【摘要】 本文对柯希霍夫薄板弯曲问题的边界积分方程直接法的理论与具体实施进行了探讨。在理论方面,文中首先建立了与薄板弯曲问题对应的双调和方程的位势理论,然后由广义瑞雷——格林等式出发,利用位势理论导出基本积分方程。在具体实施方面,本文对采用解析法计算边界积分、区域积分向边界的转化、“二阶奇异积分”的解析算法、角点集中力和自由角点的处理、对称性的利用等问题进行了探讨,提出了较为有效的解决方法,并获得了令人满意的计算结果。文章最后对解析方案与数值积分方案进行了比较,并得出了相应的结论。更多还原

【Abstract】 This paper deals with the theory and application of the direct boundary integral equation-boundary element method to Kirchhoff thin plate bending problems. The potential theory corresponding to biharmonic equation is first established and from this theory is derived the basic integral equation from the generalized Rayleigh-Green identity. Some particular problems are explored: the evaluation of boundary integral by analytical formulations, the transformation of the domain integral, the computation of integral with twoorder singularity, the proper treatment of corner forces and free corners, the utilization of the symmetry of the plate, etc. The method presented here is effective, and numerical results satisfactory. Finally, a comparison between schemes of analytical integral and numerical integral is made, and a relevant conclusion is reached更多还原