A mutual energy formulation for optimal structural design

This paper presents a variational formulation for the design of elastic structures where the function to be minimized by the optimal design, i.e. the objective, is expressed in abstract form. The resulting statement of necessary conditions is uniformly applicable for all admissible objectives. Both state and adjoint state variables appear directly in the problem statement, and all objectives and the arguments of constraints are scalars. The adjoint pair of state variables appear in symmetric roles via the expression termed “mutual energy". Application of the generalized formulation is demonstrated by treatment of the following examples: design to minimize the maximum value of displacement or to minimize a global measure of stress, design for generalized compliance, design where self-weight is taken into account, and multicriterion design.