Stress wave fields in plates weakened by curvilinear holes with edge cracks

The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 79–84, February 2006.     

The influence of multiple cracks on tensile and compressive buckling of shear deformable beams

In this work the static stability of the uniform Timoshenko column in presence of multiple cracks, subjected to tensile or compressive loads, is analyzed. The governing differential equations are formulated by modeling the cracks as concentrated reductions of the flexural stiffness, accomplished by the use of Dirac’s delta distributions. The adopted model has allowed the derivation of the exact buckling modes and the corresponding buckling load equations of the Timoshenko multi-cracked column, as a function of four integration constant only, which are derived simply by enforcing the end boundary conditions, irrespective of the number of concentrated damage. Since shear deformability has been taken into account, the buckling load equation allows capturing both compressive and tensile buckling. The latter phenomenon has been recently investigated with reference to rubber bearing isolators, modeled as short beams, but it has been shown to occur also in slender beams characterized by high distributed shear deformation, like composite and layered beams. The influence of multiple concentrated cracks on the stability of shear deformable beams, particularly under the action of tensile loads, has never been assessed in the literature and is here addressed on the basis of an extensive parametric analysis. All the reported results have been compared with the Euler multi-cracked column in order to highlight its limits of applicability.     

Elastodynamic analysis of a plane weakened by several cracks

The stress fields in an infinite plane containing Volterra type climb and glide edge dislocations under time-harmonic excitation are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type which are solved numerically for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.     

Equilibrium of a plane weakened by a hole and two cracks

Kharkov Aviation Institute. Translated from Prikladnaya Mekhanika, Vol. 25, No. 8, pp. 105–111, August, 1989.     

Effects of lateral loads and constraints on buckling of cracked thin plates under compressive edge loads

Critical buckling load is important in investigation of behaviors of thin plates or shells. The presence of cracks in these structures can affects their safety factor with respect to the common modes of failure such as buckling. Some analytical solutions were obtained for un-cracked plates with different boundary conditions. Their numerical results have good agreement with these solutions. In this paper, we also studied the effects of lateral loads and constraints on the critical buckling load of cracked plates under axial compression, experimentally and numerically. Effects of length and orientation of cracks are investigated in presence of the lateral loads. Finally, tests data are compared with the results of numerical calculations.     

First fundamental problems of anisotropic elastic plane weakened by periodic collinear cracks

Using the method of complex functions, we discuss the first fundamental problems of an anisotropic infinite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cracks. This problem was considered by Cai [Engineering Fracture Mechanics 46（1）, 133-142 （1993）]. However, the previous method is imperfect. Therefore, the results are incorrect. Here, we revise the method and give a correct solution.     

Local buckling of extended plates containing cracks and cracklike defects, subject to the influence of geometrical parameters of the plates and the defects

An experimental study of the local buckling of plates containing cracks and cracklike defects is reported, where the influence of the geometrical parameters of the plate and the defect are taken into account. An empirical curve is plotted to estimate the critical stresses at which buckling takes place. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 80–84, December, 1999.     

Rock burst of deep circular tunnels surrounded by weakened rock mass with cracks

Rock masses containing pre-existing cracks are considered as non-homogeneous geomaterials. During excavation of tunnels, pre-existing cracks may nucleate, grow and propagate through rock matrix, then secondary cracks may appear. The stress concentration at the tips of secondary cracks is comparatively large, which may lead to the unstable growth and coalescence of secondary cracks, and consequently the occurrence of fractured zones. For brittle rocks, the dissipative energy of slip and growth of pre-existing cracks and secondary crack growth is small, but the elastic strain energy storing in rock masses may be larger than the dissipative energy of slip and growth of pre-existing macrocracks and secondary crack growth. The sudden release of the residual elastic strain energy may lead to rock burst in crack-weakened rock masses. Based on this understanding, the criteria of rock burst in crack-weakened rock masses are established. The influences of the in situ stresses, micromechanical parameters and physico-mechanical parameters on the distribution of rock burst zones and area of rock burst zones are investigated in detail.