连续体结构的拓扑与形状集成优化算法

Optimization strategy for integration of topology and shape optimization of continuum structures

以连续体结构的拓扑与形状优化设计技术作为研究对象,将拓扑优化、形状优化、有限元分析和计算机辅助设计有机地集成在一起,构建了优化设计模型;研究了用B样条曲线曲面逼近拓扑优化后的结构体边界,进行边界光滑处理;在形状优化中,设计变量定义为B样条曲线或曲面的控制顶点的运动,建立了边界节点移动速度场计算方法和边界形状调整方法及模型更新理论,有效地控制节点的运动,给出了相应的算法和计算表达式,寻求较快的搜索方向,以合理速度分布尽快使形状变为最佳。设计实例的结果表明了本文所建立的模型的合理性和方法的有效性。

The topology and shape optimization design technology of continuous structure are adopted as research objective. This paper presents an integrated approach that supports the topology optimization, the shape optimizes, the finite element analysis and the computer-aided design. The optimized design models are constructed. That B-spline curve and curved surface are used to approach continuum structure boundary after topology optimization is researched, which is the way of smoothing boundary. The control point movements of the B-spline curves or surfaces are defined as design variables for shape opti- mization in shape optimization. The new algorithm of movement velocity field on boundary node is es- tablished, which includes the construction theory of boundary movement velocity field, calculation method of boundary movement velocity field and boundary shape adjustment, also model updating theory and boundary shape adjustment, also model updating theory. The design velocity field governs the movement of the structural material points due to design changes. The corresponding algorithm and the computation expression are set up in this paper. Seeking the quick search direction, the shape becomes best by the reasonable velocity distribution. The rationality of the model and the effectiveness of the method are illustrated by example.