Mechanics |
|
 |
2007, No. 6
A.N. Roshtova
ON LIMIT STATICAL DETACHMENT CONDITIONS FOR A COMPRESSIBLE ANISOTROPIC SOLID
In this paper limit statical detachment conditions in the case when this conditions depend on average pressure and detachment direction are considered. A spatial problem is discussed for the case of equating two principal stresses to the limit detachment value and for the case of equating a principal stress to the limit detachment value. Properties of the a stress-strain state observed at a detachment are studied. Analytical type of the involved equations is analyzed and characteristic surfaces are obtained.
S.V. Tikhonov
ON AN ELASTIC-PLASTIC STATE OF THICK-WALLED INHOMOGENEOUS TUBE UNDER INTERNAL PRESSURE
In this paper an elastic-plastic state of a thick-walled tube under internal pressure is considered. The tube is isotropic, inhomogeneous, keeping constant value of a yield strength to constants along lines of concentric ellipses. The effect of inhomogeneity on a stress state of the tube is analyzed. A method of identification of material heterogeneity properties on an example of concentric ellipses can be extended to other various curves along which the yield strength keeps constant value. It is demonstrated by an example given in the paper.
M.M.Aliev, M.M. Bayburova
ANISOTROPIC MATERIALS SHORT-TIME STRENGTH CRITERIA AND THEIR APPLICATION TO LIMIT STATE PROBLEMS
In the paper short-time strength criteria for anisotropic constructional materials, metals and rocks and their application to derivation of limit equilibrium state estimates are considered. K.V. Zakharov’s and I.I.Goldenblatt–V.A.Kopnov’s criteria are analysed in detail. Independent experiments, which are necessary to material constants identification (five strength constants) and used in K.V. Zakharov’s criterion formulation are discussed for plane stress state. General equations of plane strain state in the six-constant form due to K.V. Zakhrov’s plasticity criterion are analysed.
A.V. Belokon, O.A. Belokon, A.I. Bolgova
WAVES IN THREE-DIMENSIONAL LAYER WITH A THIN PLATE ON THE TOP
The paper is devoted to a study of the influence of the effect of irregularly distributed load in arbitrary area to the forming wave fields and energy flow. For rectangular area asymptotic formulas for evaluation of wave fields forming from effect of the load which changes along the Y axis and is constant along the X axis are given.
V.A. Kovalev, O.V. Taranov
Problems of application of asymptotic methods to a non-stationary stressstrain state are studied at face effect of normal type on shock of half-stripe. The solution is analysed on the basis of approximate asymptotic equations obtained by the symbolic Lurye method. The exact solution of the 3D elasticity equations found with the help of Laplace and Fourier transforms is analysed. For a boundary layer in a vicinity of conditional front of superficial Rayleigh waves in the half-stripe are shown that the main components of solutions by the exact and approximate theories are asymptotically coincided.
V.A. Kolesnickov
WAVE FIELD IN THE EXTERIOR OF A MOVING CYLINDER IN ELASTOPLASTIC MEDIUM
The propagation of cylindrical waves radiated by a cylinder expanding and moving along its axis in elastoplastic medium is studied. In the paper the elastoplastic medium with shear characteristics described by Saint-Venant-Mises formulas is considered. Asymptotic representation of the problem solution for various material parameters is discussed in details. The solution of a boundary layer type is used in a vicinity of cylindrical surface. The limits of applicability of asymptotic expansion are found.
A.A. Lukyanov, V.B. Pen’kov
NUMERICAL SIMULATION OF SOLIDS DEFORMATION BY A MESHLESS METHOD
A meshless method used in the numerical simulation of solid body deformation is considered. A brief description of the method and basic discrete relations used in the numerical simulations are presented. The finite elasto-plastic plate impact problem is numerically resolved. The state parameters distribution of solid bodies (effective plastic strain, stress) are obtained.
A.A. Markin, Dao VanDoan
A DISCRETE MODEL OF SEPARATION PROCESS IN SOLIDS
A process of formation of new material surfaces is considered from thermomechanical viewpoint. The typical length scale — an interaction layer, material of which forms surface layers of separated bodies — is introduced. Processes of steady and unsteady separation are discussed.
N.N. Okulova
NUMERICAL AND ANALYTICAL ANALYSIS OF STRESSES DISTRIBUTION PROBLEM IN A VISCOPLASTIC BAND
Formulation and solution of the problem of distribution of stresses in a viscoplastic band are given. One boundary of the band is tractions to be free of stress as well as shear stress acts along another one. An analysis of the problem is carried out by numerical and analytical ways. A method for solving of this kind of problems is proposed. The finite difference scheme of the problem is constructed such that an obtaining of mesh knots and corresponding stress values there as well as a thickness of flow zone is carried out in parallel regime in process of transition from one time layer to another.
S.A. Panteleyev
The problem of stability under uniaxial compression for a nonlinearly elastic body of the shape of rectangular parallelepiped (the block) is considered in the paper. The energy criterion is used as the criterion for stability/instability. The work is aimed at determining the sufficient conditions for instability of the equilibrium state of the block under compression. The method of analysis is based upon usage of some kinematic hypotheses, i.e. upon reduction of the class of kinematically admissible displacement fields. The method used results in obtaining some upper estimates for the critical value of the loading parameter, by which the coefficient of axial compression of the block is taken here. Used are the following two reduced classes of the fields: 1) the one corresponding to hypothesis of the orthogonal flat cross-sections; 2) that formed by the extremals of corresponding modified Korn’s problem. The estimates for the critical values of compression coefficient are obtained in an analytical form and depend on mutual relations of spatial dimensions of the block. A comparative analysis of the estimates corresponding to the above-mentioned two classes, is carried out. It is revealed that the estimate corresponding to the second class appears to be lower (i.e. better) for every geometry considered, but for thin blocks the difference between the estimates is small, whereas the thicker the block, the more appreciable is the difference. For each class there is its own range of thickness beyond which the instability is not found; however, for the second one it is significantly wider and includes the blocks of rather great thickness.
Y.N. Radayev
ON THE ISHLINSKY COMMUTATIVE EQUATIONS IN THE MATHEMATICAL THEORY OF PLASTICITY
A new discussion of fundamental principles of incremental mathematical theory of plasticity for three-dimensional states is given. Relations consequent to the generalized flow rule formulated for an edge of the Coulomb-Tresca prism are analyzed. The Ishlinsky constitutive equations of the mathematical plasticity proposed in 1946 are shown can be derived from the generalized flow rule stating the commutative law for the stress tensor and plastic strain increment tensor.