On some simplified models for optimal design of structural systems

Abstract

Some simplified models for optimal design of large structural systems are reviewed. The design variables represent the members' cross-sections and the constraints are related to stress, displacement and design considerations. Using displacement analysis formulation, several explicit behavior models which do not involve multiple implicit analyses are presented. It is shown that approximations of the displacements, often used in optimization of large systems, essentially lead to solutions which do not satisfy equilibrium. Approximations along a line in the design variables space are developed, and simplifications based on the virtual load method and inverse design variables formulations are presented. The relationships between the various models are derived; it is shown that, under the usual assumption of linear relationship between the stiffness matrix elements and the design variables, some of the approximations become equivalent.