Pontificia Universidad Católica de Chile Pontificia Universidad Católica de Chile
Gutiérrez S. and Zegpi E. (2014)

Stress constrained compliance minimization by means of the small amplitude homogenization method

Revista : Structural and Multidisciplinary Optimization
Volumen : 49
Número : 6
Páginas : 1025-1036
Tipo de publicación : ISI Ir a publicación


Under the assumption of small contrast between the elasticity tensors of two materials, we derive an algorithm based on an approximate relaxation of a problem that minimizes the compliance under a constraint on stress.Numerical results are presented for the short cantilever problem, where we see that, for a 1 to 2 contrast in Young moduli, and when compared with a configuration that only minimizes compliance, one can get up to a 46 % reduction in peak stress, while compliance increases by only 1 %.The basis of the method is the small amplitude homogenization technique derived by Allaire and Gutiérrez, which relies on the use of H-measures introduced by Tartar to study the quadratic interaction of weakly convergent sequences offunctions.