Stress state of a transversely-isotropic body with elliptical inclusion

We present an exact solution for the problem in elasticity theory of a transversely Isotropic body containing an elliptical inclusion. We assume that the tensile stresses act at a distance sufficiently far away from the inclusion, along the axes of the ellipse and perpendicular to the plane of the ellipse. We find that two fracture mechanisms are possible under the action of the type of force under consideration: detachment of the material from the inclusion, and fracture near the stress concentrator. We obtain formulas for the stress intensity factors for each case.     

Three-dimensional static problem for an elliptical crack in an elastic body with initial stress

Conclusions Thus, the influence of the initial stress on the displacement distribution in the crack plane is significant. In [6], it was concluded that, for a shear crack, it is impossible to show in the general case that the initial stress has no influence on the stress-intensity coefficients (which is the case for a normal-rupture crack). For the example of an elliptical shear crack, it is shown that the initial stress influences the stress distribution close to the crack and hence the stress-intensity coefficient, in contrast to the plane and axisymmetric problems.Close to the value of ₁ equal to the surface instability of the half space, as follows from a consideration of quantitative dependences, its influence is sharply expressed.The stress and displacement distribution in a body with initial stress (y ₃0) will differ from the corresponding distribution in a linear isotropic and transversally isotropic elastic body with no initial stress.Institute of Mechanics. Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 20, No. 10, pp. 22–31, October, 1984.     

Plane problem for an orthotropic body with a crack whose lower side is reinforced by an elastic membrane

We study the stress state of an orthotropic plane with one linear defect whose lower side is reinforced by an elastic membrane. The Lekhnitskii potentials are constructed as solutions of the Riemann two-dimensional boundary-value problem. They are obtained in closed form. It is shown that the asymptotic behavior of stresses at the tips of the defect can have a singularity of any order from −1 to 0, depending on the stiffness of the membrane. The cases of low and high stiffness are considered separately. Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 150–155, March–April, 1998. Tekhnicheskaya Fizika, Vol. 39, No. 2, pp.150–155, March–April, 1998.     

Mixed problem of crack theory for antiplane deformation

The elastic equilibrium of an isotropic plane with one linear defect under conditions of longitudinal shear is considered. The strain field is constructed by the solution of a twodimensional boundary-value Riemann problem with variable coefficients. A special method that reduce the general two-dimensional problem to two one-dimensional problems is proposed. The strain field is described by three types of asymptotic relations: for the tups of the defect, for the tips of the reinforcing edge, and also at a distance from the closely spaced tips of the defect and the rib. The general form of asymptotic relations for strains with finite energy is deduced from analysis of the variational symmetries of the equations of longitudinal shear. A paradox of the primal mixed boundary-value problem for cracks is formulated and a method of solving the problem is proposed. Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 163–172, May–June, 1998.     

Creep characterization of transversely-isotropic metallic materials

A constitutive equation for modelling secondary creep in directionally-solidified eutectic alloys is proposed, based on a generalization of the Bailey-Norton law to transversely-isotropic materials. In addition to the power-law index, it is found that three material parameters are required to characterize secondary-creep behaviour and their experimental determination is discussed. The theory is compared with creep data obtained on a Co-Cr-C eutectic alloy.     

An internal crack problem for an infinite elastic layer

The elastostatic plane problem of an infinite elastic layer with an internal crack is considered. The elastic layer is subjected to two different loadings, (a) the elastic layer is loaded by a symmetric transverse pair of compressive concentrated forces P/2, (b) it is loaded by a symmetric transverse pair of tensile concentrated forces P/2. The crack is opened by an uniform internal pressure p ₀ along its surface and located halfway between and parallel to the surfaces of the elastic layer. It is assumed that the effect of the gravity force is neglected. Using an appropriate integral transform technique, the mixed boundary value problem is reduced to a singular integral equation. The singular integral equation is solved numerically by making use of an appropriate Gauss–Chebyshev integration formula and the stress-intensity factors and the crack opening displacements are determined according to two different loading cases for various dimensionless quantities.     

Axisymmetric displacement boundary value problem for a penny-shaped crack

Summary A solution is derived from equations of equilibrium in an infinite isotropic elastic solid containing a penny-shaped crack where displacements are given. Abel transforms of the second kind stress and displacement components at an arbitrary point of the solid are known in the literature in terms of jumps of stress and displacement components at a crack plane. Limiting values of these expressions at the crack plane together with the boundary conditions lead to Abel-type integral equations, which admit a closed form solution. Explicit expressions for stress and displacement components on the crack plane are obtained in terms of prescribed face displacements of crack surfaces. Some special cases of the crack surface shape functions have been given in the paper.     

A two dimensional asymmetrical crack problem

The distribution of stress in the neighborhood of a Griffith crack located asymmetrically in an infinitely long elastic strip is considered. It is assumed that the edges of the strip are stress free and that the crack is opened by an internal pressure varying along its length. Expressions are derived up to the order of δ^?8, where 2δ denotes the thickness of the strip, for the stress intensity factor, the shape of the deformed crack, and the crack energy.     

Torsion problem for elastic multilayered finite cylinder with circular crack

An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and the conditions of an ideal mechanical contact are fulfilled between them. A circular crack is situated parallel to the cylinder's faces in the internal layer with branches free from stress. The upper face of the cylinder is also free from stress. Concretization of the problem is done on examples of two-and three-layered cylinders. An analysis of cylinders' stress state is conducted and the stress intensity factor is evaluated depending on the crack's geometry, its location and ratio of the shear modulus. Advantages of the proposed method include reduction of the solution constants' number regardless of the number of layers, and presentation of the mechanical characteristics in a form of uniformly convergent series.     

Uniquencess for the penny-shaped crack equilibrium problem in linear elasticity

Two uniqueness theorems for the equilibrium problem of an elastic body containing a circular crack (penny-shaped crack) are proved.

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Sommario Si dimostrano due teoremi di unicità per il problema al contorno associato all'equilibrio di un corpo elastico tridimensionale contenente una fessura circolare.

     

反平面断裂问题的无单元伽辽金比例边界法

将比例边界法与无单元伽辽金法相结合,建立了反平面断裂分析的无单元伽辽金比例边界法。这是一种边界型无网格法,在环向方向上采用无单元伽辽金法进行离散,因此计算时仅需要边界上的节点信息,不需要边界元所要求的基本解。为了便于施加本质边界条件,通过建立节点值和虚拟节点值之间的关系给出了修正的移动最小二乘形函数。在径向方向上,该方法利用解析的方法求解,因此是一种半解析的数值方法。最后,给出了数值算例,并验证了所提方法后处理简单和计算精度高的特点,适合于求解反平面断裂问题。