Consideration of friction between layers in determining the stress-strain state of structures with nonideal layer contact

A mathematical model for calculation of structures in a three-dimensional installation allowing for layer slippage with friction was constructed. The examples examined show that consideration of friction in problems of calculating laminated structures with nonideal layer contact can introduce an essential correction in the stress—strain state of the structure. In slabs with a freely sagging lower surface, friction is perceived for important friction coefficients and increases when the slippage surface approaches the loaded surface. In masses with a rigidly attached lower surface, even insignificant friction coefficients lead to essential redistribution of the stress—strain state.Ukraine Transportation University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 192–199, March–April, 1997.     

Model of a layered plate considering nonideal contact between layers

We propose a mathematical model for doing calculations for layered plates, allowing for both rigid and sliding contact in the presence of frictional forces between the sliding layers. The model takes into account the distribution of tangential and normal displacements across the thickness of the sliding layered stack, and also the distribution of transverse normal stresses. The strain tensor is obtained using the Cauchy relations; the stress tensor is obtained based on Hooke's law. Tne Lagrange variational principle allows us to obtain the resolvent system of differential equations and the corresponding boundary conditions. The spatial model for deformation of a layered plate has a number of special features compared with familiar models. The system of differential equations has operators no higher than second order. It is described relative to displacements on the faces of the stack. This is convenient in solving problems involving sliding of layers with and without friction.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 671–676, September–October 1995.     

Nonstationary heat transfer in multilayer anisotropic shells of revolution

On the basis of the variational principle of least scattering in nonequilibrium thermodynamics we obtain an approximate equation and boundary conditions describing the process of nonstationary heat conduction in multilayer anisotropic shells of arbitrary shape. The structure of the equation obtained is independent of the number of layers and the types of boundary conditions. We give an example of the computation of a one-dimensional nonstationary temperature field for an infinite hollow homogeneous cylinder. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 106–114.     

Stress-strain state and stability of composite sandwich shells with a scaling zone between the core and facings

A finite element model is presented for analyzing the strength and stability of sandwich shells of arbitrary configuration with an adhesion failure zone between the core and one of the facings. The model is based on the assumptions that both facings are laminated Timoshenko-type composite shells, only transverse shear stresses in the core and normal stresses in the thickness direction have nonzero values, a free slip in the tangential plane in the adhesion failure zone and unilateral contact along the normal are possible, and the prebuckling state in the stability problem is linear. Biquadratic nine-node approximations for all functions and numerical integration were used. The displacements and rotation angles of the normals toward the facings as well as stresses in the core are taken as global degrees of freedom. The algebraic problem is solved using a special step-by-step procedure of determining the contact area in the scaling zone and employing unilateral constraints for some of the unknowns. Numerical examples are also given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 640–652, September–October, 1993.     

Axisymmetric contact of anisotropic shells of rotation with rigid and elastic foundations

A class of problems are investigated on determining the stressed-strained state of anisotropic shells of rotation that are in axisymmetric one-sided contact with rigid and elastic surfaces. The shells are under the action of surface and contour loads. For some combinations of these quantities the shell may break away from the surface. To determine the contact zone, the method of successive approximations is utilized. In contrast to most investigations in which the contact zone is first determined, the method proposed makes use of a special quantity characterizing the size of the contact zone. The load on contours is determined from the solution to the problem on the stressed state of the shell and the condition specified on the boundary of the contact zone. Some examples of solving concrete problems are given. Bibliography: 5 titles. Translated fromObchyslyuval’ na ta Prykladna Matematyka, No. 76, 1992, pp 70–74.     

Refined linear theory of elastic anisotropic multilayer shells. Part 2

On the basis of the refined linear theory of elastic anisotropic multilayer shells of arbitrary shape derived in [1] it is established that a number of theorems of the linear theory of elasticity have analogues in the theory of multilayer anisotropic shells.For Part 1 see [1].Institute of Fluid Mechanics, Bucharest. Translated from Mekhanika Polimerov, No. 1, pp. 100–109, January–February, 1976.     

Static and extending interface cracks with contact zones in anisotropic as well as in piezoelectric bimaterials

An interface crack with an electrically permeable and mechanically frictionless contact zone in a piezoelectric bimaterial under the action of a remote mixed mode mechanical loading as well as thermal and electrical fields is considered in the first part of this paper. By use of the matrix‐vector representations of thermal, mechanical and electrical fields via sectionally‐holomorphic functions the problems of linear relationships are formulated and solved exactly both for an electrically permeable and an electrically impermeable interface crack. For these cases the transcendental equations and clear analytical formulas are derived for the determination of the contact zone lengths and the associated fracture mechanical parameters. A plane strain problem for a crack with a frictionless contact zone at the leading crack tip extending stationary along an interface of two semi‐infinite anisotropic spaces with a subsonic speed under the action of various loading is considered in the second part of this paper. By introducing of a moving coordinate system connected with the crack tip and by using the formal similarity of static and propagating crack problems the combined Dirichlet‐Riemann boundary value problem is formulated and solved exactly for this case as well and a transcendental equation is obtained for the determination of the real contact zone length. It is found that the increase of the crack speed leads to an increase of the real contact zone length and the correspondent stress intensity factors which increase significantly for a quasi‐Rayleigh wave speed.     

The stressed state of a transversally isotropic medium with a spheroidal inclusion under nonideal mechanical contact

We study the problem of the stressed state of a transversally isotropic medium containing a foreign inclusion in the form of a prolate spheroid under an arbitrary homogeneous stress field at infinity. On the “medium-inclusion” interface there is slipping without flaking. The stressed state is constructed in the medium and in the inclusion using the exterior and interior problems for a prolate spheroid on the basis of potential functions. The solution of the problem is reduced to studying infinite systems of linear algebraic equations. The results of numerical studies are shown as graphs that describe the stress distribution in both the transversally isotropic medium and in the inclusion under various boundary conditions. Four figures. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 15–26.