This study deals with 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 modelled 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 modelling are implemented. The sensitivity of the objective function is found with the adjoint method and the optimization problem is solved using both the Method of Moving Asymptotes (MMA) and BESO’s update methods. Objective function of complementary work is evaluated. Special technique called continuation method is applied to solve the instability of nonlinear structure optimization. ANSYS APDL is also used to perform finite element analysis (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 they can be large in some cases, especially for structures involving buckling behavior.

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