A method for treating damage related criteria in optimal topology design of continuum structures

In this paper we present a formulation of the wellknown 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 the problem of finding the topology of a structure where we seek maximal stiffness under service loads with a constraint on the amount of damage which occurs under a separate set of damage loads.

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