Local versus global stress constraint strategies in topology optimization: a comparative study

2021 ◽  
Author(s):  
Gustavo Assis da Silva ◽  
Niels Aage ◽  
André Teófilo Beck ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Stress Constraint ◽  
Global Stress

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

A Comparative Study of the Formulations for Topology Optimization of Compliant Mechanisms

2008 ◽  
Author(s):  
Sangamesh R. Deepak ◽  
M. Dinesh ◽  
Deepak Sahu ◽  
Salil Jalan ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Compliant Mechanisms ◽  
Computation Time ◽  
Initial Guess ◽  
Benchmark Problems ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Frame Element ◽  
Force Direction

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the last 15 years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parameterizations, namely, the frame element based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, the ability to converge from an unbiased uniform initial guess, and the computation time are analyzed. Some observations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

Topological Optimum Design Considering Stress Constraint Using Approximate Function

2009 ◽  
Vol 419-420 ◽  
pp. 25-28
Author(s):  
Chien Jong Shih ◽  
Kuang You Chen
Keyword(s):  
Topology Optimization ◽  
Numerical Optimization ◽  
Volume Fraction ◽  
Stress Constraint ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Integrated Process ◽  
Approximate Function ◽  
Material Volume ◽  
Element Technique

This paper presents an integrated process of structural topology optimization in minimizing both compliance and structural weight. The material volume fraction acts an additional design variable subjected to the empirical approximate stress constraint in terms of material volume fraction. This explicitly approximate function can provide a convenient way to calculate its gradient information for numerical optimization. An engineer does not require advanced topology optimization and superior finite element technique in applying proposed method.

A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
M. Dinesh ◽  
Deepak K. Sahu ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Compliant Mechanisms ◽  
Initial Guess ◽  
Benchmark Problems ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Frame Element ◽  
Force Direction ◽  
Computer Codes

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the past 15years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parametrizations, namely, the frame element-based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, and the ability to converge from an unbiased uniform initial guess are analyzed. Some observations and recommendations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

Design of flexure hinges based on stress-constrained topology optimization

2016 ◽  
Vol 231 (24) ◽  
pp. 4635-4645 ◽  
Author(s):  
Min Liu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Topology Optimization ◽  
Stress Concentration ◽  
Stress Constraints ◽  
Stress Constraint ◽  
Flexure Hinges ◽  
Weighted Sum Method ◽  
Stress Measure ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Sharp Corners

Stress concentration is one of the disadvantages of flexure hinges. It limits the range of motion and reduces the fatigue life of mechanisms. This article designs flexure hinges by using stress-constrained topology optimization. A weighted-sum method is used for converting the multi-objective topology optimization of flexure hinges into a single-objective problem. The objective function is presented by considering the compliance factors of flexure hinges in the desired and other directions. The stress constraint and other constraint conditions are developed. An adaptive normalization of the P-norm of the effective von Mises stresses is adopted to approximate the maximum stress, and a global stress measure is used to control the stress level of flexure hinges. Several numerical examples are performed to indicate the validity of the method. The stress levels of flexure hinges without and with stress constraints are compared. In addition, the effects of mesh refinement and output spring stiffness on the topology results are investigated. The stress constraint effectively eliminates the sharp corners and reduces the stress concentration.

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