奇性校正特解场法计算任意点应力和位移

PARTICULAR SOLUTIONS METHOD TO ADJUST SINGULARITY FOR THE CALCULATION OF STRESS AND DISPLACEMENT AT ARBITRARY POINT

本文将边界应力积分方程中的强奇性边界积分化为Ｃａｕｃｈｙ主值积分，证明了该主值积分的存在性，并给出它在变量替换中的比尺附加项显式；运用刚体位移法和单位应力场法将强奇性主子块和应力奇性系数矩阵表为同行副子块的线性组合，再配用极坐标变换和适当的数值求积计算各副子块。本法无论对平面问题还是空间问题，是光滑边界点、侧棱点还是角点，有限域或无限域，受载还是变温，都一概适用，而且可以扩展用来计算近边界点，公式统一，程序通用，数值效果良好。

In this paper,super singularity boundary iutegral is transformed into Cauchy principal value integral in boundary stress integral equation,The existance of theprincipal value integral is demenstrated and the explicit formula of its scale extra term in thesubstitution of variables is given out.Then the main submatrix of supersingularity and thematrix of stress singularity parameters are expressed as a linear combination of non-diagonalsubmatrices in the same row by using rigidbody movement method and unit stress fieldmethod respectively. Furthermore,these non-diagonal submatrices are calculated by usingpolar coordinate transformation technic and proper numerical integration. The method isfeasible for plane and space problems;smooth boundary points,arris points and cornerpoints;finite and infinite domains;load and temperature induced field problems。And it canbe expantled to calculate the values at points adjacent to boundary。With unified formulaeand computing program,the method has an excellent numerical accuracy.