Topology Optimization Of Continuum Structure Considering Geometrical Nonlinearity

As the rapid development of computer technology and refinement of structural optimization theory, the structural topology optimization techniques have been widely used in more and more fields while the industrial manufacturing techniques are innovating. Since the practical engineering structures may undergo large deformations, structural geometrical nonlinearity is an important aspect for assessing a structural design, yet there are still some major difficulties when the geometrically nonlinear effect is considered in topology optimization of continuum structures. This dissertation makes an investigation on the topological optimization design of geometrically nonlinear structures. The main contents are listed as follows.Firstly, the topology optimization of continuum structure for minimum structural compliance with limited volume is studied. The fundamental theory and models of topology optimization are introduced; the SIMP density-stiffness interpolation schemes and numerical difficulties in topology optimization for geometrically nonlinear structure, such as unstable elements, are also discussed. Numerical examples reveal the negative effects of the low-density region in topology optimization considering geometrical nonlinearity.Secondly, numerical instability in the finite element simulations can often be observed, due to excessive distortion in low-density regions. An interpolation schemes for fictitious domain and topology optimization approaches with structures undergoing large displacements are introduced in order to stabilize the numerical simulations. Numerical results show that the proposed method alleviates the problems in the low-density regions, and for the simulated cases, the appropriate values of the threshold variable and the sharpness parameter are discussed.Thirdly, to alleviate the numerical instability of topology optimization when using the SIMP density-stiffness interpolation schemes, the mathematical model of topology optimization based on the hybrid stress elements is established, in which the nodal densities are used as design variables. The method proposed in the paper was applied to some numerical examples, and the results show that the topologies obtained by this approach are reasonable with clear topology configuration without using any filtering schemes.Finally, all the research work is summarized, and the prospect of the future work is presented.