钉载作用下多裂纹板的裂纹闭合接触问题

Frictional Contact Problems of a Finite Plate with Multiple Closed Cracks under Fastener Loads

基于摩擦接触问题的数学规划解法,采用各向异性体平面弹性理论中的复势方法,建立了含裂纹群有限大各向异性板,在钉载作用下裂纹闭合或局部闭合问题的有效分析方法。忽略钉与孔间的摩擦,假设钉载沿孔边呈余弦分布,通过在可能闭合的裂纹边界引入互补变量函数并将其展成Fourier级数形式,以Faber级数为工具,应用保角映射技术和最小二乘边界配点法,导出裂纹面摩擦接触的线性互补模型,并通过算例验证了方法的有效性。数值结果表明,由于采用级数解描述板应力场和位移场,本方法具有较高的计算精度和效率,便于研究裂纹闭合对应力强度因子等断裂参数的影响。

Based on the mathematical programming procedure of the contact problem with friction and using the complex potential method in the anisotropic plane theory of elasticity, an efficient approach is presented to deal with the frictional contact of a finite anisotropic plate containing multiple cracks subjected to arbitrary loads of fasteners. The complementary parameters introduced to the contact boundary are expanded into the Fourier series, and the linear complementary model considering the crack closure is obtained by means of the Faber series expansion, conformal mapping and the least square boundary collocation technique. Some examples are given to demonstrate the correctness and effectiveness of the method. Numerical results indicate that the present method has many advantages such as high accuracy, good convergence, and is convenient to investigate the effects of crack closure on the fracture capabilities of structures .