Scattering of love waves by an interface crack between a piezoelectric layer and an elastic substrate

The scattering of Love waves by an interface crack between a piezoelectric layer and an elastic substrate is investigated by using the integral transform and singular integral equation techniques. The dynamic stress intensity factors of the left and the right crack tips are determined. It is found from numerical calculation that the dynamic response of the system depends significantly on the crack configuration, the material combination and the propagating direction of the incident wave. It is expected that specifying an appropriate material combination may retard the growth of the crack for a certain crack configuration. Project supported by the National Natural Science Foundation of China (No. 19891180), the Fundamental Research Foundation of Tsinghua University (JZ 2000.007) and the Fund of the Education Ministry of China.     

Various methods of reconstruction of a cavity in an orthotropic layer

Direct and inverse problems of oscillations of an anisotropic layer with a cylindrical cavity of an arbitrary cross-sectional shape under the action of a load applied to the layer surface are considered. An asymptotic approach to solving these problems with cavities of small relative sizes is proposed. Numerical results of solving direct and inverse problems are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 181–189, May–June, 2009.     

Problem of coupled thermoelasticity for a half-layer with a tunnel cavity: An antisymmetric case

A boundary-value problem of coupled thermoelasticity for a half-layer with a hole and mixed boundary conditions is solved. The problem is reduced to a system of four singular integral equations. It is solved numerically using the mechanical-quadrature method. A numerical experiment is conducted to study the dynamic stress concentration around cavities of different cross sections. The effect of the coupled thermal and elastic fields on the wave processes in the body is established Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 28–36, October 2008.     

Interaction between curved crack and elastic inclusion in an infinite plate

Summary In this paper, the curved-crack problem for an infinite plate containing an elastic inclusion is considered. A fundamental solution is proposed, which corresponds to the stress field caused by a point dislocation in an infinite plate containing an elastic inclusion. By placing the distributed dislocation along the prospective site of the crack, and by using the resultant force function as the right-hand term in the equation, a weaker singular integral equation is obtainable. The equation is solved numerically, and the stress intensity factors at the crack tips are evaluated. Interaction between the curved crack and the elastic inclusion is analyzed. Received 8 October 1996; accepted for publication 27 March 1997     

Integral transform solution of multi-material structure with finite crack perpendicular to the interface

The plane elasticity problem for layered elastic systems containing a finite crack perpendicular to the interface is considered. To derive the singular integral equations. Fourier transform in conjunction with dislocation is used. The singular integral equation is solved with the Lobatto-Chebyshev method commonly applied to such problems. In order to have an idea about the usefulness of the method described, a two-layer structure which contains a cut parallel toh is considered.     

Interaction of a spherical shockwave and an elastic circular cylindrical shell

The paper studies the interaction of a spherical shock wave with an elastic circular cylindrical shell immersed in an infinite acoustic medium. The shell is assumed infinitely long. The wave source is quite close to the shell, causing deformation of just a small portion of the shell, which makes it possible to represent the solution by a double Fourier series. The method allows the exact determination of the hydrodynamic forces acting on the shell and analysis of its stress state. Some characteristic features of the stress state are described for different distances to the wave source. Formulas are proposed for establishing the safety conditions of the shell.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 94–104, September 2004.     

Vibrations of an elastic orthotropic layer with a cavity

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 95–97, January–February, 1991.     

On the free energy and variational theorem of elastic problem in thermal shock

In some investigations on variational principle for coupled thermoelastic problems, the free energy Φ(e_ij,θ) ,where the state variables are elastic strain e_ij and temperature increment θ, is expressed as Φ(e_ij,θ)=λ/2e_kke_ij=ue_k1e_k1-γe_kkθ-c/2 p θ²/T₀(0.1) This expression is employed only under the condition of |θ|≤T₀(absolute temperature of reference) But the value of temperature increment is great, even greater than T₀ in thermal shock. And the material properties (λ ,μ ,ν ,c , etc.) will not remain constant, they vary with θ. The expression of free energy for this condition.is derived in this paper. Equation (0.1) is its special case.Euler’s equations will be nonlinear while this expression of free energy has been introduced into variational theorem. In order to linearise, the time interval of thermal shock is divided into a number of time elements Δt_k, (Δt_k=t_k-t_k-1,k=1,2…,n), which are so small that the temperature increment θ_k within it is very small, too. Thus, the material properties may be defined by temperature field T_k-1=T(x₁,x₂,x₃,t_k-1) at instant t_k-1 , and the free energy Φ_k expressed by eg. (0.1) may be employed in element Δt_k.Hence the variational theorem will be expressed partly and approximately.     

Collision of an elastic finite-length cylinder with a rigid barrier

The paper proposes an approximate solution describing a collision of an elastic finite-length cylinder with a rigid barrier when the lateral boundary conditions of the first fundamental problem of elasticity are satisfied. A finite-difference approach with respect to time and the integral transform method are used to reduce the original initial-boundary-value problem to a one-dimensional one. It is solved using the matrix Green’s function. The final expressions for displacements are obtained by solving a singular integral equation by the orthogonal-polynomial method. The values of displacements and strains are analyzed for short periods of time __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 74–82, September 2007.     

Nonstationary indentation of a blunt rigid body into an elastic layer: An axisymmetric problem

The nonstationary indentation of a blunt rigid body into an elastic layer is studied. The general formulation of the problem includes different boundary conditions in the contact area and on the free surface of the layer. The simplified nonmixed problem that arises at the early stage of interaction and allows obtaining approximate results for later times is solved exactly. The solution obtained is compared with that for the plane case __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 35–46, July 2008.     

A class of two-dimensional dual integral equations and its application

Because exact analytic solution is not available,we use double expansion and boundary collocation to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics.The integral equations by this procedure are reduced to infinite algebraic equations.The accuracy of the solution lies in the boundary collocation technique.The application of which for some complicated initial- boundary value problems in solid mechanics indicates the method is powerful.     

Influence of the coupling of mechanical and thermal fields on the amplitude-frequency characteristics of a cylinder

A dynamic boundary-value problem of coupled thermoelasticity for a finite cylinder with mixed boundary conditions is solved. The problem is reduced to a system of four singular integral equations solved by the mechanical-quadrature method. A numerical experiment is conducted to obtain amplitude-frequency characteristics for finite cylinders with different cross sections. The effect of thermoelastic coupling on stress distribution is assessed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 86–95, October 2006.     

Transient compressible boundary layer on a wedge impulsively set into motion

Summary The development of a compressible boundary layer over a wedge impulsively set into motion is studied in this paper. The initial motion is independent of the leading edge effect and the solutions are those of a Rayleigh-type problem. The motion tends to an ultimate steady state of Falkner-Skan type. The equations governing the transient boundary layer from the initial steady state to the terminal steady-state change their character after certain time due to the leading edge effect and thereafter solution depends on both the end conditions. Numerical solutions are obtained through the second-order accuracy upwind scheme. The effects of the Falkner-Skan parameter and the surface temperature on the transient flow and heat transfer are also studied. It has been found that the flow separation does not occur form–0.0707 when _w = 1.5 (hot wall), andm–0.118 when _0.5 (cold wall).     

The influence of elastic waves on dynamic stress intensity factors (two-dimensional problems)

Summary In this paper, an indirect boundary integral equation method for the solution of dynamic crack problems is presented. The Laplace transform method is used to derive the fundamental solutions for the opening mode (mode I) and the sliding mode (mode II) displacement discontinuity. Accurate dynamic stress intensity factorsK _N (t) (N=I,II) resulting from different time-dependent loads on the crack surface are obtained. The specific influences of the various elastic waves on the stress intensity factors can be clearly seen from the results.On leave Central-South University of Technology Changsha, P.R. China     

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

ＡＵＮＩＦＯＲＭＬＹＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭＦＯＲＡＳＥＭＩＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＭＩＸＥＤＢＯＵＮＤＡＲＹＶＡＬＵＥＣＯＮＤＩＴ...     

Solving the elastic bending problem for a plate with mixed boundary conditions

The bending problem for an arbitrarily outlined thin plane with mixed boundary conditions is solved. A technique based on the methods of potentials and balancing loads is proposed for constructing Green’s function for the Germain-Lagrange equation. This technique ensures high accuracy of approximate solutions, which is checked against Levi’s solution for rectangular plates __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 104–112, May 2006.     

Contact interaction of a rigid heat-conducting punch with an elastic layer involving nonstationary frictional heating

A mathematical formulation is given and a solution is found to the quasistatic contact problem of thermoelasticity for a rigid heat-conducting punch moving over an elastic layer with fixed base. The interaction is accompanied by heating due to frictional forces obeying Amonton’s law. The problem is reduced to a system of integral equations with time-varying limits of integration. The structure of these equations depends on the type of thermal and physical conditions on the contact surface. An algorithm is proposed for the numerical solution of this kind of equations. The variation in the contact pressure and contact area with time is studied __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 35–46, December 2005.     

Wave processes in a perfect liquid layer impacted on by a blunted solid

The problem of impact of a smooth blunt solid upon a compressible-liquid layer of finite depth is addressed. A mixed initial-boundary-value problem with an unknown moving boundary is formulated. In the general case, the problem is reduced to an infinite system of integral Volterra equations of the second kind. It is solved numerically, using quadrature formulas and truncation method. An exact analytic solution to the problem is obtained in the special case where the body moves with a constant velocity at the initial stage of submergence. This solution makes it possible to examine the effect of successive wave reflections on the pressure at the frontal point and inside the layer __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 37–47, March 2007.     

Dynamics of an elastic half-space with a reinforced cylindrical cavity under moving loads

Partial separation of variables and reexpansion of cylindrical and plane waves are used to find the solution describing the uniform motion of a load along a thin circular cylindrical shell in an elastic half-space with the free surface parallel to the axis of the shell. This is a model problem for studying the dynamics of tunnels and shallow-buried pipelines under transport loads. Dispersion curves for the cases of sliding and tight contact between the shell and the half-space are plotted and analyzed. The effect of the shell parameters on the stress–strain state of the half-space is examined