The Research Of Multiple Materials Structure Topology Optimization Problems Based On The Level Set Method

The purpose of structural optimization is to find the best power transmission path when considering the reasonable layout,manufacturability and other restraining factors,which also can reduce the structure weight and cost.Generally,the methods of structural optimization can be divided into size optimization,shape optimization and topology optimization.But comparing with other two methods,topology optimization need construct the optimization algorithm to find the optimal shape of structure,which is the most challenging method in structural optimization design.Besides the topological optimization based on the level set method can simultaneously realize shape and topological optimization,which can effectively avoid the phenomenon of checkerboard etc.This paper does related improvement and extended research which based on the reaction diffusion equations solving the level set method for topology optimization.Firstly,this paper deduces the basic theory of level set method,which is regarded as the basis of related improvement.On the one hand,considering the defects of this method can't simultaneously satisfy the structural volume stability constraints and objective function convergence conditions in solving some models,this paper propose a bi-direction level set method,which improve the basic theory of this method.On the other hand,aimed at the phenomenon of dentate boundary after optimization,this paper proposes mesh refinement improved method of element nodes,which can get relatively smooth boundary and be easy to manufactory.Secondary,this paper introduce the element stress and nodal displacement into the level set method in which we construct arithmetic based on those constrains of element stress and nodal displacement to drive the structural volume.What's more,this method proposed above not only can accelerate the optimization progress in the early period of the optimization but also can enhance the accuracy of numerical calculation,ensure the reliability and accuracy of the optimization structures and enlarge the usable range of this method when is about to satisfy the constraint condition.Finally,this paper applies level set method into the topological optimization of multiple materials structure and constructs the solving model which regards the element stress as themain constrain and the configuration stability as the condition of convergence.Moreover,this method not only can get the Multi-material optimization that put the sum of multiple materials structure stiffness as the objective but also can get the model that conform to the processing technology when simultaneously satisfy constrain condition.We comparing the numerical examples and the calculation results by ANSYS,verify the validity of this method.Therefore,those methods mentioned above make the structural topology optimization of level set method has stronger practical significance.