Optimal design of geometrically nonlinear structures using topology optimization

This study deals with comparing the stiffness design of geometrically nonlinear structures and linear structures using topology optimization. Bi-directional Evolutionary Structures Optimization (BESO) is used for the design process. The geometrically nonlinear behavior of the structures is analyzed using a total Lagrangian finite element formulation and the equilibrium is achieved by Newton-Raphson iterative scheme. The topology optimization of linear and nonlinear modeling is performed. The sensitivity of the objective function is found with the adjoint method and the optimization problem is solved using BESO’s update method. Objective function of complementary work is evaluated. A special technique, the continuation method, is applied to eliminate the instability of nonlinear structure optimization. ANSYS APDL is also used to do FEA of optimal topology to verify the effectiveness of geometrically nonlinear modelling. The results show that differences in stiffness of structures optimized using linear and nonlinear modelling are generally small but it can be large in some cases, especially structure highly involving buckling behaviour.