十次对称二维准晶中的热应力分析

THERMAL STRESS ANALYSIS FOR DECAGONAL QUASICRYSTALS

推导了当考虑热效应时十次对称二维准晶体平面应变问题的通解表示.作为应用,采用所获得的通解首先得到了十次对称二维准晶体中的一个点热源所引起的声子场和相位子场,给出了点热源所引起的声子场和相位子场应力分量的解析表达式;接着获得了在均匀热流作用下十次对称二维准晶体中一绝缘椭圆孔洞所引起的热应力问题的弹性解答,给出了沿椭圆边界环向应力分布的解析表达式;当椭圆的短轴趋于零时,则获得了裂纹问题的解答,给出了应力强度因子、裂纹表面张开位移及能量释放率的解析表达式;推导了在任意热载荷作用下裂尖附近的渐近场.

The general solution for plane strain problems in decagonal quasicrystals accounting for thermal effect is derived. As applications, the obtained general solution is employed to investigate the phonon and phason fields induced by a point heat source in an infinite decagonal quasicrastal. Analytical expressions for phonon and phason stress field caused by the point heat source are presented. The obtained general solution is also employed to investigate thermal stresses due to disturbance of uniform heat now by an insulated elliptical hole in an infinite decagonal quasicrystal. Explicit expression for the hoop stress around the elliptical hole is given. The solutions for the crack problems are obtained by setting the minor axis of the ellipse to be zero. Analytic expressions for stress intensity factors, crack opening displacements and energy release rate are derived. The asymptotic phonon and phason stress fields at the crack tip caused by arbitrary thermal loading are also derived.