Optimization of structures with nonlinear behavior using equivalent loads

Nonlinear Response Optimization using the Equivalent Loads (NROEL) method/algorithm is proposed to perform optimization of non-linear response structures. The conventional method spends most of the design time on nonlinear analysis. The NROEL algorithm makes the equivalent load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent loads are defined as the loads in linear analysis, which generate the same response fields as those in nonlinear analysis. The algorithm is validated for convergence and optimality. The proposed algorithm is applied to a simple mathematical problem to verify the convergence and the optimality. The NROEL algorithm is applied to several structural problems with geometric and/or material nonlinearity. Conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples. The results of the optimizations are compared. The proposed NROEL method is found to be very efficient and good solutions are derived.