Optimization of statically indeterminate beams subjected to uniformly distributed load

This paper gives analytical solutions of an optimization problem for beams with rectangular cross section which are supported by statically indeterminate conditions and are subjected to a uniformly distributed load. The problem is based on the inverse variational principle in which the shape and displacement that make the total potential energy stationary are considered under the condition of volume constancy. The problem becomes one of searching for the positions where the sign of the bending moment changes. The beams obtained have the property of uniform strength.