Shape determination problem of structures considering multiple loading conditions. Extension of inverse variational shape determination method.

Abstract

Shape determination method of structures based on the Inverse Variational Principle is extended to the multiple loading case. Given several sets of loads which are not active at the same time, such a shape is determined that makes the weighted sum of the potential energies for each load set stationary with the constraint of the volume constancy. The problem has the same form as the multiobjective optimization one. The Pareto optimal solutions can be obtained easily by the Energy-Ratio-Method proposed in the single loading case. It is observed through numerical examples that in the Pareto optimal structures, stress levels under each set of loads are relaxed somewhat compared with the worst case. If the weight to each loading case is taken as the probability that the load is actually active, then the obtained shape is interpreted as the one that will yield the highest expected value of the potential energy among the shapes with the same volume.