有限元应力场可视化的一种新方法

New method for visualization of FEM stress fields

提出一种画二维和三维等参单元彩色云图的新方法。首先,根据单元覆盖象素的数量在正方形母元上均匀布置足够数量的点。第二,用单元的结点坐标、结点应力以及等参插值函数,插值计算这些点的总体坐标及应力。第三,根据预先设立的颜色与应力之间的函数关系,求出每个点对应的象素的颜色。最后,逐个把单元覆盖的象素设置为求出的颜色。与消隐技术以及画家算法结合起来,这种方法可以清晰画出三维应力场的云图。实例表明,本文方法简单、准确、易于实现。

A method for the stress representation by colored patterns on two-dimensional or three-dimensional isoparametric surfaces is presented. Firstly, enough points are arranged evenly on a square parent element according to the number of pixels spanned by an element on the screen. Secondly, the global coordinates and stress values of the points are calculated by using the standard isoparametric interpolations, the node coordinates and the known node stresses. Thirdly, the color values of the corresponding pixels of points are computed based on the present function relation between color and stress. Lastly, the pixels are set to the calculated colors one by one. In 3D case, the method is combined with hidden surface removal techniques and painter's algorithm to easily generate perceptible pictures. Some examples demonstrate that the method is simple, efficient, accurate and easily implemented.