Optimum topology design of structures under varying loads is formulated as a min-max problem, where the maximum compliance is minimized. By discretizing the range of load as a set of discrete load conditions, the problem is then transformed to a standard mathematical programming problem. The artificial material approach with a power law between the elastic modulus and the density is used to describe the design status of each design pixel. An analytic design sensitivity formula for the compliance is implemented in the program developed. The use of superposition of basis solutions for the displacements enhances computational efficiency drastically.
Through several examples, the method of putting grid on the ranges of the load is shown robust in obtaining the min-max solution. It is shown that the present approach is one useful way of dealing with uncertainty in the load, and the solutions under varying loads are more meaningful than those obtained for a single or at most some multiple load conditions.
