弹性力学问题的虚边界元－最小二乘法及误差评估

本文从［１］提出的虚边界原理出发,采用最小二乘法建立满足弹性力学问题边界条件的边界积分方程,再用线性虚边界元将其离散化。然后详细地研究了这些离散化的边界积分方程的解折特性。文中引用了误差分析的拉依达（ｐａИＴａ）准则,用来衡量解的误差水平,取得了理想的效果。编制了微机程序,程序中采用高斯积分格式,并考虑了虚,实边界对称条件的具体处理。本文方法不仅可以成功地处理边界条件连续的情况,而且对边界条件不连续的情况也能得出满意的结果。数值算例表明,程序可靠,虚边界变动时算法稳定,具有较高的处理精度。

A VIRTUAL BOUNDARY ELEMENT-LEAST SQUARE METHOD FOR SOLVING PROBLEMS OF ELASTICITY AND ERROR EVALUATION

Based on the authors earlier work entitled "A virtual boundary elementcollocation method for solvinhg problems of elasticity" published in the journal of Computational Structural Mechanics and its Applications, 8(1), 1991, in this paper the least square method is used to formulate the boundary integral equations satisfying the boundary conditons of the problem of elasticity and these integral equations are discretized by linear virtual boundary element. And then the analytical characteristics of these equations are studied. The Raita's (pa Ta) criterion of error analysis is introduced for judgying the level of solution's error and an ideal effect is obtained. A VBELSM microcomputer programm is coded in which the Gaussion integral scheme is adopted and the symmetric conditions are considered to simplify calculation. The method can treat not only the smooth boundary but also the rough ones. The numerical examples show that this method has higher accuracy, the computer programm is reable and the algorithm is stable when the virtual boundary is selected suitably.