Topology optimization of structures composed of one or two materials

Maximization of the integral stiffness of a structure composed of one or two isotropic materials of large stiffness is considered using the homogenization technique. Material is modelled by a second rank composite, and we use the concentrations and orientations of the composite as design variables. Numerical results are presented at the end of the paper.

[1]  B. Esping,et al.  Minimum weight design of membrane structures using eight node isoparametric elements and numerical derivatives , 1984 .

[2]  R. Kohn,et al.  Optimal design and relaxation of variational problems, III , 1986 .

[3]  M. Zhou,et al.  Generalized shape optimization without homogenization , 1992 .

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

[5]  J. Thomsen,et al.  Optimization of composite discs , 1991 .

[6]  R. Haftka,et al.  Structural shape optimization — a survey , 1986 .

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

[8]  John Rasmussen,et al.  The structural optimization system CAOS , 1990 .

[9]  Robert V. Kohn.  Composite materials and structural optimization , 1989 .

[10]  C. Bert,et al.  The behavior of structures composed of composite materials , 1986 .

[11]  P. Pedersen.  Bounds on elastic energy in solids of orthotropic materials , 1990 .

[12]  Marco Avellaneda,et al.  Optimal bounds and microgeometries for elastic two-phase composites , 1987 .

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

[14]  Helder C. Rodrigues,et al.  Shape optimal design of elastic bodies using a mixed variational formulation , 1988 .

[15]  Pauli Pedersen,et al.  On thickness and orientational design with orthotropic materials , 1991 .

[16]  Robert V. Kohn,et al.  Optimal design in elasticity and plasticity , 1986 .

[17]  Niels Olhoff,et al.  Optimization of Fiber Orientation and Concentration in Composites , 1993 .

[18]  Robert V. Kohn,et al.  Recent progress in the mathematical modelling of composite materials , 1988 .

[19]  Claus Mattheck,et al.  Engineering Optimization in Design Processes , 1991 .

[20]  Björn J.D. Esping,et al.  The oasis structural optimization system , 1986 .

[21]  P. Pedersen.  On optimal orientation of orthotropic materials , 1989 .

[22]  Martin P. Bendsøe,et al.  Integrated topology and boundary shape optimization of 2-D solids , 1991 .

[23]  C. Mattheck,et al.  Engineering Optimization in Design Processes: Proceedings of the International Conference, Karlsruhe Nuclear Research Center, Germany, September 3-4, 1990 , 1991 .

[24]  N. Kikuchi,et al.  A homogenization method for shape and topology optimization , 1991 .

[25]  Martin P. Bendsøe,et al.  Topology and Boundary Shape Optimization as an Integrated Tool for Computer Aided Design , 1991 .

[26]  Niels Olhoff,et al.  On CAD-integrated structural topology and design optimization , 1991 .

[27]  Robert V. Kohn,et al.  Optimal bounds for the effective energy of a mixture of isotropic, incompressible, elastic materials , 1988 .

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

[29]  Panos Y. Papalambros,et al.  An Integrated Environment for Structural Configuration Design , 1990 .

[30]  M. Zhou,et al.  Applications of the COC Algorithm in Layout Optimization , 1991 .

[31]  V. Braibant,et al.  Shape optimal design using B-splines , 1984 .

[32]  Pauli Pedersen,et al.  On the optimal layout of multi-purpose trusses , 1972 .