Research And Application On Topology Optimization Methods Of Continuum Structure Based On Kuhn-Tucker Optimization Criteria

As industrial technology-especially aerospace technology-evolves, a lighter and steadilyload-borne structure becomes the pursuit of structural design. A emerging and hot topic instructural design is topology optimization technique, which is to reasonably find a optimaldesign of a structure under a set of loads. In this thesis, basic theories underlying topologyoptimization and achievements in this area are introduced. Furthermore, the structural designconcerning the continuum structure is given special treatments in this article.This work firstly introduces the knowledge about structural design. And modelingmethods, solving algorithm, and numerical stability treatment are thoroughly explained.The basic theories of finite element method is exhibited, deriving the continuum’s elementstiffness matrix which comprises4nodes and the coefficients related. This is theprerequisite of pre-treatment of topology optimization.The derivation of algorithm basedon SIMP model and Kuhn-Tucker optimization criteria and iterative process are illustrated.And analysis of convergence is made and iterative model is provided.Then the numericalinstability phenomenon arising in the process of solving topology optimization problem ofcontinuum structure and its cause are analysed. The solution to the appearance of Meshdependency and checkboards is also given in detail.Finally, algorithm of topology optimization is applied to the construction of bridge.Solving model is built and the derivative of the model is obtained by using matlab codes.And the effects of choosing different penalty powers and sens itive filtering radii inmathematical model on results of optimization are discussed.