三维有限体中两平行裂纹干扰问题的有限部积分与边界元法

FINITE-PART INTEGRAL AND BOUNDARY ELEMENT METHOD FOR INTERACTION BETWEEN TWO PARALLEL PLANAR CRACKS IN THREE-DIMENSIONAL FINITE BODIES

利用Somigliana公式及有限部积分的概念，导出了含两平行平片裂纹三维有限体裂纹干扰问题的超奇异积分方程组，联合使用有限部积分与边界无法，建立了数值求解方法．为提高数值计算结果的精度，在裂纹前沿附近单无，采用平方根位移模型，并在此基础上，给出直接计算应力强度因子的公式．最后计算了若干典型例子裂纹前沿的应力强度因子．

By using the Somigliana representation and the concept of finite-part integrals, a set of hypersingular integral equations for the interaction between two parallel planar cracks in a three-dimensional finite they subjected to arbitrary loads is derived, and then the numerical methed for solving is proposed by combining the finite-part integral methed with boundary element method.According to the analytic theory of hypersingular integral equations, the equare root medels of displacement discontinuities in the elements near the crack front are applied, and thus the computing precision is ralsed. Based on this, the stress intensity factors can be directly calculated. Finally, thestress intensity factors of several typical interaction probletns are calculated.