Simultaneous topology optimization of structure and supports

Abstract.The purpose of this paper is to demonstrate a method for and the benefits of simultaneously designing structure and support distribution using topology optimization. The support conditions are included in the topology optimization by introducing a new set of design variables that represents supported areas. The method is applied to compliance minimization and mechanism design. In the case of mechanism design, the large displacements of the mechanism are modelled using geometrically nonlinear FE-analysis.Examples with minimization of the compliance demonstrate the effects of using variable cost of supports in a design domain. Other examples show that more efficient mechanisms are obtained by introducing the support conditions in the topology optimization problem.

[1]  G. I. N. Rozvany,et al.  Optimization of Unspecified Generalized Forces in Structural Design , 1974 .

[2]  George I. N. Rozvany,et al.  Plastic design of beams: Optimal locations of supports and steps in yield moment , 1975 .

[3]  Zenon Mróz,et al.  Optimal design of structures with variable support conditions , 1975 .

[4]  J. Z. Zhu,et al.  The finite element method , 1977 .

[5]  Z. Mroz,et al.  Column Design: Optimization of Support Conditions and Segmentation , 1977 .

[6]  J. E. Taylor,et al.  Designing Continuous Columns for Minimum Total Cost of Material and Interior Supports , 1978 .

[7]  K.E. Petersen,et al.  Silicon as a mechanical material , 1982, Proceedings of the IEEE.

[8]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[9]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[10]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[11]  G. Rozvany,et al.  Michell layouts for various combinations of line supports. I , 1990 .

[12]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[13]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[14]  N. Olhoff,et al.  Minimum stiffness of optimally located supports for maximum value of column buckling loads , 1991 .

[15]  H. Mlejnek,et al.  An engineer's approach to optimal material distribution and shape finding , 1993 .

[16]  D. Tortorelli,et al.  Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity , 1994 .

[17]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[18]  Ole Sigmund,et al.  Some Inverse Problems in Topology Design of Materials and Mechanisms , 1996 .

[19]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[20]  M. A. Crisfield,et al.  Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics , 1997 .

[21]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[22]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[23]  Ole Sigmund,et al.  Compliant thermal microactuators , 1999 .

[24]  Ole Sigmund,et al.  Topology synthesis of large‐displacement compliant mechanisms , 2001 .

[25]  Sridhar Kota,et al.  An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms , 1999 .

[26]  Moshe B. Fuchs,et al.  Optimal structural topologies with transmissible loads , 2000 .

[27]  O. Sigmund,et al.  Stiffness design of geometrically nonlinear structures using topology optimization , 2000 .

[28]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .