边界元法中的改进等参变换

The Improved Isoparametric Transformation in BEM

首先考察三维边界元法中八结点等参单元边中结点的敏感性,指出对于常规等参变换计算,边中结点同有限元计算情形一样,仍必须遵守位于相邻角点间距离的三分之一内的建议,且限制应更严格,才能保证计算的有效性.其次,将改进等参变换引入到边界元法,并解决了相应的奇异积分处理等问题,提出了一个比常规等参变换时更加一般的坐标变换关系式.最后,对于立方块受单向拉伸和纯弯曲两种情况作了计算,结果表明,在边界元法中,改进等参变换的引入,使得计算具有更大的适应性.

The midside node seasritivity of eighty-node isoparametric element in 3-D BEM is investigated. The paper points out that the suggestion, based upon which the midsize nodes should be located in the 'middle third' of distance between the adjacent corners, should be followed even more strictly for the conventional isoparametric transformation (CIT) in BEM as that in FEM. A new coordinate transformation relation has been, put forward to solve the singular integral problem. The computation is carried to two cases:a cubic body subjected to tensile stress and to pure bending. The numerical results show that the improved isoparametric transformation(IIT) is easier and more flexible to practice