uncertainty are more commonly found in engineering applications. This paper presents a method to solve a system which contains multiple independent loadings with load uncertainty. First, a two-level optimization problem is formulated. The upper level problem is a typical topology optimization problem to minimize the mean compliance in the design using the worst case conditions. The lower level optimization problem is to solve for the worst loadings corresponding to the critical structure response. At the lower level formulation, an unknown-but-bounded model is used to define uncertain loadings. There are two challenges in finding the worst loading case: non-convexity and multi-loadings. The non-convexity problem is addressed by reformulating the problem as an inhomogeneous eigenvalue problem by applying the KKT optimality conditions and the multi-uncertain loadings problem is solved by an iterative method. After the worst loadings are generated, the upper level problem can be solved by a general topology optimization method. The effectiveness of the proposed method is demonstrated by numerical examples.

Multi-material topology optimization of compliant mechanisms via solid isotropic material with penalization approach and alternating active phase algorithm

2020 ◽  
Vol 234 (13) ◽  
pp. 2631-2642
Author(s):  
Behzad Majdi ◽  
Arash Reza
Keyword(s):  
Topology Optimization ◽  
Isotropic Material ◽  
Close Agreement ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Active Phase ◽  
Maximum Displacement ◽  
Topology Optimization Problem ◽  
Solid Phases ◽  
Ansys Workbench

The present study aims at providing a topology optimization of multi-material compliant mechanisms using solid isotropic material with penalization (SIMP) approach. In this respect, three multi-material gripper, invertor, and cruncher compliant mechanisms are considered that consist of three solid phases, including polyamide, polyethylene terephthalate, and polypropylene. The alternating active-phase algorithm is employed to find the distribution of the materials in the mechanism. In this case, the multiphase topology optimization problem is divided into a series of binary phase topology optimization sub-problems to be solved partially in a sequential manner. Finally, the maximum displacement of the multi-material compliant mechanisms was validated against the results obtained from the finite element simulations by the ANSYS Workbench software, and a close agreement between the results was observed. The results reveal the capability of the SIMP method to accurately conduct the topology optimization of multi-material compliant mechanisms.

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