摘要:
本文系统地研究了具有对角线化的一致质量矩阵的协调动力有限元.前文[1],[2]中,作者研究了具有对角线化的一致质量矩阵的动力有限元,并用此处理弹塑性撞击问题,但这些有限元都是不协调的.本文对空间四面体有限元和轴对称的三角环有限元求得了既有对角线化的一致质量矩阵,又有协调性质的形函数.这种有限元既可以用来处理撞击等和时间过程有关的问题,也可以处理振动计算,包括线性和非线性问题.
Abstract:
In this paper, the compatible dynamic finite elements with diagonalized consistent mass matrix are studied. In previous papers[1,2], the author studied the dynamic finite elements with diagonalized consistent mass matrix, but all of them are incompatible elements. In this paper,the compatible form functions are obtained not only for the tetrahedron elements, but also for the triangular ring elements, with diagonalized consistent mass matrices. This kind of finite elements can be used for the treatment of impact problems, vibration problems, and problems involving time coordinates, including the linear and nonlinear equations.
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