Optimal Synthesis of Compliant Mechanisms Using Subdivision and Commercial FEA

2004 ◽  
Author(s):  
Patrick V. Hull ◽  
Stephen Canfield
Keyword(s):  
Topology Optimization ◽  
Mechanism Design ◽  
Compliant Mechanism ◽  
Rapid Prototype ◽  
Optimization Procedure ◽  
Design Tool ◽  
Design Parameters ◽  
Solid Model ◽  
Control Points ◽  
Numerical Instabilities

The field of distributed-compliance mechanisms has seen significant work in developing suitable topology optimization tools for their design. These optimal design tools have grown out of the techniques of structural optimization. This paper will build on the previous work in topology optimization and compliant mechanism design by proposing an alternative design space parameterization through control points and adding another step to the process, that of subdivision. The control points assist a specific design to be represented as a solid model during the optimization process. The process of subdivision creates an additional number of control points that help smooth the surface (for example a C2 continuous surface depending on the method of subdivision chosen) creating a manufacturable design free of traditional numerical instabilities. Note that these additional control points do not add to the number of design parameters. This alternative parameterization and description as a solid model effectively and completely separates the design variables from the analysis variables during the optimization procedure. The motivation behind this work is to avoid several of the numerical instabilities that occur in topology optimization and to create an automated design tool from task definition to functional prototype created on a CNC or rapid-prototype machine. This paper will describe the complaint mechanism design process including subdivision and will demonstrate the procedure on several common examples.

Optimal Synthesis of Compliant Mechanisms Using Subdivision and Commercial FEA

2005 ◽  
Vol 128 (2) ◽  
pp. 337-348 ◽  
Author(s):  
Patrick V. Hull ◽  
Stephen Canfield
Keyword(s):  
Topology Optimization ◽  
Mechanism Design ◽  
Compliant Mechanism ◽  
Rapid Prototype ◽  
Optimization Procedure ◽  
Design Tool ◽  
Design Parameters ◽  
Solid Model ◽  
Control Points ◽  
Compliant Mechanism Design

The field of distributed-compliance mechanisms has seen significant work in developing suitable topology optimization tools for their design. These optimal design tools have grown out of the techniques of structural optimization. This paper will build on the previous work in topology optimization and compliant mechanism design by proposing an alternative design space parametrization through control points and adding another step to the process, that of subdivision. The control points allow a specific design to be represented as a solid model during the optimization process. The process of subdivision creates an additional number of control points that help smooth the surface (for example a C2 continuous surface depending on the method of subdivision chosen) creating a manufacturable design free of some traditional numerical instabilities. Note that these additional control points do not add to the number of design parameters. This alternative parametrization and description as a solid model effectively and completely separates the design variables from the analysis variables during the optimization procedure. The motivation behind this work is to create an automated design tool from task definition to functional prototype created on a CNC or rapid-prototype machine. This paper will describe the proposed compliant mechanism design process and will demonstrate the procedure on several examples common in the literature.

A simple evolutionary topology optimization procedure for compliant mechanism design

2007 ◽  
Vol 44 (1-2) ◽  
pp. 53-62 ◽  
Author(s):  
Rubén Ansola ◽  
Estrella Veguería ◽  
Javier Canales ◽  
José A. Tárrago
Keyword(s):  
Topology Optimization ◽  
Mechanism Design ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Compliant Mechanism Design

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.

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 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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