Structural Topology Optimization Of Multi-phase Materials Based On Parameterized Level-set Method

In the stage of structural conceptual design,the structural topology optimization is mainly to find the optimal distribution of materials in the design domain.As one of the popular methods of topology optimization research,the level set method has good smoothness and high efficiency.In the process of structural topology optimization,the conventional level set method updates the level set equation by solving the partial differential equation(PDE),and this step does not guarantee the efficiency and stability of the optimization results.Based on the level set method,this paper puts forward a more efficient and stable parametric level set method,and verifies the feasibility of the algorithm from three aspects: optimized rate,optimized efficiency and stability.Firstly,the radial basis function(RBF)is used to interpolate the level set equations,therefore,the Hamilton-Jacobi partial differential equation(PDE)are transformed into ordinary differential equations(ODEs),which avoids the steps such as re-initialization used in solving PDE and enhance numerical stability of solution.This interpolation is to transform the design variables of the optimization process into the expansion coefficients of the RBFs.By calculating the ODEs,the values of the extension coefficient are updated,and then the level set equation is updated.The examples show that the interpolation model is beneficial to the numerical stability in the optimization process.Secondly,in the case of ensuring the same optimized effectiveness,the compactly supported radial basis function(CS-RBF)with less computation is used to instead of the global radial basis function(GS-RBF),and the method of moving asymptote(MMA)based on gradient is also used to update the design variables.In the process of design variables updating,this paper present a new updating algorithms with a shape constraint factor,and a numerical example is used to analyze the size selection range of constraint factor.Then the algorithm is applied to the single-phase material structural topology optimization.Experiments show that the algorithm can greatly improve the optimized rate,optimized efficiency and stability.Finally,this paper extends the improved parametric level set method to multi-phase materials structural topology optimization,and the recursive model is used to establish the mathematical model of multi-phase material structural topology optimization,and the sensitivity of the objective function is calculated.And then,the method is applied to the topology optimization of two-phase materials and three-phase materials respectively.The examples show that the proposed algorithm perform well in multi-phase material structural topology optimization.