TY - JOUR

T1 - Topology optimization of compliant circular path mechanisms based on an aggregated linear system and singular value decomposition

AU - Takezawa, A.

AU - Kitamura, M.

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012/2/10

Y1 - 2012/2/10

N2 - This paper proposes a topology optimization method for the design of compliant circular path mechanisms, or compliant mechanisms having a set of output displacement vectors with a constant norm, which is induced by a given set of input forces. To perform the optimization, a simple linear system composed of an input force vector, an output displacement vector and a matrix connecting them is constructed in the context of a discretized linear elasticity problem using FEM. By adding two constraints: 1, the dimensions of the input and the output vectors are equal; 2, the Euclidean norms of all local input force vectors are constant; from the singular value decomposition of the matrix connecting the input force vector and the output displacement vector, the optimization problem, which specifies and equalizes the norms of all output vectors, is formulated. It is a minimization problem of the weighted summation of the condition number of the matrix and the least square error of the second singular value and the specified value. This methodology is implemented as a topology optimization problem using the solid isotropic material with penalization method, sensitivity analysis and method of moving asymptotes. The numerical examples illustrate mechanically reasonable compliant circular path mechanisms and other mechanisms having multiple outputs with a constant norm.

AB - This paper proposes a topology optimization method for the design of compliant circular path mechanisms, or compliant mechanisms having a set of output displacement vectors with a constant norm, which is induced by a given set of input forces. To perform the optimization, a simple linear system composed of an input force vector, an output displacement vector and a matrix connecting them is constructed in the context of a discretized linear elasticity problem using FEM. By adding two constraints: 1, the dimensions of the input and the output vectors are equal; 2, the Euclidean norms of all local input force vectors are constant; from the singular value decomposition of the matrix connecting the input force vector and the output displacement vector, the optimization problem, which specifies and equalizes the norms of all output vectors, is formulated. It is a minimization problem of the weighted summation of the condition number of the matrix and the least square error of the second singular value and the specified value. This methodology is implemented as a topology optimization problem using the solid isotropic material with penalization method, sensitivity analysis and method of moving asymptotes. The numerical examples illustrate mechanically reasonable compliant circular path mechanisms and other mechanisms having multiple outputs with a constant norm.

KW - Compliant mechanisms

KW - Finite element method

KW - Path generation

KW - Sensitivity analysis

KW - Singular value decomposition

KW - Topology optimization

UR - http://www.scopus.com/inward/record.url?scp=84856358907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856358907&partnerID=8YFLogxK

U2 - 10.1002/nme.3259

DO - 10.1002/nme.3259

M3 - Article

AN - SCOPUS:84856358907

SN - 0029-5981

VL - 89

SP - 706

EP - 725

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

IS - 6

ER -