关键词: B样条, 水平集方法, 拓扑优化, 形状导数, 形状优化

Abstract: The optimization result which is got by optimization algorithm aimed at continuum structure only reflect the saw-shaped boundary area owning best force-passed path. Based on this, topology optimization, shape optimization, finite element analysis and computer aided geometric design are integrated effectively. A new evolutionary integrated optimization algorithm of topology and shape for continuum structure is presented based on level set method of implicit boundary representation. The shape derivative analysis and Lagrangian multipliers are applied to sensitivity analysis of optimization to dominate the dynamic evolvement for the embedded level set function and further to control the movement of structural boundary with the flexibility of handing structure changes. B-spline curve and curved surface are used to approach continuum structure boundary after topology optimization, which transform the concept solution that reflects force passing path got by the above optimization process to the parametrical precision solution. In the shape optimization, the control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization, and then the corresponding calculation algorithm of boundary movement velocity field and the method of boundary shape adjustment for the boundary node are set up. Finding the fast look for orientation, the shape turns into best by the rational velocity assign. The effectiveness of the method is illustrated by example.

Key words: B-spline, Level set method, Shape derivative, Shape optimization, Topology optimization