一个对角化部分杂交元柔度矩阵θ的方法

A Method for Diagonalizing Flexural Matrix θ of Partial Hybrid Finite Element

给出了利用 H阵对角化建立部分杂交元的方法 .通过构造部分杂交元的应力模式 Hilbert空间 ,详细讨论了应力模式正交化方法 ,并且论证了正交化前后的应力模式可以形成相同的部分杂交元 .由于正交应力模式使 H矩阵成为对角矩阵 ,因此可以完全避免繁杂的 H矩阵求逆运算 ,从而从根本上改进了部分杂交元方法的计算效率 .特别对于假设应力模式个数比较多 ,从而 H矩阵阶数比较大的情况 ,该方法更能体现其优越性 .

The paper presents a method for constructing partial hybrid finite element by diagonalization of matrix H. The orthogonalization of stress modes in Hilbert space of stress modes is discussed in detail. It is shown that the orthogonalized stress modes and original stress modes form the same partial hybrid finite element. Orthogonalized stress modes make matrix H diagonal, so that multifarious calculation of solving H -1 is avoided. Thus the computational efficiency of partial hybrid finite element is improved. Especially, when the more the stress modes, the higher the rank of H, and the more superior the methods are. Examples given in the paper show that the method is efficient.