Optimal design of beams for prescribed compliance under alternative loads

A global optimality condition is established for minimum-weight design of sandwich beams with elementwise constant cross section for prescribed compliances in alternative states of loading. This condition requires a nonnegative linear combination of the mean-square curvatures of an element in the considered states of loading to have the same value for all elements. The use of the condition in the determination of the minimum-weight design is illustrated by examples.This research was sponsored by the Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, under Contract No. F33615-69-C-1826. The authors wish to express their thanks to Professor J. B. Martin, Brown University, for helpful discussions.