scholarly journals Structural Optimization of a Linearly Elastic Structure using the Homogenization Method

1991 ◽  
pp. 183-203 ◽  
Author(s):  
Noboru Kikuchi ◽  
Katsuyuki Suzuki
Keyword(s):  
Structural Optimization ◽  
Homogenization Method ◽  
Elastic Structure

Two-Scale Topology Optimization With Parameterized Cellular Structures

2021 ◽  
Author(s):  
Sina Rastegarzadeh ◽  
Jun Wang ◽  
Jida Huang
Keyword(s):  
Topology Optimization ◽  
High Resolution ◽  
Structural Optimization ◽  
Optimization Problem ◽  
Material Design ◽  
Homogenization Method ◽  
Elasticity Tensor ◽  
Structure Design ◽  
Cellular Structures ◽  
Mapping Technique

Abstract Advances in additive manufacturing enable the fabrication of complex structures with intricate geometric details. It also escalates the potential for high-resolution structure design. However, the increasingly finer design brings computational challenges for structural optimization approaches such as topology optimization (TO) since the number of variables to optimize increases with the resolutions. To address this issue, two-scale TO paves an avenue for high-resolution structural design. The design domain is first discretized to a coarse scale, and the material property distribution is optimized, then using micro-structures to fill each property field. In this paper, instead of finding optimal properties of two scales separately, we reformulate the two-scale TO problem and optimize the design variables concurrently in both scales. By introducing parameterized periodic cellular structures, the minimal surface level-parameter is defined as the material design parameter and is implemented directly in the optimization problem. A numerical homogenization method is employed to calculate the elasticity tensor of the cellular materials. The stiffness matrices of the cellular structures derived as a function of the level parameters, using the homogenization results. An additional constraint on the level parameter is introduced in the structural optimization framework to enhance adjacent cellulars interfaces’ compatibility. Based on the parameterized micro-structure, the optimization problem is solved concurrently with an iterative solver. The reliability of the proposed approach has been validated with different engineering design cases. Numerical results show a noticeable increase in structure stiffness using the level parameter directly in the optimization problem than the state-of-art mapping technique.

Structural Configuration Examples of an Integrated Optimal Design Process

1994 ◽  
Vol 116 (4) ◽  
pp. 997-1004 ◽  
Author(s):  
M. Chirehdast ◽  
H.-C. Gea ◽  
N. Kikuchi ◽  
P. Y. Papalambros
Keyword(s):  
Structural Optimization ◽  
Design Process ◽  
Homogenization Method ◽  
Optimization Techniques ◽  
Phase Iii ◽  
Design Problems ◽  
Novel Approach ◽  
Three Phase ◽  
Bicycle Frame ◽  
Automated Procedures

Structural optimization procedures usually start from a given design topology and vary proportions or boundary shapes of the design to achieve optimality of an objective under various constraints. This article presents examples of the application of a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated. A three-phase design process is used. In Phase I, an optimal initial topology is created by a homogenization method as a gray-scale image. In Phase II, the image is transformed to a realizable design using computer vision techniques. In Phase III, the design is parameterized and treated in detail by conventional size and shape optimization techniques. Fully-automated procedures for optimization of two-dimensional solid structures are outlined, and several practical design problems for this type of structures are solved using the proposed procedure, including a crane hook and a bicycle frame.

Structural Configuration Examples of an Integrated Optimal Design Process

1992 ◽  
Author(s):  
Mehran Chirehdast ◽  
Hae Chang Gea ◽  
Noboru Kikuchi ◽  
Panos Y. Papalambros
Keyword(s):  
Structural Optimization ◽  
Design Process ◽  
Homogenization Method ◽  
Optimization Techniques ◽  
Phase Iii ◽  
Design Problems ◽  
Novel Approach ◽  
Three Phase ◽  
Bicycle Frame ◽  
Automated Procedures

Abstract Structural optimization procedures usually start from a given design topology and vary proportions or boundary shapes of the design to achieve optimality of an objective under various constraints. This article presents examples of the application of a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated. A three-phase design process is used. In Phase I, an optimal initial topology is created by a homogenization method as a gray-scale image. In Phase II, the image is transformed to a realizable design using computer vision techniques. In Phase III, the design is parameterized and treated in detail by conventional size and shape optimization techniques. Fully-automated procedures for optimization of two-dimensional solid structures are outlined, and several practical design problems for this type of structures are solved using the proposed procedure, including a crane hook and a bicycle frame.

Concurrent Design of Structures and Materials Based on the Bi-Directional Evolutionary Structural Optimization

2013 ◽  
Vol 438-439 ◽  
pp. 445-450 ◽  
Author(s):  
Xiao Lei Yan ◽  
Xiao Dong Huang ◽  
Yi Min Xie
Keyword(s):  
Structural Optimization ◽  
Optimization Algorithm ◽  
Effective Properties ◽  
Homogenization Method ◽  
Two Phase ◽  
Element Analysis ◽  
Evolutionary Structural Optimization ◽  
The Finite Element Analysis ◽  
Beso Method ◽  
Mean Compliance

Different from the independent optimization of macrostructures or materials, a two-scale topology optimization algorithm is developed in this paper based on the bi-directional evolutionary structural optimization (BESO) method for concurrently designing a macrostructure and its composite microstructure. The objective is to minimize the mean compliance of the structure which is composed of a two-phase composite. The effective properties of the composite are calculated through the homogenization method and integrated into the finite element analysis of the structure. Sensitivity analysis for the structure and microstructure is conducted by the adjoint method. Based on the derived sensitivity numbers, the BESO approach is applied for iteratively updating the topologies for both the structure at the macro level and the microstructure of composite at the micro level. Numerical examples are presented to validate the effectiveness of the proposed optimization algorithm.

Study on Multi-Void Microstructure of Asymptotic Homogenization for Topology Optimization

2011 ◽  
Vol 233-235 ◽  
pp. 1935-1939
Author(s):  
Yan Hui Qie ◽  
Bo Liu ◽  
Xiu Hong Wang ◽  
Xiao Lei Li ◽  
Bao Wang Ban
Keyword(s):  
Topology Optimization ◽  
Potential Energy ◽  
Structural Optimization ◽  
Mathematical Models ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Total Potential Energy ◽  
Asymptotic Homogenization ◽  
Total Potential ◽  
Porous Microstructure

One kind of multi-void three-dimensional microstructure models based on homogenization method is constructed. Based on multi-void microstructure, the mathematical models for the topological structural optimization which takes maximizing the total potential energy as the objective function is constructed, then the Kuhn-Tucker optimality condition of the update method about the designs variable based on the porous microstructure can be gotten when optimization iterates. Finally, in explaining the employed algorithm an example is provided.

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