Homologous topology optimization in large displacement and buckling problems

The paper deals with homologous topology optimization of structures undergo ing large deformations. The objective function is defined so that the load- displacement curve follows the prescribed trajectory, which shows a typical snap-through buckling. The geometrically non-linear behavior of the struct ures is modeled using the total-Lagrangian finite element formulation and t he equilibrium is found using a Newton-Raphson iterative scheme. In order t o escape from the singularity at critical points, the displacement control is utilized. The sensitivities of the objective functions are found with th e adjoint method and the optimization problem is solved using the sequentia l linear programming method. Two algorithms are proposed to obtain homologo us deformation. Several numerical examples are demonstrated to validate the present optimization method.