Topological Optimization Of Continuum Structures And Heat Radiation Structures

Topological optimization, which is an innovative design method, can synchronously optimize the topology, shape and size of the objects to be designed. The method of topological optimization is one of the most challenging methods in the designs of continuum structures, compliant mechanisms, composite materials and heat radiation structures. In this thesis, theories and numerical experiments for topological optimization of continuum structures and heat radiation structures are studied using Solid Isotropic Material with Penalization (SIMP) and Level Set Method (LSM).Basic theories of SIMP and Optimality Criteria (OC) are introduced. Application models of SIMP in topological optimization of continuum structures and heat radiation structures are discussed. Computer programs for topological optimization of continuum structures and heat radiation structures are developed in MATLAB. Furthermore, numerical experiments for a series of examples are implemented.Numerical algorithms of Hamilton-Jacobi equation and LSM are studied. The processes of signed distance function initialization, velocity extension and interface motion are demonstrated. Optimization model of continuum structures is analyzed combining LSM and linear elasticity mechanics. Optimization model of heat radiation structures is analyzed combining LSM and heat conduction analysis. Key steps of continuum structures optimization, such as Heaviside and Dirac delta functions discretization, up-wind computation schemes of level set function, re-initialization of level set function are implemented. Computer programs for topological optimization of continuum structures are developed in MATLAB and FEMLAB using LSM. Numerical experiments for representative examples, such as cantilever beam, MBB beam and Michell structure are implemented.Finally, the optimization results of continuum structures using SIMP and LSM are compared and analyzed. The advantages and disadvantages of these two methods are discussed.