三维断裂力学的超奇异积分方程方法

本文利用有限部积分的概念和方法,严格地证明了三维弹性体中受任意载荷作用的平片裂纹问题的超奇异积分方程组,并对未知解的性态作了理论分析,得到了性态指数,在此基础上通过主部分析,精确地求得了裂纹前沿光滑点附近的奇性应力场,从而找到了以裂纹面位移间断(位错)表示的应力强度因子表达式,最后对所得的超奇异积分方程组建立了数值法,并用此计算了若干典型的平片裂纹问题,数值结果令人满意。

METHOD OF HYPERSINGULAR INTEGRAL EQUATIONS IN THREE-DIMENSIONAL FRACTURE MECHANICS

Using the concepts and method of finite-part integrals, the hypersingular integral equations of a plane crack loaded by arbitrary loads is proved exactly. The behaviour of the unknown solution are analysed theoretically and its indexes are then obtained. Based on these results, the singular stresses near the smooth point of the crack front are exactly derived by use of the dominant analyses. Then the stress intensity factors are expressed in terms of the displacement discontinuities of the crack surface. Finally, the numerical method to solve the hypersingular integral equations is proposed and several typical plane cracks are then calculated. The numerical results are satisfactory.