一维六方准晶有限板孔边对称反平面双裂纹问题的边界配置法

Boundary Collocation Method for Anti-Plane Problems of One-Dimensional Hexagonal Quasicrystals with Cracks

从断裂力学的观点出发,采用边界配置法研究了一维六方准晶中带双裂纹的圆孔口反平面问题.通过选取恰当的位移函数,求得声子场与相位子场的应力和应力强度因子.而板的边界条件由边界配置法近似满足.通过数值算例,讨论了裂纹长度、板的宽度、幂级数项数以及圆孔半径等对应力强度因子的影响.结果表明圆孔半径对应力强度因子的影响非常明显.在有限大板与无限大板两种情况下,裂纹长度与幂级数项数对应力强度因子的影响恰好相反.

Base on the theory of fracture mechanics, the anti-plane problems of one-dimensional hexagonal quasicrystals with two symmetrical cracks were investigated by using the boundary collocation method. The numerical results for stresses in the phonon and quantum fields and related stress intensity factor were obtained by selecting the appropriate displacement function. It is shown that only the plate boundary conditions are needed to be satisfied approximatively with the boundary collocation method. The influence of the radius of circular hole, the length of the crack, the width of the plate and the number of the power series on the stress intensity factor is discussed through the numerical examples. It is shown that the influence of the hole＇s radius on the stress intensity factor is very obvious. The influence of the crack＇s length and the number of power series on the stress intensity factor is on the contrary in the limited plate and infinite plate.