Improvement And Extended Application Of Level Set Topology Optimization Metho

The structural topology optimization design method can effectively adjust the distribution and combination of materials to achieve optimal structural performance under specific boundary conditions and constraints.Among them,level set method is one of the most popular topology optimization methods,and its optimization results are both simple and stable.The traditional level set topology optimization method solves the first-order Hamilton-Jacobi partial differential equation by introducing a virtual time variable t to achieve the goal of structural boundary evolution.However,in order to solve this equation,it is necessary to select appropriate upwind schemes and re-initialization steps,which may affect the actual effect of the level set method.This paper proposes a more efficient and stable improved parameterized level set method,and verifies the stability and efficiency of the algorithm through 2D and 3D examples.Although radial basis functions can be introduced to parameterize the level set method to improve optimization efficiency,there is still a considerable gap in optimization speed and stability compared with the explicit expression of density penalty method,because the level set method uses implicit boundary description method.This paper proposes a SIMP post-processing method based on the level set method,which integrates the optimization stability and efficiency of the SIMP method,the clarity and smoothness of the optimization results of the level set method.The main work and innovations of this paper are as follows:(1)This paper uses the radial basis function to parameterize and interpolate the level-set equation,and converts the first-order Hamilton-Jacobi partial differential equation into the ordinary differential equation to avoid the numerical problems that may occur during the solving process.However,since the design variables of the parameterized level-set are bounded,the globally supported radial basis function restricts the application range of the parameterized level-set in practical applications.Therefore,this paper chooses tightly supported radial basis functions with a wider application range to parameterize the level-set function.(2)For the selection of solving algorithms,the optimization criterion method and ordinary differential method are not suitable for complex problems with multiple constraint conditions.However,in actual engineering,problems often involve complex constraint conditions.Therefore,to solve this problem,this paper chooses the moving asymptotic line method based on the first-order Taylor expansion to solve the level-set equation and introduces an intelligent sensitivity factor to improve the stability and computational efficiency of the algorithm.(3)This paper proposes a SIMP post-processing method based on the level-set method,which integrates the advantages of the level-set method and the SIMP method.The method uses the mathematical model of the SIMP method combined with finite element method for mechanical analysis and selects optimization criterion method for equation solving.The method uses sensitivity filtering and level-set method for topology result post-processing,successfully solving numerical problems such as local extreme values and checkerboard mesh patterns,as well as graphic problems such as grayscale elements and boundary sawtooth.