基于水平集方法的连续体结构拓扑优化方法研究

The Research for Structural Topology Optimization Based on the Level Set Method

采用水平集方法描述结构的拓扑及其变化,使用紧支径向基函数对计算区域的水平集进行插值以得到参数化的水平集方法。针对给定体积约束下结构最小柔度的拓扑优化问题,推导了目标函数对插值系数的灵敏度及拓扑优化的迭代格式,数值计算表明,使用该方法进行结构拓扑优化得到的结果边界形状光滑连续且计算稳定性较好。

The levd set method was adopted to describing the structural topology and its change, and the compactly supported radial basis function was introduced to getting the parametric levd set method. Considering to the topology optimization for structural mean compliance constrained by the predefined volume, the parametric sensitivities of objective function with respect to the coefficients of RBF were derived and the iteration formulation for optimization was proposed. According to numerical results, it suggests that the topology optimization method using this parametric level set method can get smooth boundary and be robust in the numerical calculating process.