全特解场边界元方法及其在计算振动体声辐射中的应用

ALL PARTICULAR SOLUTIONS BOUNDARY ELEMENT METHOD AND ITS APPLICATION TO CALCULATING SOUND RADIATION FROM VIBRATING OBJECTS

文章提出边界元全特解场法原理，并给出了关于线弹性静力学和声辐射问题的有关计算公式．该方法通过一系列给定的特解场来计算边界积分方程的系数矩阵，不仅可以避免计算奇异积分，也不需要插值和数值求积．计算量大幅度减少，而且对边界角点的处理也很方便．全特解场方法不仅可以求出边界未知量，而且可以方便地计算出包括边界点和近边界点在内的任意点的位移和应力．文中给出了关于弹性静力学和声辐射问题的两个算例，计例结果表明：本文提出的方法计算量小、精度高、是求解偏微分方程边值问题的有效方法．

In this paper,the principle of all particular solutions boundary element method is developed,and the calculation formulas concenring linear elastic statics and sound radiation are given. By this method,the coefficient matrix of the boundary integratingequation can be calculated through a calculating singular integrals, and the numercial integration is not needed. The displacement and stress of an arbitrary point can also be obtained which is either on the bounbary or adjacent to the boundary. The example in this paper shows the method is less in calculation,higher in precision and very effective.