Optimal Beam and Plate Foundations for Minimum Compliance

Abstract

Uniform beams and circular plates on nonuniform elastic foundations are considered. They are subjected to a uniformly distributed load and have various boundary conditions. For a specified total stiffness of the foundation, the distribution of foundation stiffness is determined which minimizes the compliance (i.e., the work done by the applied load). The optimal solutions for the beams consist of either a single elastic support or a region of uniform foundation bounded by elastic supports (except at free ends). For the plates, there is a central, circular region with a uniform foundation, bounded by a circular elastic support. In comparison to a uniform foundation, the decrease in compliance may be substantial.