Topology Optimization Of Continuum Structure Based On Improved Level Set Method

Structural optimization aim to find the best design scheme according to a certain goal on the premise of satisfying the structural design requirements,Compared with size and shape optimization,topological optimization has more degrees of freedom and larger design space,which can reconfigure the given material and generate new topological structure.Therefore,topology optimization has gradually become a research hotspot in the field of structural optimization.The level set topology optimization method,based on reaction diffusion equation,can realize the shape and topology optimization of the structure as well as avoid the numerical problems effectively,such as grid dependence which is likely to occur in traditional topology optimization methods.In this paper,the problems and applications of level set topology optimization method based on reaction-diffusion equation are researched.This paper mainly completed the following research works:Firstly,the theory of level set topology optimization method is deduced in detail,and related improvements are made on this basis.On the one hand,the Lagrange multiplier in the optimization process is adjusted by strain energy to control the volume fraction,which makes the iteration converge more stable,and then it effectively solves problems caused by the non convergence of volume constraints which result in the incorrect results in the process of three-dimensional structural topology optimization.On the other hand,two methods are proposed to improve the accuracy of solution by increasing the number of element nodes and nonconforming element method.The improved level set topology optimization method is used to research the axisymmetric and periodic problems,and the effectiveness of the method is verified by some examples.Secondly,Empirical distribution weight factor method for topology optimization of continuum structures under multiple load cases.A new performance index is proposed to measure the reliability of the final optimization results,and a dynamic weighting coefficient method is proposed to solve the disadvantage that the weighting factor can not be changed in the static weighting coefficient method,which improves the optimization efficiency and makes the optimization results more reasonable.The applied value of this method is verified by some examples.Finally,in order to realize the practical application of the level set topology optimization method,the improved level set topology optimization method is use for optimizing the structure of deck crane boom,and then the lightweight boom structure can be obtained.After analysis and calculation,the optimized boom satisfies all performance requirements.