双圆孔的动应力集中

Dynamic Stress Concentration around Two Circular Holes in an Infinite Elastic Medium

关于双圆孔的静应力集中问题,林致平教授早在1948年就进行过研究[1],但其动态问题的理论于1991年才由作者在另一篇论文中完成[2]. 从文献[2]的理论出发,本文研究了孔边受余弦分布动载作用下含双圆孔无限介质的动应力集中问题,目的在于模拟孔边紧固件的压力分布,为处理钉孔动态接触问题打下基础.

The solution to the static stress concentration around two circular holes was obtained as early as 1948 by the well-known investigator, Prof. C.B.Ling[1], but only until 1991, did the authors successfully solve the corresponding dynamic problem in a previous paper[2]. Starting from the theory in Ref.[2], this paper deals with the dynamic stress concentration around two circular holes in an infinite elastic medium under the action of transient loads with ccsine distribution in order to simulate the pressure distribution of pin-hole contact problem as a prerequisite for the analysis of the corresponding dynamic contact problem. The geometry and coordinate systems are shown in Fig.1 and the external loads are symmetrical with respect to both the X-and the Y-axis. The two typical transient loads are in the following form (1) σ_r(b, θ, t)=-σ_0cosGH(t), τ_(rθ)(b, θ, t)=0, 0≤θ≤2π (2)τ_(rθ)(b, θ, t)=0, 0≤θ≤2π where H(t) is the Heaviside function. Numerical results of the variation with repect to time of circumferential stresses on edges of both holes at the five points (0=0°, 45°, 90°, 135°, 180°) under the two cases of transient loads mentioned above are shown in Figs.2-4, and Figs.5-7, respectively. In the figures, C_2 is the shear wave speed, C_1 is the dilatational wave speed, C_2/ C_1 is taken as 0.57735 in numerical computation, corresponding to Poisson's ratio v=1 / 3 (for plane stress) or v=1 / 4 (for plane strain). Numerical results show that the effect of the distance between the two holes on the dynamic stress concentration factors decreases with increasing distance. When the distance is greater than a certain value, e.g., h/ b≥ 10.0, the effect almost vanishes, which can be seen from Figs. 4 and 7, where the dashed lines stand for the corresponding static solutions of one hole problem. This conclusion coincides with that drawn by derivation and computation in Ref.[2] and also confirms the validity, readability and effectiveness of the solution given in Ref.[2]. Thus the dynamic stress concentration problem for two holes becomes equivalent to that for one hole when h/b≥10. When h/b≥ 10, the results shown in Figs.4 and 7 are also the results for one hole. It is worth poining out that the results for one hole have not yet been seen in published literature.