一种有效的边界元/有限元混合法迭代算法及其在回转体自由扭振分析中的应用*

本文给出一种新的边界元/有限元混合法迭代算法,基本做法是将近似的固有频率值代入自由振动问题的基本解,按一般混合法列式,通过迭代逐步修正近似解的值.这种算法避开了一般边界元法需要求解非代数特征值问题的困难,同时数值结果的精度基本上不依赖于区域内单元网格的疏密程度,这都给实际计算带来很多方便.应用于回转体自由扭振问题的分析,得到令人满意的数值结果.

An Efficient Iteration Algorithm of Mixed Boundary/Finite Element Method and Application to Free Torsional Vibration Analysis of Bodies of Revolution

In this paper, the general formulation of a new proposed iteration algorithm of mixed BEM/FEM for eigenvalue problems of elastodynamics is described. Approximate fundamental solutions of elastodynamics are adopted in the normal mixed BEM/FEM equations. The accuracy of solutions is progressively improved by the iteration procedure. Not only could the awkwardness of non-algebraic eigenvalue equations be avoided but also the accuracy of numerical solutions is almost independent of the interior meshing. All these give many advantages in numerical calculation. The algorithm is applied to free torsional vibration analysis of bodies of revolution. A few cases are studied. All of the numerical results are very good.