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Article
NUMERICAL STUDY OF WAVE PROPAGATION IN NONLINEAR DISSIPATIVE MATERIAL
We have investigated a class of materials whose experimental stress–strain behavior does not allow them to be considered plastic or elastic. They are not elastic since unloading occurs along a curve significan...
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Article
NUMERICAL SOLUTION OF THE PROBLEM OF DEFORMATION OF ELASTIC SOLIDS UNDER PULSED LOADING
Three methods of approximation of lower non-differential terms in equations of dynamic problems of mechanics of deformable solids are studied with the use of explicit algorithms of the numerical solution based...
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Article
Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves
Regularization techniques for the trace and the traction of elastic waves potentials previously built for domains of the class C2 are extended to the Lipschitz case. In particular, this yields an elementary way t...
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Article
Modified equations of finite-size layered plates made of orthotropic material. Comparison of the results of numerical calculations with analytical solutions
This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by ...
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Article
Nonclassical models of the theory of plates and shells
Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are ...
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Article
Equation of a layered packet with transverse shears and compression taken into account
The equations describing a layered packet with transverse shears and compression taken into account in all layers are constructed in this paper. The layer material is assumed to be elastic and transversely iso...
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Article
Equations of cylindrical bending of orthotropic plates with arbitrary conditions on their front surfaces
Based on approximations of solutions of elasticity theory equations by Legendre polynomial segments, differential equations for bending of orthotropic plates are constructed. In contrast to equations construct...
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Article
Numerical solving dynamic problems of elastoplastic deformation of solids
Numerical schemes for solving two-dimensional dynamic problems of elasticity theory based upon several local approximations for each of the required functions are discussed. The schemes contain free parameters...
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Article
Rabotnov’s two-layer model of a shell and critical time of shell buckling during creep
The main propositions of Rabotnov’s two-layer model of a shell are given. It is shown that the Rabotnov’s functional can be obtained from the mixed variational principle of creep theory. The notion of critical...
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Article
Solution of contact problems on the basis of a refined theory of plates and shells
Solutions of contact mixed boundary-value problems for a plate and for a cylindrical shell are given. These solutions are obtained with the use of equations for shells constructed by expanding solutions of ela...
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Article
Reducing three-dimensional elasticity problems to two-dimensional problems by approximating stresses and displacements by legendre polynomials
Shell equations are constructed in orthogonal curvilinear coordinates using approximations of stresses and displacements by Legendre polynomials. The order of the constructed system of differential equations i...
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Article
Equations of an Elastic Anisotropic Layer
Differential equations of an elastic orthotropic layer are constructed on the basis of expansion of the solutions of the elasticity theory in terms of the Legendre polynomials. The order of the system of diffe...
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Article
Quasi-one-dimensional model of the rod-target interaction
Numerical techniques are proposed for determining the integral characteristics of penetration of a rod into an target. An algorithm for solving two-dimensional elastoplastic problems is employed. To construct ...
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Article
Edge effects in the stress state of a thin elastic interlayer
The edge effects in the stress state of an interlayer in stretching and shearing by rigid slabs are studied. On the basis of the equations of momentless and moment elastic layers, we solve problems modeling qu...
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Article
Numerical modeling of stress states in two-dimensional problems of elasticity by the layers method
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Article
Calculation of plane equilibrium shapes of thin rods by the method of self-equilibrating variances
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Article
Estimate of limit load of elastic-plastic shells of revolution
