Research Of Continuum Structure Topology Optimization Based On MPM

As a conceptual design of structure, topology optimization has been becoming one of hot research object in structure optimization. Despite the large number of scholars has been thoroughly studied on the topology optimization method, but it is still get topology optimization results by"delete"nodes. Based on Element-free Galerkin method and through optimization criterion to get node density and structure density gradient operator, a new topology optimization method—moving particle method (MPM) is used for solving two-dimensional continuum structure problems in this paper. The main courses are summarized as follows:1. The numerical instabilities exist in most topology optimization method is because there get topology optimization results by"delete"elements or nodes. The proposal which by"move"nodes to get topology optimization results was proposed to solve these problems.2. A mathematical model for continuum structure topology optimization is established based on MPM by using solid isotropic material with penalization method and variable density method, taking nodal density and nodal location as design variables and selecting compliance as objective function. The update scheme for design variables is deduced by establish density gradient operator and particle movement governing equation. The algorithm is implemented with FORTRAN, and numerical results show that MPM is feasible and superiority.3. On the basis of the analysis the phenomenon mobile step length have great influence on topology optimization results, the best mobile step length which costs least iteration steps to get better results can be found.4. According to the topology optimization results, singular stiffness matrix and very long computing time is discussed, and two improved algorithms are proposed to solve these problems. The calculation results show that to a certain extent particle accumulation can be eliminated with the center mobile method, but the computing time is not reduced. In variable mobile step length and regional insertion point method can effectively eliminate the particle accumulation problems, and requires only half the computing time. So the second improved algorithm has better effect.Moving particle method is successfully used in topology optimization in this paper, and the improved method can effectively eliminate the particle accumulation and long computing time problems. The study makes a good use of Element-free method and pioneers a new way for topology optimization method.