| Topology optimization of continuum structures has been applied to the wide range of design problems with the assumption of small deformation. But in some applications such as energy absorbing structures or compliant mechanisms, the assumption is not valid any more due to large deformation in their operational conditions. Geometrical and material nonlinearities resulted from large deformation should be simultaneously implemented in optimization process. In this thesis, design sensitivity of general displacement functional is derived using the adjoint method for structures under large deformation and topology optimization is applied to the design of nonlinear structures. Design problem of negative Poisson's ratio materials is formulated and is solved using linear and geometrical nonlinear analysis. Then compliant mechanism is designed using materially nonlinear analysis to maximize Mechanical Advantage. Finally, design problem for energy absorbing structures is formulated using three phase material model to accommodate two conflict design needs of engineering structures and both geometrical and material nonlinearities are considered during optimization process. |
