This dissertation focuses on improving the behavior of plate structures under out-of plane static and transient dynamic loadings and also in-plane loads in post-buckling regimes. Both linear as and geometrical nonlinear behaviors are of concern in this thesis. A topology optimization approach is employed to achieve an optimal configuration for a plate-like structure. The finite element model is constructed based on both Poisson-Kirchhoff and Mindlin-Reier hypotheses. To consider nonlinear behavior, Green-Lagrangian strain tensor is utilized through a von-Karman type of formulation. The optimization problems are solved using the method of moving asymptotes (MMA). For static problems, the sensitivity analysis is performed with the aid of a suitable adjoint method. Also, in transient dynamic regimes, a new and consistent adjoint method has been proposed for the first time in this thesis. Several forms of design variables are considered for obtaining the optimal plate configuration, among them are; the thickness of the plate and the material density, based on nodal or element values. To overcome the numerical instabilities, e.g. mesh dependent and checkerboard patterns, a new sequential strategy has been proposed for refining the discretized field of design variables. Several examples followed by discussion are given to demonstrate the performance of the method in comparison with a well-known filtering technique, available in the literature, for the sensitivities values.
