Bimodal Optimization of Compressed Columns on Elastic Foundations

We consider columns attached to elastic foundations and compressed by axial end loads. Pinned-pinned, clamped-clamped, and pinned-clamped boundary conditions are treated. The columns have rectangular sandwich cross sections with a fixed lightweight core and identical face sheets of variable thickness. For given total volume, we optimize the variation of the thickness along the column so as to maximize the buckling load. In most cases, the optimal design is bimodal (i.e., associated with two buckling modes). The optimal designs depend on the foundation stiffness, and the largest increase in buckling load relative to a column with constant thickness is 22 percent.