弹性理论几类导数边界积分方程之间的变换关系

导数场边界积分方程通常难以应用，因为存在着超奇异主值积分的计算障碍。弹性理论中有几类不同的位移导数边界积分方程，本文采用算子δij和∈ij(排列张量)作用于这些导数边界积分方程，做一系列变换，原有的超奇异积分被正则化为强奇异积分获解。从而建立了这些位移导数边界积分方程之间的转换关系，它们均可以归结为自然边界积分方程。自然边界积分方程仅存在容易计算的Cauchy主值积分。自然边界积分方程分析可直接获得边界应力和位移导数。     

ISOTROPICALIZED SPLINE INTEGRAL EQUATION METHOD FOR THE ANALYSIS OF ANISOTROPIC PLATES

In the view of Reissner’s and Kirchhoff’s theories,respectively,we formulate theisotropicalized governing equations for the anisotropic plates,and give the proof of theequivalence relation between these two plate-models for the simply-supported rectangularorthotropic plates.The well-known fundamental solutions of the isotropic plates are utlizedfor the spline integral equation analysis of anisotropic plates.Even with sparse meshes thesatisfactory results can be obtained.The analysis of plates on two-parameter elasticfoundation is so simple as the common case that only a few terms should be added to theformulas of fictitious loads.     

Reissner型板样条边界元

本文用Hormander法导出Reissner型板含有修正Bessel函数的基本解,边界量采用B样条基插值,即使结点布置很稀也能达到良好的效果,而且成果不受边界效应干扰,计算稳定,还可独立算求板上任一点任一向的位移和内力,对轴对称问题则可给出精确解答。     

Kirchhoff型扁壳样条边界元

本文将扁壳分析化为对两块比拟薄板的分析,耦合该二板的样条边界元解,就可得到相应的扁壳解,在少量自由度下也有良好的计算精度,并能一次给出边界和内点的全部物理量,而且扁壳和薄板的线性或非线性分析可以根据需要在同一程序内实现。     

NONSINGULAR KERNEL BOUNDARY ELEMENT METHOD FOR THIN-PLATE BENDING PROBLEMS

In this paper,the nonsingular fundamental solutions are obtained from Fourierseries under some given conditions.These solutions can be taken as the kernels ofintegral equation.So a new boundary element method is presented,with which allkinds of thin-plate bending problems can’be solved,even with complicated loadings andsinuous boundaries.The calculation is much simpler and more accurate.