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.

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.

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

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Stress Constraint ◽  
Cell Problem ◽  
Design Variables ◽  
Design Cell

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 gray 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. No postprocessing is required for topology uncertainty caused by either point connection or gray cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Hybrid Discretization

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 no matter 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 grey cell problem that is usually caused by intermediate material states. Von Mises 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 choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions require no postprocessing or interpretation, and have no point flexure, unsmooth boundary and zigzag member. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples in compliant mechanisms.

The Discrete Topology Optimization of Structures Using the Modified Quadrilateral Discretization Model

2012 ◽  
Author(s):  
Hong Zhou ◽  
Ravinder G. Malela
Keyword(s):  
Topology Optimization ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Cell Problem ◽  
Design Variables ◽  
Design Cell

The modified quadrilateral discretization model is introduced for the discrete topology optimization of structures 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 eradicated. In the proposed discrete topology optimization method of structures, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the optimized structure safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented discrete topology optimization procedure is illustrated by two topology optimization examples of structures.

Optimizing the Topologies of Compliant Mechanisms Using the Improved Modified Quadrilateral Discretization Model

2012 ◽  
Author(s):  
Hong Zhou ◽  
Venkata Krishna Perivilli ◽  
Praveen Chilukuri
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Local Stress ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Sharp Corner ◽  
Material Utilization ◽  
Design Cell

The improved 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 and each quadrilateral design cell is further subdivided into 16 triangular analysis cells. All kinds of dangling full and half quadrilateral design cells and sharp-corner triangular analysis cells are removed in the improved modified quadrilateral discretization model to enhance the material utilization. Every quadrilateral design cell or triangular analysis cell is either solid or void to implement the discrete topology optimization and eradicate topology uncertainty caused by intermediate material states. The local stress constraint is directly imposed on each triangular analysis cell to make the synthesized compliant mechanism safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. Two topology optimization examples of compliant mechanisms are solved based on the proposed improved modified quadrilateral discretization model to verify its effectiveness.

Topology Optimization of Compliant Mechanisms Using the Improved Quadrilateral Discretization Model

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Hong Zhou ◽  
Avinash R. Mandala
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Local Stress ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Sharp Corner ◽  
Material Utilization ◽  
Design Cell

The improved quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into triangular analysis cells. All kinds of dangling quadrilateral design cells and sharp-corner triangular analysis cells are removed in the improved quadrilateral discretization model to promote the material utilization. Every quadrilateral design cell or triangular analysis cell is either solid or void to implement the discrete topology optimization and eradicate the topology uncertainty caused by intermediate material states. The local stress constraint is directly imposed on each triangular analysis cell to make the synthesized compliant mechanism safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. Two topology optimization examples of compliant mechanisms are solved based on the proposed improved quadrilateral discretization model to verify its effectiveness.

Dynamic Topology Optimization of Compliant Mechanisms and Piezoceramic Actuators

2002 ◽  
Author(s):  
Hima Maddisetty ◽  
Mary Frecker
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Method ◽  
Mechanical Efficiency ◽  
Optimal Topology ◽  
Driving Frequency ◽  
Spring Stiffness ◽  
Piezoceramic Actuator ◽  
Near Resonance

A topology optimization method is developed to design a piezoelectric ceramic actuator together with a compliant mechanism coupling structure for dynamic applications. The objective is to maximize the mechanical efficiency with a constraint on the capacitance of the piezoceramic actuator. Examples are presented to demonstrate the effect of considering dynamic behavior compared to static behavior, and the effect of sizing the piezoceramic actuator on the optimal topology and the capacitance of the actuator element. Comparison studies are also presented to illustrate the effect of damping, external spring stiffness, and driving frequency. The optimal topology of the compliant mechanism is shown to be dependent on the driving frequency, the external spring stiffness, and if the piezoelectric actuator element is considered as design or non-design. At high driving frequencies, it was found that the dynamically optimized structure is very near resonance.

An Evolutionary Soft-Add Topology Optimization Method for Synthesis of Compliant Mechanisms With Maximum Output Displacement

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Chih-Hsing Liu ◽  
Guo-Feng Huang ◽  
Ta-Lun Chen
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Volume Fraction ◽  
Compliant Mechanism ◽  
Optimization Method ◽  
Computational Time ◽  
Maximum Output ◽  
Spring Stiffness ◽  
Output Displacement ◽  
Topology Optimization Method

This paper presents an evolutionary soft-add topology optimization method for synthesis of compliant mechanisms. Unlike the traditional hard-kill or soft-kill approaches, a soft-add scheme is proposed in this study where the elements are equivalent to be numerically added into the analysis domain through the proposed approach. The objective function in this study is to maximize the output displacement of the analyzed compliant mechanism. Three numerical examples are provided to demonstrate the effectiveness of the proposed method. The results show that the optimal topologies of the analyzed compliant mechanisms are in good agreement with previous studies. In addition, the computational time can be greatly reduced by using the proposed soft-add method in the analysis cases. As the target volume fraction in topology optimization for the analyzed compliant mechanism is usually below 30% of the design domain, the traditional methods which remove unnecessary elements from 100% turn into inefficient. The effect of spring stiffness on the optimized topology has also been investigated. It shows that higher stiffness values of the springs can obtain a clearer layout and minimize the one-node hinge problem for two-dimensional cases. The effect of spring stiffness is not significant for the three-dimensional case.

Multiobjective Topology Extraction of the Compliant Mechanisms

2014 ◽  
Vol 971-973 ◽  
pp. 1941-1948
Author(s):  
Zhao Kun Li ◽  
Hua Mei Bian ◽  
Li Juan Shi ◽  
Xiao Tie Niu
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Threshold Value ◽  
Jump Discontinuity ◽  
Engineering Practice ◽  
Distribution Method ◽  
Black And White ◽  
Design Variables

Homogenization or material distribution method based topology optimization will create final topologies in grey level image and saw tooth jump discontinuity boundaries that are not suitable for direct engineering practice, so it is necessary to extract the topological diagram. And a new topology extraction method for compliant mechanisms is presented. In the fist stage, the grey image is transferred into the black-and white finite element topology optimization results. The threshold value meeting to objective function is obtained so that each element is either empty or solid; in the second stage, the density contour approach is used by redistributing nodal densities to generate the smooth boundaries; in the third stage, Smooth boundaries are represented by parameterized B-spline curves whose control points selected from the viewpoint of stiffness and flexibility constitute the parameters ready to undergo shape optimization; Then shape optimization is executed to improve stress-based local performance, The parameters that present the outer shape of the compliant mechanism are used as design variables; In the final stage, simulations of numerical examples are presented to show the validity of the proposed method.

Topology Optimization of Compliant Mechanisms Using Evolutionary Algorithm With Design Geometry Encoded as a Graph

2002 ◽  
Author(s):  
Shamim Akhtar ◽  
Kang Tai ◽  
Jitendra Prasad
Keyword(s):  
Topology Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Evolutionary Process ◽  
Optimization Procedure ◽  
Structural Topology ◽  
Mutation Operators ◽  
Design Variables ◽  
Straight Line

This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using an evolutionary algorithm (EA). The geometry representation scheme works by defining a skeleton which represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any EA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a graph which reflects this underlying topology so that the genetic crossover and mutation operators of the EA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point.

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