多种参数对自由曲面形态优化的影响研究

自由曲面结构的形态优化通常是在给定材料参数和曲面厚度的情况下进行的，因此有必要对材料参数和曲面厚度取值对曲面形态优化的影响进行研究。基于梯度法，采用非均匀有理B样条（NURBS）技术生成自由曲面，以最小应变能为优化目标，对自由曲面进行形态优化，并研究了材料弹性模量、泊松比和曲面厚度对优化结果的影响。研究表明，弹性模量的取值对曲面的优化结果几乎没有影响，而材料泊松比和曲面厚度的取值对曲面形态优化均有影响，其中曲面厚度的影响最为显著。

Effects of several parameters on optimal shapes of free-form shells

Shape optimization of free-form shell is usually performed with given material parameters and shell thickness.Thus，it is necessary to study the effects of material parameters and shell thickness on the optimal shape.In this paper，a non-uniform rational B-spline（NURBS） technique was employed to generate free-form shell.The objective function was to minimize the total strain energy of structures.The optimization procedure was based on the gradient method to study the effects of Young′s modulus，Poisson′s ratio and shell thickness on optimal shapes.The study showed that the magnitude of Young′s modulus almost had no effect on optimal shapes.However，the Poisson′s ratio and the thickness had influence on optimal shape，and the influence of the thickness was the most significant.