Stressed State of a Plane with Periodic System of Closely Located Curvilinear Holes with Edge Cracks

Materials Science - A plane periodic problem of the theory of elasticity for an isotropic plane with infinite row of closely located curvilinear holes with edge cracks is solved by the method of...     

Deformation of an Isotropic Plate with Periodic System of Curvilinear Holes and Plasticity Bands

Materials Science - By the method of singular integral equations, we solve a plane elastoplastic problem of fracture mechanics for an isotropic plane with an infinite series of curvilinear holes...     

Elastic Equilibrium of an Anisotropic Half Plane with Periodic System of Holes and Cracks

We present integral equations of a problem of the theory of elasticity for a half plane weakened by holes and curvilinear cracks (including the case of their periodic arrangement). We consider the cases where the boundary of the half plane is stress-free or rigidly fixed. The integral equations are solved numerically by the method of mechanical quadratures.     

Plane Problem for Layered Composites with Periodic Array of Interfacial Cracks Under Compressive Static Loading

The current paper addresses the problem of 2-D modelling of the onset of failure process in a layered composite with periodic array of interfacial cracks under static compression along layers. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium. The condition of plane strain state is considered. The shear and the extensional buckling modes are examined. The laminae are modelled by transversally isotropic material (a matrix reinforced by continuous parallel fibres). The complex non-classical failure mechanics problem is solved utilizing finite element analysis. It is found that the 0°-plies volume fraction, the crack length and the mutual position of cracks influence the critical strain in the composite.     

Stressed State of a Quasiorthotropic Half Plane with Curvilinear Edge

Materials Science - By the method of singular integral equations, we consider a plane periodic problem of the theory of elasticity for a quasiorthotropic half plane containing an infinite row of...     

Solution of Multiple Edge Cracks in an Elastic Half Plane

This paper is concerned with the numerical solution of an elastic half plane containing multiple edge cracks. A general procedure is proposed to formulate the multiple crack problem based on the distributed dislocation method. Three different patterns of modeling dislocation density at the crack mouth are discussed. The correct form of the weight function for the dislocation density is adopted in this analysis. The induced integral involving Cauchy kernel is evaluated by means of recursion relations. Numerical computations of problems with up to 100 edge cracks show that the current method is computationally efficient and accurate. Comparisons of 2D and 3D multiple edge cracks are also discussed. Dedicated to Prof. Zdeněk Bažant on the occasion of his 70th birthday.     

Analytic Solution of the Plane Problem of the Theory of Elasticity for a Nonuniform Strip

We construct the analytic solution of the plane problem of the theory of elasticity in stresses for a strip nonuniform across the width. To deduce the key equations, we perform the direct integration of the original differential balance and continuity equations. In the space of Fourier transforms, the key equations are reduced to an integral Volterra equation of the second kind, which is solved by the method of successive approximations.__________Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 1, pp. 114–116, January–February, 2005.     

A New Boundary Element for Plane Elastic Problems Involving Cracks and Holes

By applying the new boundary integral formulation proposed recently by Chau and Wang (1997) for two-dimensional elastic bodies containing cracks and holes, a new boundary element method for calculating the interaction between cracks and holes is presented in this paper. Singular interpolation functions of order r^-1/2 (where r is the distance measured from the crack tip) are introduced for the discretization of the crack near the crack tips, such that stress singularity can be modeled appropriately. A nice feature for our implementation is that singular integrands involved at the element level are integrated analytically. For each of the hole boundaries, an additional unknown constant is introduced such that the displacement compatibility condition can be satisfied exactly by the complex boundary function H(t), which is a combination of the traction and displacement density. Another nice feature of the present formulation is that the stress intensity factors (both K_{_I} and K_{_II}) at crack tips are expressed in terms of the nodal unknown of H(t) exactly, and no extrapolation of numerical data is required. To demonstrate the accuracy of the present boundary element method, various crack problems are considered: (i) the Griffith crack problem, (ii) the interaction problem between a circular hole and a straight crack subject to both far field tension and compression, and (iii) the interaction problem between a circular hole and a kinked crack subject to far field uniaxial tension. Excellent agreement with existing results is observed for the first two problems and also for the last problem if the crack-hole interaction is negligible. This revised version was published online in August 2006 with corrections to the Cover Date.     

A Numerical Method for the Solution of the Second Boundary Value Problem of Elasticity for Solids with Cracks

A series of experiments detecting electromagnetic radiation (EMR) emitted during percussion drilling were carried out. The electromagnetic signals obtained could be classified into four groups. Three groups are similar to former pulse types observed during conventional uniaxial and triaxial compression experiments, while the fourth is a new one possibly emanating from conical fracturing or fragmentation of chips.     

具中心直裂纹复合材料圆板周期焊接问题

研究了焊接垫圈弹性平面的剪切模数相同而其它模数不同的具中心直裂纹的复合材料圆板周期焊接问题,利用复分析方法将原问题转化为周期Riemann边值问题,进而转化为具周期核奇异积分方程,最后利用Lobatto-Chebyshev求积公式得到数值解,并计算出应力强度因子的数值。     

Variational Principle for the Temperature Problem of the Elasticity Theory for Stresses

The variational formulation of a problem is frequently used in strength analysis of parts and structural elements. The authors present a variational principle whose Euler's equations are the differential equations of thermoelasticity for stresses.     

Singular Integral Equations in Two-Dimensional Problems of the Theory of Cracks

We present a brief survey of the results of investigations devoted to the application of the method of singular integral equations to the solution of two-dimensional problems of fracture mechanics and carried out at the Karpenko Physicomechanical Institute of the Ukrainian National Academy of Sciences. Special attention is given to integral equations on piecewise smooth closed or nonclosed contours appearing in the boundary-value problems for domains with corners. We propose a new method for the solution of equations of this sort taking into account the singularities of stresses at angular points. The modified singular integral equations obtained as a result have continuous kernels and right-hand sides, i.e., belong to the same type of equations as in the case of smooth contours.     

Crack Spacing Effect on the Brittle Fracture Characteristics of Semi-infinite Functionally Graded Materials with Periodic Edge Cracks

The effect of crack spacing on the brittle fracture characteristics of a semi-infinite functionally graded material (FGM) with periodic edge cracks is discussed. The incompatible eigenstrain induced in the material due to mismatch in the coefficients of thermal expansion is considered in the analysis. The nonhomogeneity of the material is simulated by an equivalent eigenstrain, whereby the problem is reduced to that of a cracked homogeneous material with incompatible and equivalent eigenstrains. A method is then formulated to calculate the stress intensity factor of periodic edge cracks in such a semi-infinite homogeneous medium and applied to calculate apparent fracture toughness of a semi-infinite FGM from its prescribed composition profile. Inverse calculation is also carried out to compute composition profile from prescribed apparent fracture toughness of the semi-infinite FGM. Numerical calculations are carried out for semi-infinite TiC/Al₂O₃ FGM and the results are shown in the figures.     

Mixed Approximation Scheme of the Finite-Element Method for the Solution of Two-Dimensional Problems of the Elasticity Theory

For the solution of two-dimensional boundary-value problems of the elasticity theory, a triangular finite element, ensuring stability and convergence of mixed approximation, is proposed. The system of resolving equations of the mixed method is derived with account of strict satisfaction of static boundary conditions at the surface. To solve matrix equations of the mixed method, various algorithms of the conjugate-gradient method with the pre-conditional matrix have been considered. Numerical data on convergence and accuracy of the solution for a number of test problems of the elasticity theory and fracture mechanics are given. The results obtained by the conventional and mixed finite-element method approaches are compared.