Formulas are derived to evaluate the intensity factors of stresses, electric-flux density, and electric-field strength in two-dimensional problems of elasticity, thermoelasticity, electroelasticity, magnetoelasticity, thermoelectroelasticity, and thermomagnetoelasticity for anisotropic bodies with holes and plane (rectilinear) cracks Keywords: intensity factors for stresses, electric-flux density, and electric-field strength, two-dimensional problem, anisotropic bodyIntroduction. Fracture strength analysis of structural members based on energy failure criteria necessarily involves calculation of stress intensity factors (SIFs), which requires a reliable method.Solution of two-dimensional problems of elasticity, thermoelasticity, electroelasticity, and magnetoelasticity is often based on complex potentials, which are determined from the boundary conditions on crack faces and smooth boundaries (external edge and holes).The boundary conditions on crack faces in isotropic plates are often reduced to the Riemann-Hilbert (linear conjugation) problem whose solution contains an isolated singularity at the crack tips. This allows deriving an analytic formula to calculate the SIFs [1-3, 10, 12, 14-18].In the case of two-dimensional problems of anisotropic elasticity, the boundary conditions on cracks lying along one straight line can also be reduced to the Riemann-Hilbert problem to derive analytic expressions for the 15,19]. The use of the linear conjugation method to solve problems of elasticity for multiply connected anisotropic bodies that have holes besides cracks (even if they lie along one straight line) involves severe mathematical and computational difficulties. Therefore, an approximate method was proposed in [7,9] to determine the SIFs for an arbitrary multiply connected domain with arbitrarily arranged rectilinear cuts. The method employs numerical limiting processes to find derivatives of complex potentials or even normal and tangential stresses in small neighborhood of crack tips. This method made it possible to determine the SIFs for arbitrary multiply connected bodies and to solve such problems for anisotropic media that could not be solved by other methods. Later, this method was extended to thermoelasticity [20], electroelasticity [8], magnetoelasticity [21], and thermoelectroelasticity [13]. However, this method may become unstable if a crack is close to a smooth boundary or concentrated forces act on the body. Note that problems for anisotropic inelastic and electroelastic cracked bodies were also addressed in [22,23].The present paper proposes a new approach to the determination of the intensity factors for stresses, electric-flux density, and electric-field strength that does not require passing to the limit.1. Two-Dimensional Problem of Anisotropic Elasticity. Consider an anisotropic body with elliptic cavities under external forces that induce a two-dimensional stress-strain state constant along the cavity generatrix, which coincides with the Oz-axis of a Cartesian coordinate system Oxyz. The ellipt...

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A general method based on complex variable theory is proposed to determine the magnetic and elastic fields of a piezomagnetic body. This method is used to derive the basic relations for complex potentials in the two-dimensional problem of magnetoelasticity, their general representations for a multiply connected domain, expressions for stresses, displacements, vectors of magnetic field intensity and magnetic flux density, and magnetic field potential. A closed-form solution is obtained for a body with an elliptic (circular) hole or crack subjected at infinity to the action of a constant magnetoelastic field. Numerical results for a piezomagnetic plate with a circular hole are presented Keywords: anisotropic body, complex potentials, crack, hole, inclusion, magnetic field intensity, magnetic flux density, magnetoelasticity, plane problemIntroduction. In recent years, interest in piezomagnetic materials has heightened. Development of analytic and numerical methods for solving specific classes of problems is still one of the urgent tasks in the theory of magnetoelasticity of anisotropic piezomagnetic bodies. The governing equations of magnetoelasticity were derived in [6], internal and external two-dimensional problems of magnetostatics were solved in [1], and the interaction of mechanical strains in solids with an electromagnetic field was investigated in [12]. The great prospects for piezomagnetic materials in modern electronics and engineering generate interest in their effective properties [3-5], interaction of magnetic and mechanical fields [9], and magnetoelastic problems for piezomagnetic plates [10,11], bodies with inclusions [7], holes, and cracks [2].In the present paper, we extend the general approaches to the solution of two-dimensional electroelastic problems for multiply connected bodies [8] to magnetoelastic problems for piezomagnetic bodies with holes and cracks. We will introduce complex potentials for a two-dimensional magnetoelastic problem, derive formulas for the basic magnetoelastic characteristics, formulate boundary conditions for the potentials, obtain their general representations for multiply connected domains, find a magnetoelastic solution for a body with an elliptic (circular) cavity or a crack, and present numerical results.1. Problem Formulation. Let us consider a multiply connected cylindrical anisotropic piezomagnetic body weakened by L longitudinal cavities with generatrices parallel to the cylinder axis. We will use a rectangular coordinate frame Oxyz with the z-axis directed along the cavity generatrices. The cross section of the body by the plane Oxy is a multiply connected domain S bounded by the external boundary L 0 and the outlines L l ( , ) l L = 1 of the holes. As a special case where the outside surface is at

We present a method of determining the two-dimensional generalized stress-strain state and the stress intensity factors for an anisotropic body with cylindrical cavities and plane cracks. The method is based on the use of generalized complex potentials, conformal mappings, the method of least squares, and numerical passage to the limit to determine the stress intensity factors. We apply the method to study the stress-strain state and the change in stress intensity factors as functions of the geometric and elastic characteristics of an orthotropic cylinder with one or two cracks, an infinite anisotropic body with elliptic cavities and cracks, and an infinite body with a curvilinear cavity. Five figures. Six tables. Bibliography: 7 titles

The thermoelastic problem for an infinite multiply connected anisotropic plate with holes and cracks in a linear heat flow is solved. The stress distribution and the stress intensity factors on heat-insulated boundaries are analyzed numericallyThe thermostressed state of isotropic plates with holes and cracks was analyzed in [7,10]. In the anisotropic case, such studies were conducted for plates with holes [8,9], with either concentrated heat sources or predefined peripheral temperature. No problems were solved for anisotropic plates with cracks or with holes and cracks, let alone heat flows. Three-dimensional stress problems for elastic and magnetoelastic bodies with cracks and inclusions are addressed in [13][14][15][16].The present paper sets forth a method for thermostress analysis of anisotropic plates with an arbitrary number, arrangement, and combination of holes and cracks under various thermal actions. Numerical results for plates with holes with heat-insulated boundaries in a linear heat flow acting at infinity will be presented.