共查询到20条相似文献,搜索用时 596 毫秒
1.
This paper deals with the numerical solution of the wheel - rail rolling contact problems. The unilateral dynamic contact problem between a rigid wheel and a viscoelastic rail lying on a rigid foundation is considered. The contact with the generalized Coulomb friction law occurs at a portion of the boundary of the contacting bodies. The Coulomb friction model where the friction coefficient is assumed to be Lipschitz continuous function of the sliding velocity is assumed. Moreover Archard's law of wear in the contact zone is assumed. This contact problem is governed by the evolutionary variational inequality of the second order. Finite difference and finite element methods are used to discretize this dynamic contact problem. Numerical examples are provided. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally
supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model
(a slip bound is given a priori) but with a coefficient of friction $
\mathcal{F}
$
\mathcal{F}
which depends on a solution. It is shown that a solution exists for a large class of $
\mathcal{F}
$
\mathcal{F}
and is unique provided that $
\mathcal{F}
$
\mathcal{F}
is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite
elements, and convergence of discrete solutions is established. Finally, methods for numerical realization are described and
several model examples illustrate the efficiency of the proposed approach. 相似文献
3.
Andrzej Myśliński 《PAMM》2007,7(1):2060005-2060006
This paper deals with the numerical solution of a topology and shape optimization problems of an elastic body in unilateral contact with a rigid foundation. The contact problem with the prescribed friction is considered. The structural optimization problem consists in finding such shape of the boundary of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. In the paper shape as well as topological derivatives formulae of the cost functional are provided using material derivative and asymptotic expansion methods, respectively. These derivatives are employed to formulate necessary optimality condition for simultaneous shape and topology optimization. Level set based numerical algorithm for the solution of the shape optimization problem is proposed. Level set method is used to describe the position of the boundary of the body and its evolution on a fixed mesh. This evolution is governed by Hamilton – Jacobi equation. The speed vector field driving the propagation of the boundary of the body is given by the shape derivative of a cost functional with respect to the free boundary. Numerical examples are provided. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
5.
L. -E. Andersson 《Applied Mathematics and Optimization》2000,42(2):169-202
We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration
condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved
by the aid of an established shifting technique used to obtain increased regularity at the contact surface. The analysis is
carried out by the aid of auxiliary problems involving regularized friction terms and a so-called normal compliance penalization
technique.
\par
Accepted 15 May 2000. Online publication 6 October 2000. 相似文献
6.
7.
In this paper, a shape optimization problem over a multi-dimensional starlike domain with boundary payoff is considered. The
function, which characterizes the boundary of the domain with respect to some ball contained inside domain, is shown to be
Lipschitz continuous. The existence of an optimal solution is proved. 相似文献
8.
《数学物理学报(B辑英文版)》2017,(6)
We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator,the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle. 相似文献
9.
The present paper is concerned with the solution of a Bernoulli type free boundary problem by means of shape optimization. Two state functions are introduced, namely one which satisfies the mixed boundary value problem, whereas the second one satisfies the pure Dirichlet problem. The shape problem under consideration is the minimization of the L 2-distance of the gradients of the state functions. We compute the corresponding shape gradient and Hessian. By the investigation of sufficient second order conditions we prove algebraic ill-posedness of the present formulation. Our theoretical findings are supported by numerical experiments. 相似文献
10.
Using Ball's approach to non-linear elasticity, and in particular his concept of polyconvexity, we treat a unilateral three-dimensional contact problem for a hyperelastic body under volume and surface forces. Here the unilateral constraint is described by a sublinear function which can model the contact with a rigid convex cone. We obtain a solution to this generally non-convex, semicoercive Signorinin problem as a limit of solutions of related energy minimization problems involving friction normal to the contact surface where the friction coefficient goes to infinity. Thus we extend an approximation result of Duvaut and Lions for linear-elastic unilateral contact problems to finite deformations and to a class of non-linear elastic materials including the material models of Ogden and of Mooney-Rivlin for rubberlike materials. Moreover, the underlying penalty method is shown to be exact, that is a sufficiently large friction coefficient in the auxiliary energy minimization problems suffices to produce a solution of the original unilateral problem, provided a Lagrange multiplier to the unilateral constraint exists. 相似文献
11.
This paper is devoted to the study of a general dynamic variational–hemivariational inequality with history-dependent operators. These operators appear in a convex potential and in a locally Lipschitz superpotential. The existence and uniqueness of a solution to the inequality problem is explored through a result on a class of nonlinear evolutionary abstract inclusions involving a nonmonotone multivalued term described by the Clarke generalized gradient. The result presented in this paper is new and general. It can be applied to study various dynamic contact problems. As an illustrative example, we apply the theory on a dynamic frictional viscoelastic contact problem in which the contact is modeled by a nonmonotone Clarke subdifferential boundary condition and the friction is described by a version of the Coulomb law of dry friction with the friction bound depending on the total slip. 相似文献
12.
I.A. Soldatenkov 《Journal of Applied Mathematics and Mechanics》2013,77(2):245-255
A solution of the plane problem of the contact interaction of a periodic system of convex punches with an elastic half-plane is given for two forms of boundary conditions: 1) sliding of the punches when there is friction and wear, and 2) the indentation of the punches when there is adhesion. The problem is reduced to a canonical singular integral equation on the arc of a circle in the complex plane. The solution of this equation is expressed in terms of simple algebraic functions of a complex variable, which considerably simplifies its analysis. Asymptotic expressions are obtained for the solution of the problem in the case when the size of the contact area is small compared with the distance between the punches. 相似文献
13.
《Journal of Applied Mathematics and Mechanics》2007,71(4):632-642
The plane problem of the sliding contact of a punch with an elastic foundation when there is friction and wear is considered. Assuming the existence of a steady solution in a moving system of coordinates, relations are derived between the sliding velocity, the wear, the contact stresses and the displacements for an arbitrary dependence of the wear rate on the contact pressure. Taking into account the presence of a deformation component of the friction force, an equation is written for the balance of the mechanical energy for the punch - elastic base system considered. It is shown that the equality of the work of the external force in displacing the punch to the losses due to friction and the change in the shape of the foundation due to wear is satisfied when the work done by the contact stresses on the increments of the boundary displacements is equal to zero, and the frictional losses must be determined taking into account the non-uniformity of the distributions of the shear contact stresses and the sliding velocity in the contact area. Two special cases of the foundation in the form of a wide and narrow strip are considered, for which the total coefficient of friction is calculated, taking into account the deformation component of the friction force. 相似文献
14.
V.I. Ostrik 《Journal of Applied Mathematics and Mechanics》2013,77(4):433-444
The axisymmetric problem of the contact interaction of a punch of polynomial profile and an elastic half-space when there is friction and partial adhesion in the contact area is considered. Using the Wiener–Hopf method the problem is reduced to an infinite system of algebraic Poincare–Koch equations, the solution of which is obtained in series. The radii of the contact area and of the adhesion zone, the distribution of the contact pressures and the indentation of the punch are obtained. 相似文献
15.
《Journal of Applied Mathematics and Mechanics》2006,70(4):621-635
The main terms of the asymptotic form of the solution of the contact problem of the compression without friction of an elastic body and a punch initially in point contact are constructed by the method of matched asymptotic expansions using an improved matching procedure. The condition of unilateral contact is formulated taking account of tangential displacements on the contact surface. An asymptotic solution of the problem for the boundary layer is constructed by the complex potential method. An asymptotic model is constructed, extending the Hertz theory to the case where the surfaces of the punch and elastic body in the vicinity of the contact area are approximated by paraboloids of revolution. The problem of determining the convergence of the contacting bodies from the magnitude of the compressive force is reduced to the problem of calculating the so-called coefficient of local compliance, which is an integral characteristic of the geometry of the elastic body and its fixing conditions. 相似文献
16.
In this paper we study the problem of three-dimensional layout optimization on the simplified rotating vessel of satellite. The layout optimization model with behavioral constraints is established and some effective and convenient conditions of performance optimization are presented. Moreover, we prove that the performance objective function is locally Lipschitz continuous and the results on the relations between the local optimal solution and the global optimal solution are derived. 相似文献
17.
L. C. Ceng B. S. Mordukhovich J. C. Yao 《Journal of Optimization Theory and Applications》2010,146(2):267-303
This paper studies a general vector optimization problem of finding weakly efficient points for mappings from Hilbert spaces
to arbitrary Banach spaces, where the latter are partially ordered by some closed, convex, and pointed cones with nonempty
interiors. To find solutions of this vector optimization problem, we introduce an auxiliary variational inequality problem
for a monotone and Lipschitz continuous mapping. The approximate proximal method in vector optimization is extended to develop
a hybrid approximate proximal method for the general vector optimization problem under consideration by combining an extragradient
method to find a solution of the variational inequality problem and an approximate proximal point method for finding a root
of a maximal monotone operator. In this hybrid approximate proximal method, the subproblems consist of finding approximate
solutions to the variational inequality problem for monotone and Lipschitz continuous mapping, and then finding weakly efficient
points for a suitable regularization of the original mapping. We present both absolute and relative versions of our hybrid
algorithm in which the subproblems are solved only approximately. The weak convergence of the generated sequence to a weak
efficient point is established under quite mild assumptions. In addition, we develop some extensions of our hybrid algorithms
for vector optimization by using Bregman-type functions. 相似文献
18.
19.
Stanis?aw Migórski Anna Ochal Mircea Sofonea 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,94(3):99-113
We consider two mathematical models that describe the vibrations of spring-mass-damper systems with contact and friction.
In the first model, both the contact and frictional boundary conditions are described with subdifferentials of nonconvex functions.
In the second model, the contact is modeled with a Lipschitz continuous function, and the restitution force is described by
a differential equation involving a Volterra integral term. The two models lead to second-order differential inclusions with
and without an integral term, in which the unknowns are the positions of the masses. For each model, we prove the existence
of a solution by using an abstract result for first-order differential inclusions in finite dimensional spaces. For the second
model, in addition, we prove the uniqueness of the solution by using a fixed point argument. Finally, we provide examples
of systems with contact and friction conditions for which our results are valid. 相似文献
20.
Stanisław Migórski Anna Ochal Mircea Sofonea 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,62(1):99-113
We consider two mathematical models that describe the vibrations of spring-mass-damper systems with contact and friction. In the first model, both the contact and frictional boundary conditions are described with subdifferentials of nonconvex functions. In the second model, the contact is modeled with a Lipschitz continuous function, and the restitution force is described by a differential equation involving a Volterra integral term. The two models lead to second-order differential inclusions with and without an integral term, in which the unknowns are the positions of the masses. For each model, we prove the existence of a solution by using an abstract result for first-order differential inclusions in finite dimensional spaces. For the second model, in addition, we prove the uniqueness of the solution by using a fixed point argument. Finally, we provide examples of systems with contact and friction conditions for which our results are valid. 相似文献