The shirink-fit problem for aeolotropic nonlinearly elastic bodies

This paper is dedicated to the memory of Guo Zhong-heng     

One-dimensional deformations of nonlinearly elastic micropolar bodies

We find families of finite deformations of a Cosserat elastic continuum on which the system of equilibrium equations is reduced to a system of ordinary differential equations. These families can be used to describe the expansion, tension, and torsion of a hollow circular cylinder, cylindrical bending of a rectangular slab, straightening of a circular arch, reversing of a cylindrical tube, formation of screw and wedge dislocations in a hollow cylinder, and other types of deformations. In the case of a physically nonlinear material model, the above-listed families of deformations can be used to construct exact solutions of several problems of strong bending of micropolar bodies.     

The solving problem and the difference solving process for the shear of a bounded elastic bodies

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Numerical method of solving the problem of the contact of an elastic plate with an obstacle

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 142–146, September–October, 1994.     

Notes on the nonlinearly elastic Boussinessq problem

The nonlinearly elastic Boussinesq problem is to find the deformation produced in a homogeneous, isotropic, elastic half space by a point force normal to the undeformed boundary, using the exact equations of elasticity for an incompressible or compressible material. First we derive the governing equations from the Principle of Stationary Potential Energy and then we examine some of the implications of the conservation laws of elastostatics when applied to the entire half space, assuming that the well-known linear Boussinesq solution is valid at large distances from the point load. Next, we hypothesize asymptotic forms for the solutions near the point load and, finally, we seek solutions for two specific materials: an incompressible, generalized neo-Hookean (power-law) material introduced by Knowles and a compressible Blatz-Ko material. We find that the former, if sufficiently stiffer than the conventional neo-Hookean material, can support a finite deflection under the point load, but that the latter cannot.This research was supported by the U.S. Army Research Office under Grant DAAL 03-91-G-0022 and by the National Science Foundation under Grant MSS-9102155.     

Plane strain problem for an incompressible nonlinearly elastic solid

The plane strain of an incompressible body is studied with geometrical and physical nonlinearity and potential forces taken into account. A nonlinear system of equations for strains is obtained in actual variables, and conditions of its ellipticity are derived in terms of the elastic potential. Boundary conditions for strains are found from specified loads. Analytical solutions of the boundary problem in strains and their corresponding stress fields are found for the case of identical elongations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 217–225, March–April, 2009     

The plane frictionless contact of two elastic bodies — the inclusion problem

Summary The mixed boundary value problem of the contact of two plane elastic bodies of arbitrary shape is solved for zero friction in their contact zone. It is reduced to a system of four singular integral equations referred to the contact zone and the remaining parts of the boundaries of the two bodies. The system is complemented by two more equations derived from the single-valuedness of the displacements along the contact boundaries. The solution of these equations yields the distribution of the contact stresses and the contact length. The method is applied to the symmetric case of an infinite elastic plate containing an oversized elastic inclusion, with and without axial forces applied to the plate at infinity. The evolution of contact relaxation and the progress of the gap between the inclusion and the plate is also given.

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Der ebene reibungslose Kontakt von zwei elastischen Körpern — Das Problem der Einlagerung

Übersicht Das gemischte Randwertproblem der Berührung zweier ebener elastischer Körper von beliebiger Form wird im Falle verschwindender Reibung in der Kontaktzone gelöst. Das Problem wird reduziert auf ein System von vier singulären Integralgleichungen, welche sich auf die Kontaktzone und die übrigen Ränder der zwei Körper beziehen. Das System wird mit zwei weiteren Gleichungen vervollständigt, welche von der Eindeutigkeit der Verschiebungen längs der berührenden Ränder hergeleitet werden. Die Lösung dieser Gleichungen gibt die Verteilung der Kontaktspannungen und die Kontaktlänge. Die Methode wird auf den symmetrischen Fall einer unendlichen elastischen Platte (mit und ohne axiale Kräfte auf den unendlich fernen Rändern), welche eine elastische Einlagerung mit Übermaß enthält, angewandt. Die Entwicklung der Kontaktauflösung und der Vorschrift der Lücke zwischen Einlagerung und Platte werden mit Hilfe der Lösung obiger Gleichungen angegeben.

     

Saint-Venant's problem for inhomogeneous and anisotropic elastic bodies

A method of solving Saint-Venant's problem for inhomogeneous and anisotropic elastic bodies is presented.     

Quasiperiodic contact problem for an elastic half-plane

Chuvash State University, Cheboksary. Translated from Prikladnaya Mekhanika, Vol. 28, No. 6, pp. 22–28, June, 1992.