1 Department of Mathematics, Technical University of Denmark2 Office for Research and Relations, Administration, Technical University of Denmark3 Michigan State University
In this paper we present a formulation of the well-known structural topology optimization problem that accounts for the presence of loads capable of causing permanent damage to the structure. Damage is represented in the form of an internal variable model which is standard in continuum damage mechanics. Here we employ an interpretation of this model as an optimum remodeling problem for maximal compliance over all damage distributions, making also the analysis of the damage model a study in structural optimization. The damage criterion can be included in the optimal design model in a number of ways. We present results for finding the optimal topology of the reinforcement of an existing design with the goal of minimizing damage. Also, we treat a problem of finding the topology of a structure were we seek maximal stiffness under service loads with a constraint on the amount of damage which occurs under a separate set of damage loads.