Based On The Structure Of The Variable Density Method Dynamic Response Of The Topology Optimization

This thesis focuses on structural topology optimization using variable density method and its applications in dynamics response optimization. Form theoretical aspect, a new variable density method with gray-scale filter function is adopted compared with the classic variable density method. As applications, dynamic response topology optimization under harmonic foundation excitation and structural bandwidth frequency response optimization are investigated.Firstly, the fundamental theory of continuum topological optimization by variable density approach is discussed, where the SIMP density-stiffness interpolation scheme as well as the optimally criteria method based on Kuhn-Tucker optimal condition are mainly concerned. Numerical instabilities, such as checkboards, mesh dependencies and intermediate densities in optimization result are discussed. A structural mean density index is proposed to check the gray-scale element in final optimized structure and its convergence ability during iteration.Secondly, a new gray-scale filter function was added on traditional variable density approach for topology optimization, in order to solve the presence of gray-scale material in optimization result and low convergence efficiency during optimization procedure. Based on the properties of filter function, two proper gray-scale filter functions were adopted. Illustrated examples are presented both for verification and application for the filter method. The newly proposed gray-scale filter function method takes effect on enhancing the 0-1 convergence of the optimization result and decreasing iteration number caused by low convergence efficiency of gray elements.Thirdly, structural dynamic response optimization under foundation harmonic excitation is investigated. First, the optimization model is established with an aim for minimization concerned point's dynamic response under global volume constraint. Based on the optimization model, sensitivity of aim function is derived then optimized by optimality criteria method. In order to improve the low convergence ability of gray density variables, a gray variable filter method is adapted in this paper. Illustrated examples are presented both for verification and application for the dynamic response optimization and the effect of new gray variable filter method.Finally, a structural dynamics response optimization under bandwidth frequency excitation is considered. A differentiable q-norm form of response function's peak value is introduced according to properties of frequency response function. This equivalent aim function can be used in multiple-bandwidth situation. Sensitivities of equivalent aim function then can be derived from structure's eigen-sensitivity. Besides, frequency constraints were introduced for prohibiting clustered or repeated frequencies during optimization. Illustrated examples of truss sizing and shape optimization and continuum topology optimization are presented for verification and application for proposed method.