A Displacement based optimization for nonlinear frame structures

An extension of the displacement based optimization method to frames with geometrically nonlinear response is presented. This method, when applied to trusses with linear and nonlinear response, provides a substantial reduction in computational time for design optimization. The efficiency of the method is due to the elimination of numerous finite element analyses that are required in using the traditional optimization approach. For frame problems, the number of degrees of freedom is typically larger than the number of cross sectional area design variables leading to difficulties in the implementation of the method compared to the truss implementation. A scheme that relaxes the nodal equilibrium equations is introduced, and the method is validated using test examples. The optimal designs obtained by using the displacement based optimization and the classical approaches are compared to demonstrate the computational efficiency of the method for frame structures.