形状优化中基于物理模拟的参数化方法

A New Approach to Parameterization Based on Physical Simulation for Shape Optimization

提出了一个同时改变多个控制点和权因子的ＮＵＲＢＳ曲线形状修改方法．该方法用物理方法对齐次坐标系中ＮＵＲＢＳ曲线的控制多边形进行运动模拟，运用有限元法求解模拟系统的振动模态，并将ＮＵＲＢＳ的控制点和权因子映射到模态坐标系，然后根据模态坐标控制ＮＵＲＢＳ的形状．在形状优化中，这种方法可以减少设计变量，防止边界形状奇异．

A new method is described which provides the shape modification of NURBS involving simultaneous alteration of control points and weights. The movement of the control polygon of NURBS in the homogeneous coordinate system is simulated by a physical frame structure, and the vibration modes of the physical system are calculated by finite element method. The control points and weights of NURBS are mapped into the mode coordinate system, and the shape of NURBS is to be controlled according to the mode coordinates. It is shown that by the present method, the number of design variables can be reduced and boundary shape singularity can be avoided during shape optimization.