共查询到20条相似文献,搜索用时 421 毫秒
1.
《Journal of Applied Mathematics and Mechanics》2005,69(2):263-267
A three-dimensional linearly elastic (viscoelastic) domain (finite or infinite) containing a physically non-linear inclusion of arbitrary shape is considered. The possibility of creating a prescribed uniform stress-strain state in the inclusion by a suitable choice of loads on the outer boundary of the domain is considered. A solution is constructed in closed form. Some examples are considered, including, in particular, the case of an ellipsoidal inclusion with the property of non-linear creep. 相似文献
2.
N. A. Kazarinov E. M. Rudoy V. Yu. Slesarenko V. V. Shcherbakov 《Computational Mathematics and Mathematical Physics》2018,58(5):761-774
A boundary value problem describing the equilibrium of a two-dimensional linear elastic body with a thin rectilinear elastic inclusion and possible delamination is considered. The stress and strain state of the inclusion is described using the equations of the Euler–Bernoulli beam theory. Delamination means the existence of a crack between the inclusion and the elastic matrix. Nonlinear boundary conditions preventing crack face interpenetration are imposed on the crack faces. As a result, problem with an unknown contact domain is obtained. The problem is solved numerically by applying an iterative algorithm based on the domain decomposition method and an Uzawa-type algorithm for solving variational inequalities. Numerical results illustrating the efficiency of the proposed algorithm are presented. 相似文献
3.
R. S. Ismagilov 《Functional Analysis and Its Applications》2003,37(3):191-202
A compact oriented surface with a given area form is considered. For each coordinate domain, we take the group of diffeomorphisms supported in this domain and preserving the area form. Finally, consider codimension 1 normal subgroups in these groups. For each pair of coordinate domains one of which contains the closure of the other, there is an obvious inclusion of the corresponding groups. We describe the inductive limits (amalgams) of these two families of groups. 相似文献
4.
Ants Aasma 《Applied Mathematics Letters》2012,25(3):404-407
In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely convergent series are characterized. As an application, the special case where A is the Cesàro matrix is considered. 相似文献
5.
E. M. Rudoy 《Journal of Applied and Industrial Mathematics》2016,10(2):264-276
Under consideration is a 2D-problem of elasticity theory for a body with a thin rigid inclusion. It is assumed that there is a delamination crack between the rigid inclusion and the elastic matrix. At the crack faces, the boundary conditions are set in the form of inequalities providing mutual nonpenetration of the crack faces. Some numerical method is proposed for solving the problem, based on domain decomposition and the Uzawa algorithm for solving variational inequalities.We give an example of numerical calculation by the finite element method. 相似文献
6.
《Mathematical Methods in the Applied Sciences》2018,41(10):3605-3621
Scattering of monochromatic waves on an isolated inhomogeneity (inclusion) in an infinite poroelastic medium is considered. Wave propagation in the medium and the inclusion are described by Biot's equations of poroelasticity. The problem is reduced to 3D‐integro‐differential equations for displacement and pressure fields in the region occupied by the inclusion. Properties of the integral operators in these equations are studied. Discontinuities of the fields on the inclusion boundary are indicated. The case of a thin inclusion with low permeability is considered. The corresponding scattering problem is reduced to a 2D integral equation on the middle surface of the inclusion. The unknown function in this equation is the pressure jump in the transverse direction to the inclusion middle surface. An inclusion with a thin layer of low permeability on its interface is considered. The appropriate boundary conditions on the inclusion interface are pointed out. Methods of numerical solution of the volume integral equations of the scattering problems of poroelasticity are discussed. 相似文献
7.
M. A. Grekov 《Vestnik St. Petersburg University: Mathematics》2010,43(2):114-121
An elastic infinite plane containing a circular inclusion with given jumps of tractions and displacements along the interface
and nonzero conditions at infinity is considered. Explicit expressions are derived for the Goursat-Kolosov complex potentials
of this problem. The solution constructed can be used to examine various circular interfacial defects, including interfacial
cracks and rigid parts of the interface. The problem under consideration is fundamental for the superposition method, which
solves many problems in which a circular region is an element of a polyphase elastic medium. In such cases, the well-posedness
of the problem, which depends on the interrelation between the jumps of tractions and displacements, follows from the very
superposition method. The application techniques of this method are demonstrated for singular problems on the action of a
point force and an edge dislocation located inside an inclusion or in the matrix. Computational results for the tractions
arising at the interface under the action of a point force concentrated in the inclusion are given. 相似文献
8.
One solves the problem of the determination of the state of stress in an anisotropic half-plane in the presence of an elliptic inclusion of the same material, subjected to a preliminary strain. This problem is equivalent to the problem of the determination of the state of stress in a half-plane, due to a thermal patch, coinciding with the inclusion domain. The solution of the problem is given in complex potentials. The case of an orthotropic half-plane with a circular inclusion is considered in detail. The results are illustrated by graphs.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 79–86, 1987. 相似文献
9.
D. V. Grilitskii V. K. Opanasovich L. O. Tisovskii 《Journal of Applied Mathematics and Mechanics》1982,46(6):798-804
There is considered the problem of the state of stress of an infinite elastic plane with a bonded circular plug and an arbitrarily located thin elastic inclusion under biaxial tension. Conditions of ideal mechanical contact are satisfied on the line separating the materials. By using the complex Kolosov — Muskhelishvili potentials, the problem is reduced to a system of integro-differential equations which is solved numerically by utilization of a mechanical quadrature method. A numerical analysis is given for the solution of the problem of the elastic equilibrium of a plane with a circular hole and an arbitrarily located thin inclusion. 相似文献
10.
T. S. Popova 《Journal of Applied and Industrial Mathematics》2018,12(2):313-324
Under study are the equilibrium problems for a two-dimensional viscoelastic body with delaminated thin inclusions in the cases of elastic and rigid inclusions. Both variational and differential formulations of the problems with nonlinear boundary conditions are presented; their unique solvability is substantiated. For the case of a thin elastic inclusion modelled as a Bernoulli–Euler beam, we consider the passage to the limit as the rigidity parameter of the inclusion tends to infinity. In the limit it is the problem about a thin rigid inclusion. Relationship is established between the problems about thin rigid inclusions and the previously considered problems about volume rigid inclusions. The corresponding passage to the limit is justified in the case of inclusions without delamination. 相似文献
11.
A. A. Levakov 《Differential Equations》2018,54(10):1321-1337
In a separable Hilbert space, a stochastic differential inclusion with coefficients whose values are closed not necessarily convex sets is considered. Two existence theorems for strong solutions are proved. In the first theorem, the proof is based on the use of Euler polygonal lines; in the second, on the successive approximation method. Instead of the assumption that the coefficients of the inclusion are globally Lipschitz, which is traditional in such cases, some conditions that are less restrictive for the problems in question are used. 相似文献
12.
We consider the Poisson equation in a domain with a small inclusion. We present a simple numerical method, based on asymptotic analysis, which allows to approximate robustly the far field of the solution as the size of the inclusion goes to zero without any mesh adaptation procedure. The discretization is based on a fully standard Galerkin approach such as finite elements. We prove stability and consistency of the numerical method and provide error estimates. We end the paper with numerical experiments illustrating the efficiency of the technique. 相似文献
13.
V. V. Dyakin V. Ya. Raevskii O. V. Umergalina 《Computational Mathematics and Mathematical Physics》2009,49(1):172-182
A direct magnetostatic problem for magnets with a finite-size inclusion is considered in an integrodifferential form. An approach is used that, under certain conditions, reduces the problem to a single integral equation on a two-dimensional manifold-the inclusion surface. As an important illustrative example, finite formulas are derived to compute the resulting field of a magnetic half-space with a spherical cavity in an arbitrary external field. 相似文献
14.
A. A. Tolstonogov 《Proceedings of the Steklov Institute of Mathematics》2016,293(1):199-215
An evolution inclusion with the right-hand side containing the difference of subdifferentials of proper convex lower semicontinuous functions and a multivalued perturbation whose values are nonconvex closed sets is considered in a separable Hilbert space. In addition to the original inclusion, we consider an inclusion with convexified perturbation and a perturbation whose values are extremal points of the convexified perturbation that also belong to the values of the original perturbation. Questions of the existence of solutions under various perturbations are studied and relations between solutions are established. The primary focus is on the weakening of assumptions on the perturbation as compared to the known assumptions under which existence and relaxation theorems are valid. All our assumptions, in contrast to the known assumptions, concern the convexified rather than original perturbation. 相似文献
15.
This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously. 相似文献
16.
17.
《Journal of Applied Mathematics and Mechanics》2006,70(1):56-64
The plane motions of a controlled single-link pendulum with a fixed suspension point and a pendulum with its suspension point located at the centre of a wheel which rolls without sliding along a flat horizontal surface are considered. The control torque, applied to the pendulum at the suspension point, is bounded in absolute magnitude. A controllability domain is constructed in the linear approximation for the one and the other pendulum, from all points of which the pendulum can be brought into the upper unstable equilibrium position without oscillations about the lower equilibrium. It is shown that the domain of controllability is greater for a pendulum mounted on a wheel, as a result it is more easily stabilizable. Control laws are constructed, under which the domain of attraction is identical to the controllability domain and is thereby the largest possible domain. 相似文献
18.
《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4694-4705
The stationary differential systems with polynomial right sides are considered. Necessary and sufficient conditions are formulated when a given domain is a domain of asymptotic stability and the origin of coordinates is either the focus or the center. The problem of construction of a stabilizing control in a form of polynomial is studied. 相似文献
19.
The stationary differential systems with polynomial right sides are considered. Necessary and sufficient conditions are formulated when a given domain is a domain of asymptotic stability and the origin of coordinates is either the focus or the center. The problem of construction of a stabilizing control in a form of polynomial is studied. 相似文献
20.
Summary A family of inclusion sets for the zeros of a complex polynomial is derived from the Lagrangean interpolation formulas. The optimization of the inclusion leads to a special type of matrix eigenvalue problem previously considered by several authors in connection with minimal Gershgorin discs. 相似文献