OPTIMUM DESIGN OF GEOMETRICALLY NONLINEAR ELASTIC PLASTIC STEEL FRAMES

Abstract

A structural optimization algorithm is presented for geometrically nonlinear elastic-plastic frames. The algorithm is obtained by coupling the optimality criteria approach with a large deformation analysis method for elastic-plastic frames. The optimality criteria method is used to develop a recursive relationship for the design variables considering displacement constraints. This relationship requires the nonlinear response of the frame at every design cycle where the values of design variables change. The computation of nonlinear response is based on an Eulerian formulation which includes elastic-plastic effects. Local member force-deformation relationships are extended to cover geometric nonlinearities. An incremental load approach with Newton-Raphson iteration is adopted for the computational procedure. These iterations are terminated when the prescribed load factor is reached. A number of design examples are presented to demonstrate the application of the algorithm. The optimum designs obtained for geometrically nonlinear elastic-plastic frames are compared to those of linear-elastic frames.