Study On Topology Optimization Methods Of Continuum Structure

An improved structure topology could enhance the structure performance or decrease weight of it, and bring about direct economic benefits, so topology optimization of continuum structures have been the hot research work in the world in recent years, which is regarded as one of the most challenging research topics. Nowadays topology optimization is explored because of its complicity in models and algorithms. This paper focused on the study of topological basic theories and discussed the application in the field of bridges modeling.In this paper, a mathematical model for topology optimization of continuum structures based on SIMP was established. The objective function of the problem was the minimum compliance of the structure, and the constraint condition was the material volume. After that, an optimality criteria for topology optimization was derived. We also analyzed the numerical instabilities, such as porous, checkerboard ,which existed in topology optimization. Finally, topology optimization designs for short cantilever beams, Michell structures and MBB were implemented by MATLAB programes. Satisfactory results were obtained.This paper have also studied the level set method. An mathematical model based on level set description function was proposed. A finite element method and optimality criteria were incorporated to solve the problem. The level set description function was approximated in terms of its values on the nodals. Then a relationship between the element stiffness matrix and the values of the level set description function on its four nodes was established. The computational efforts could be saved because we needn't have to solve the complicated Hamilton-Jacobi equation, which was used in traditional level set method. And on the process of regularizing the Heaviside function, not only the shape derivative but also the topological derivative of the optimal design was considered. Convergence velocity has been accelerated. Meanwhile smooth structural boundaries could be obtained by the approach without zigzag boundaries existed in SIMP, and the numerical instabilities could be eliminated naturally. Numerical experiments demonstrate that the approach was an efficient and robust algorithm.Finally, we apply the topology optimization method to the field of bridges.we discovered that the topology optimization results of arch bridges, bridge tower and bridge anchor were similar to the actual structures. It demonstrates that the topology optimization method based on SIMP is feasible and effective in the fileld of bridges modelling. It also indicates that the main idea and the basic principle in the paper are practical in the actual project.