Optimum design of nonlinear elastic framed domes

Abstract

In this paper, an algorithm is presented for the optimum design of three-dimensional rigidly jointed frames which takes into account the nonlinear response due to the effect of axial forces in members. The stability functions for three-dimensional beam-columns are used to obtain the nonlinear response of the frame. These functions are derived by considering the effect of axial force on flexural stiffness and effect of flexure on axial stiffness. The optimum design algorithm considers displacement limitations and restricts combined stresses not to be more than yield stress. It employs the optimality criteria approach together with nonlinear overall stiffness matrix to develop a recursive relationship for design variables in the case of dominant displacement constraints. The combined stress constraints are reduced into nonlinear equations of design variables. The algorithm initiates the optimum design at the selected load factor and carries out elastic instability analysis until the ultimate load factor is reached. During these iterations checks of the overall stability of frame is conducted. If the nonlinear response is obtained without loss of stability, the algorithm then proceeds to the next design cycle. The method developed is applied to the optimum design of a number of rigid space frames to demonstrate its versatility.