A generalization of the equi-stress principle in optimizing the mechanical performance of two-dimensional grained composites

Abstract

A new optimization criterion of minimizing the variations of the boundary tractions in 2D bi-material elastostatic problems is proposed as a relaxation of the well-known equi-stress principle far beyond its primary application. This integral-type assessment of the local stresses offers significant numerical advantages over their direct minimization. In particular, it allows us to obtain reliable results at moderate computational cost through the same flexible scheme as in the author’s previous research on optimizing perforated plates. The scheme combines a genetic algorithm optimization with an efficient direct solver and with an economic shape parametrization, both formulated in the complex variable terms. After an extended analysis of the criterion, its effectiveness is illustrated, as before, by applying to a checkerboard grained plate where the equi-stress inclusions cease to exist at not-too-small volume fractions. The results obtained permit us to make some empirical conclusions which may stimulate further studies in both theoretical and practical directions.