The Thermoelastic and Viscoelastic Contact of Two Rods

Rivera, Jaime E. Muñoz; Jiang, Song

doi:10.1006/jmaa.1997.5717

Cited by 20 publications

(2 citation statements)

References 14 publications

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“…In order to model the contact with the deformable obstacle, we use a modification of the well‐known normal compliance contact condition introduced, for instance, in [], which has the following form (see []):

σ false(ℓ, t false) = - \frac{1}{ε} {[u false(ℓ, t false) - g]}_{+} - ε u_{t} false(ℓ, t false) for a.e. t \in false[0, T false],

where

0true \frac{1}{ε} > 0

is a deformability coefficient and

{false[\cdot false]}_{+}

denotes the positive part, i.e.

{[f]}_{+} = max false{f, 0 false}

for

f \in R

.…”

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

Numerical analysis of a contact problem in poro‐thermoelasticity with microtemperatures

Bazarra

2018

Z Angew Math Mech

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A dynamic contact problem, between a thermoelastic rod with voids and microtemperatures and a deformable obstacle, is numerically investigated in this work. The contact is modelled with a modification of the classical normal compliance contact condition. The mechanical problem consists of a coupled system of two hyperbolic partial differential equations and two parabolic ones. An existence and uniqueness result, and an energy decay property, are stated. Then, fully discrete approximations are introduced to approximate this nonlinear problem by using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximation and the behaviour of the solution.

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σ false(ℓ, t false) = - \frac{1}{ε} {[u false(ℓ, t false) - g]}_{+} - ε u_{t} false(ℓ, t false) for a.e. t \in false[0, T false],

where

0true \frac{1}{ε} > 0

is a deformability coefficient and

{false[\cdot false]}_{+}

denotes the positive part, i.e.

{[f]}_{+} = max false{f, 0 false}

for

f \in R

.…”

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

Numerical analysis of a contact problem in poro‐thermoelasticity with microtemperatures

Bazarra

2018

Z Angew Math Mech

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“…A direct incremental formulation of the constitutive equations for the linear viscoelastic media was presented by Zocher et al [9]. Rivera and Jiang [10] considered the thermo elastic and viscoelastic contact problem of two rods and proved the existence of a weak solution using a penalization method. Baranoglu and Mengi [11] developed a boundary element method in a unified form for the analysis of both coupled and uncoupled thermoviscoelastic problems.…”

Section: Introductionmentioning

confidence: 99%

An FEM Approach for Three-Dimensional Thermoviscoelastic Stress Analysis of Orthotropic Cylinders Made of Polymers

Ashrafi

Keshmiri

Bahadori

et al. 2013

AMR

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The objective of this study is to develop a general finite element formulation associated with an incremental adaptive procedure which established for thermoviscoelastic stress analysis of orthotropic cylinders made of polymers. This paper concerned with development of a numerical algorithm for the solution of the quasistatic initial/boundary value problems involving the linear viscoelastic media with thermal and mechanical deformations. The viscoelastic constitutive equations, represented in an integral form and involving relaxation functions, are transformed into an incremental algebraic relation. An incremental relaxation is then developed for the finite element formulation to deal with quasistatic thermoviscoelastic problems.

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Numerical analysis of a contact problem between two thermoviscoelastic beams

Copetti

2010

Numer. Methods Partial Differential Eq.

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The Thermoelastic and Viscoelastic Contact of Two Rods

Cited by 20 publications

References 14 publications

Numerical analysis of a contact problem in poro‐thermoelasticity with microtemperatures

Numerical analysis of a contact problem in poro‐thermoelasticity with microtemperatures

An FEM Approach for Three-Dimensional Thermoviscoelastic Stress Analysis of Orthotropic Cylinders Made of Polymers

Numerical analysis of a contact problem between two thermoviscoelastic beams

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