基于Bézier曲面造型的触模和摩擦条件施加算法

Algorithm of Touching Mould and the Application of Boundary Friction Based on the Formation of Bézier Surface

介绍了利用双三次 Bézier曲面块对模具表面进行拟合的方法 ,对模具表面和变形体表面采用 Bézier曲面进行了统一的描述 .提出了在刚塑性有限元模拟中相应的变形体边界自由节点与模具表面的接触算法以及摩擦边界条件的施加算法 .Bézier曲面的应用使有限元模拟系统中的模具描述更接近于实际模具造型 .模具表面与变形体表面的统一描述 ,简化了触模算法以及摩擦条件施加算法的数学计算 .而触模算法以及摩擦条件施加算法的实现 ,使拟合的曲面能够在数值模拟软件中直接应用而不需要再次转化 ,从而保证了模拟的精度 .

The mould's surface fitted with the bi cubic Bézier surface patches was introduced in the numerical simulation system. The mould's surface and the deformed body's surface are described in the form of Bézier surfaces. Correspondingly the algorithm of the contacts between the free nodes on the deformed body's boundary and the mould surface was given. Furthermore, the algorithm of the application of the boundary friction condition in the rigid plastic FE simulation was deduced. The unified description of the mould's surface and the deformed body's surface simplifies the calculation in the algorithm of the contact between the free nodes on the deformed body's boundary and the mould surface and also in the algorithm of the application of the boundary friction condition. And the implementation of these two algorithms makes the fitted curved faces directly used in the numerical simulation software without transferring once more and guarantees the precision of the simulation.