This study deals with the stiffness design of geometrically nonlinear structures using
topology optimization. Bi-directional Evolutionary Structures Optimization (BESO) is
employed to implement the design process. The geometrically nonlinear behavior of the
structures are modeled using a total Lagrangian finite element formulation and the
equilibrium is found using a Newton-Raphson iterative scheme. The topology optimization
of linear and nonlinear modeling are implemented. 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 called the continuation method is applied to solve 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 is generally small but it can be large in some cases, especially structure highly involving buckling behaviour.