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.

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.

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.

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.

Generalized Topology Optimization of Linear Elastic Structures Subjected to Thermal Loads

1993 ◽  
Author(s):  
Helder C. Rodrigues ◽  
Paulo A. Fernandes
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Computational Model ◽  
Asymptotic Methods ◽  
Generalized Topology ◽  
Thermal Loads ◽  
Equilibrium Equations ◽  
Topology Optimization Problem ◽  
Finite Element Approximations ◽  
Linear Elastic

Abstract This paper presents the development of a computational model for the generalized topology optimization problem, using a material distribution approach, of 2-D linear elastic solids subjected to thermal loads, with compliance objective function and an isoperimetric constraint on volume. The model relies on homogenization asymptotic methods to characterize the influence of the material periodic microstructure and a finite element displacement formulation is used to approximate the homogenized equilibrium equations obtained. The computational model developed is tested in several examples considering different finite element approximations and the influence of the design variables (material density and orientation) is analyzed.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Conduct Sensitivity Analysis

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is usually caused by intermediate material states. Local 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 avoid the need to select the initial guess solution and conduct sensitivity analysis. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

A Global Constraint on Relative Rotation to Avoid Lumped Compliant Mechanisms in Topology Optimization

2008 ◽  
Author(s):  
Sangamesh R. Deepak
Keyword(s):  
Topology Optimization ◽  
Finite Elements ◽  
Elastic Deformation ◽  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Compliant Mechanisms ◽  
Benchmark Problems ◽  
Global Constraint ◽  
Relative Rotation ◽  
Local Constraint

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However, it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint on the following benchmark problems — displacement inverter and gripper.

Multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition

2021 ◽  
pp. 095440622110361
Author(s):  
Jinqing Zhan ◽  
Yu Sun ◽  
Min Liu ◽  
Benliang Zhu ◽  
Xianmin Zhang
Keyword(s):  
Boundary Condition ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Impedance Matching ◽  
Large Displacement ◽  
Thermal Impedance ◽  
Output Displacement ◽  
Topology Optimization Problem

Multi-material compliant mechanisms design enables potential design possibilities by exploiting the advantages of different materials. To satisfy mechanical/thermal impedance matching requirements, a method for multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition is presented in this study. In the optimization model, the element stacking method is employed to describe the material distribution and handle material-dependent boundary condition. The maximization of the output displacement of the compliant mechanism is developed as the objective function and the structural volume of each material is the constraint. Fictitious domain approach is applied to circumvent the numerical instabilities in topology optimization problem with geometrical nonlinearities. The method of moving asymptotes is applied to solve the optimization problem. Several numerical examples are presented to demonstrate the validity of the proposed method. The optimal topologies of the compliant mechanisms obtained by the proposed method can satisfy the specified material-dependent boundary condition.

scholarly journals An Efficient Topology Description Function Method Based on Modified Sigmoid Function

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xingfa Yang ◽  
Jie Liu ◽  
Yin Yang ◽  
Qixiang Qing ◽  
Guilin Wen
Keyword(s):  
Topology Optimization ◽  
Function Method ◽  
Optimization Problem ◽  
Optimization Methods ◽  
Heaviside Function ◽  
Sigmoid Function ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Topology Description Function ◽  
Structural Compliance

Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

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