Optimal Design Of Structures For Macro Topology And Micro Configuration Of Vibration And Wave Propagation

The main purposes of structure optimization are that specified performances can be optimum and economical materials usage when satisfied the conditions of stiffness, strength and stability. An improved structure topology enhances the structure performance or decreases the weight of it, and this leads to more benefit. Topology optimization on vibration and wave propagation problems has been widely studied. In comparison with well-known static compliance minimization, various objective functions are proposed in literature to minimize the response of vibrating structures, such as power flow, sound radiation, vibration transmission, and dynamic compliances, etc. Even for the dynamic compliance, different definitions are found in literatures, which have quite different formulations and great influences on the optimization results. Some more appropriate optimization models will be proposed based on the comparison results. Furthermore, it has been found that the minimization of vibration transmission is also related with the bandgap design of wave propagation. The optimal design of the band gap can be realized by different optimization models, and the results of the optimization model in different literatures are all different.The aim of this paper is to provide a comparison of these different objective functions for design optimization of vibrating and wave propagation problems. Some more appropriate optimization models will be proposed based on the comparison results. The validity and efficiency of the objective functions are discussed for realizing the minimization of vibration response and transmission. The main contents of this thesis include1. The theory of structure optimization and dynamics is summarized and summarized. The model of structural topology optimization of vibrating and wave propagation problems is analyzed emphatically. In this paper, the mathematical model of structural optimization is established by using variable density method and the optimal solution of the model is obtained by the method of moving asymptotes.2. Provide a comparison of these different objective functions for design optimization of vibrating. Firstly, the comparison of physical meanings are given via the analytical derivation of each objective functions in both single and double degree of freedom system. Some new models for maximizing the dissipated power, minimizing the acceleration of structure and minimizing the product of dynamic compliance and volume is proposed respectively.3. The bandgap design may be realized by the maximization of the frequency gap of the free vibration of a structure, maximization of the frequency gap of wave propagation in a periodic microstructure, or maximization of the wave attenuation in a structure. The aim of this paper is to provide a comparison of these different objective functions for design optimization of wave propagation problems.4. Plane and plate structures are optimized using different optimization formulations in numerical examples for given excitation frequencies. The results are obtained by the finite element method and gradient based optimization using analytical sensitivity analysis. The optimized topologies, the iteration histories, and vibration response of the optimized structures are presented. The influence of excitation frequencies, the eigenfrequencies of the structure.