In this paper the distribution of shear stress along the anchoring section of prestressed bolt was presented. The distribution of shear stress along the anchoring section of prestressed bolt was analyzed with the plane elastic theory. The analytical solution of shear stress along the anchoring section was deduced. Several cases of shear stresses were analyzed with the analytical solution. The results show that shear stress of prestressed bolt are not uniform distribution along the anchoring section; it is has no relations with the prestress value where the shear stress peak value is; the shear stress is at a certain range along the anchoring section; the shear stress peak value increases with the increase of prestress value;the larger the diameter of the anchoring section is, the less of shear stress peak value is.

Based on a shear test for jointed rock sample conducted by former study, a numerical improved method DDARF is carried out to simulate the shear test. The simulation result of shear fracture phenomenon show high compatibility with the model test. Different fracture phenomenon and peak strength value of shear testing are explored in the condition of different colinnear and ladder echelon arrangement of cracks.

By use of complex variable theory, formulae for tangential stress on ellipse edge are derived. Sub-crack point, opening angle and maximal tangential stress on ellipse edge are studied under uniaxial compression, biaxial compression, or uniaxial compression and crack water pressure separately. Based on the maximal tension stress criterion, formulas of maximal tangential stress and critical load are presented. The results show that sub-crack point, opening angle, maximal tangential stress and critical load are varied with different aspect ratio and different inclined angle. Meanwhile, the most dangerous inclined angle is obtained.

The main draw back of the Moving Least Squares (MLS) approximate used in element free Galerkin method (EFGM) is its lack the property of the delta function. To alleviate difficulties in the treatment of essential boundary conditions in EFGM, the local transformation method and the boundary singular weight method, which are used in the reproducing kernel particle method, is combined with the element free Galerkin method. The computational method is given to analyze the stress intensity factors and the numerical simulation of crack propagation of two-dimentional problems of the elastic fracture analysis. The application examples reveal the effectiveness and feasibility of the present methods.

The analytic solution of incident P wave, SV wave and SH wave amplitudes reflected at free surface in elastic medium was presented in this paper. Taking the assumption that the wave propagation media are in elastic half space and the seismic wave is plane simple harmonic wave, the incident wave and reflected wave functions of P wave, SV wave and SH wave were deduced with elastic wave theory, and the wave amplitudes reflected at free surface in elastic media was presented