基于参数化水平集法的热传导结构拓扑优化

PARAMETRIC LEVEL SET METHOD-BASED TOPOLOGY OPTIMIZATION OF HEAT CONDUCTION STRUCTURES

针对利用传统水平集法(level set method,LSM)进行热传导结构拓扑优化计算过程复杂及计算效率低等问题,本文将参数化水平集法(parametric level set method,PLSM)引入热传导结构拓扑优化中,通过紧支径向基函数(compactly supported-radial basis functions,CS-RBFs)插值初始的水平集函数,建立了以CS-RBFs的插值系数为设计变量,结构的散热弱度为目标函数以及材料体积为约束的热传导结构拓扑优化模型,再通过移动渐近线法(method of moving asymptotes,MMA)更新CS-RBFs的插值系数,结构的优化过程转化为插值系数的更新过程,由此得到最优拓扑。数值算例结果表明利用参数化水平集法(PLSM)与传统的水平集法(LSM)得到的拓扑结果基本一致,验证了该法的可行性和有效性。

With the problems of complicated calculation process and lower computational efficiency in topology optimization using the traditional level set method（LSM） of heat conduction structures,parametric level set method（PLSM） is introduced into topology optimization for heat conduction structures.The compactly supported radial basis functions（CS-RBFs） are used to interpolate the initial level set function.The interpolation coefficients of CS-RBFs are proposed as the design variables,dissipation of heat transport potential capacity is adopted as the objective function,and the volume of material is used as the constraint.The topology optimization model for heat conduction structures is thus built.Because the method of moving asymptotes（MMA） is used to update the interpolation coefficients of CS-RBFs,the process of topology optimization for structures is transformed into that of updating interpolation coefficients and the optimal topology is finally obtained.Numerical examples show that the optimal results using PLSM are essentially in agreement with those of LSM optimal results,which illustrates the feasibility and validity of the proposed method.