Uniqueness and stability of the solution to a thermoelastic contact problem

1990 ◽  
Vol 1 (4) ◽  
pp. 371-387 ◽  
Author(s):  
Peter Shi ◽  
Meir Shillor
Keyword(s):  
Differential Equation ◽  
Contact Problem ◽  
Continuous Dependence ◽  
Initial Temperature ◽  
Integral Transform ◽  
Coupling Constant ◽  
Frictionless Contact ◽  
Linear Thermoelasticity ◽  
Thermoelastic Contact Problem ◽  
Stability Of The Solution

Uniqueness and continuous dependence on the initial temperature are proved for a onedimensional, quasistatic and frictionless contact problem in linear thermoelasticity. First the problem is reformulated in such a way that it decouples. The resulting problem for the temperature is a nonlinear integro-differential equation. Once the temperature is known the displacement is recovered from an appropriate variational inequality. Uniqueness is proved by considering an integral transform of the temperature. The steady solution is obtained and the asymptotic stability is shown. It turns out that the asymptotic behaviour and the steady state are determined by a relation between the coupling constant a and the initial gap.

scholarly journals Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 851
Author(s):  
Robert Stegliński
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Weak Solution ◽  
Variational Methods ◽  
Unique Solution ◽  
Continuous Dependence ◽  
Fractional Laplacian ◽  
Unique Weak Solution ◽  
Fractional Partial Differential Equation ◽  
Integrodifferential Operator

In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the continuous dependence of the solution on parameters. In proofs we use monotonicity and variational methods.

Effect of anisotropy on thermoelastic contact problem

2008 ◽  
Vol 29 (4) ◽  
pp. 501-510 ◽  
Author(s):  
Sakti Pada Barik ◽  
M. Kanoria ◽  
P. K. Chaudhuri
Keyword(s):  
Contact Problem ◽  
Thermoelastic Contact ◽  
Thermoelastic Contact Problem

scholarly journals On the existence of positive solutions of a state-dependent neutral functional differential equation with two state-delay functions

2020 ◽  
Vol 4 (2) ◽  
pp. 132-141
Author(s):  
El-Sayed, A. M. A ◽  
◽  
Hamdallah, E. M. A ◽  
Ebead, H. R ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Functional Differential Equation ◽  
Continuous Dependence ◽  
Neutral Functional Differential Equation ◽  
Initial Value ◽  
State Delay ◽  
State Dependent ◽  
Existence Of Positive Solutions ◽  
Functional Differential

In this paper, we study the existence of positive solutions for an initial value problem of a state-dependent neutral functional differential equation with two state-delay functions. The continuous dependence of the unique solution will be proved. Some especial cases and examples will be given.

An incremental-iterative BEM methodology to solve 3D thermoelastic contact problem including variable thermal resistance in the contact zone

2019 ◽  
Vol 31 (5) ◽  
pp. 1543-1558 ◽  
Author(s):  
J. Vallepuga-Espinosa ◽  
Iván Ubero-Martínez ◽  
Lidia Sánchez-González ◽  
J. Cifuentes-Rodríguez
Keyword(s):  
Contact Problem ◽  
Thermal Resistance ◽  
Contact Zone ◽  
Thermoelastic Contact ◽  
Thermoelastic Contact Problem

Transient Solution of the Inhomogeneous Thermoelastic Contact Problem Using Fast Speed Expansion

2004 ◽  
Author(s):  
Jiayin Li ◽  
James R. Barber
Keyword(s):  
Contact Problem ◽  
Large Scale ◽  
Computation Time ◽  
Transient Solution ◽  
New Approach ◽  
Thermoelastic Contact ◽  
Fast Speed ◽  
Transient Problems ◽  
Transient Problem ◽  
Thermoelastic Contact Problem

Numerical integration has been widely used in commercial FEA software to solve transient problems. However, for the large-scale inhomogeneous thermoelastic contact problem (ITEC), this method is found to be extremely computation-intensive. This paper introduces a new approach to solve the ITEC transient problem with much lower computational complexity. The method is based on the transient modal analysis (TMA) method in conjunction with the fast speed expansion (FSE) method. The TMA method is used to obtain the inhomogeneous transient solution by expressing the solution in modal coordinates, corresponding to eigenfunctions of the homogeneous (unloaded) problem. If the sliding speed is constant, the eigenfunctions can be found by one run of the commercial software program ‘HotSpotter’. However, if the speed varies, the eigenfunctions change and numerous runs of HotSpotter are needed, making the method computationally inefficient. However, the FSE method employs an efficient algorithm to interpolate and expand the eigenfunctions and eigenvalues over a range of speeds. This reduces the number of eigenvalue solutions required and results in a significant reduction in computation time. The method is illustrated with application to an axisymmetric transmission clutch problem.

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