Analytical solution of the thermoelasticity problem in a pressurized thick-walled sphere subjected to transient thermal loading

Shahani, A.R.; Bashusqeh, Saeed Momeni

doi:10.1177/1081286512455657

Cited by 7 publications

(2 citation statements)

References 11 publications

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“…Jabbari et al [22, 23] studied coupled linear thermoelasticity and gave exact solutions in the case of a radially symmetric problem in both spherical and cylindrical geometries. Shahani et al [24–26] analytically solved the steady-state and the dynamical problem of uncoupled linear thermoelasticity in a thick-walled cylinder and a sphere.…”

Section: Introductionmentioning

confidence: 99%

Geometric nonlinear thermoelasticity and the time evolution of thermal stresses

Sadik

Yavari

2015

Mathematics and Mechanics of Solids

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In this paper we formulate a geometric theory of nonlinear thermoelasticity that can be used to calculate the time evolution of temperature and thermal stress fields in a nonlinear elastic body. In particular, this formulation can be used to calculate residual thermal stresses. In this theory the material manifold (natural stress-free configuration of the body) is a Riemannian manifold with a temperature-dependent metric. Evolution of the geometry of the material manifold is governed by a generalized heat equation. As examples, we consider an infinitely long circular cylindrical bar with a cylindrically symmetric temperature distribution and a spherical ball with a spherically-symmetric temperature distribution. In both cases we assume that the body is made of an arbitrary incompressible isotropic solid. We numerically solve for the evolution of thermal stress fields induced by thermal inclusions in both a cylindrical bar and a spherical ball, and compare the linear and nonlinear solutions for a generalized neo-Hookean material.

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Section: Introductionmentioning

confidence: 99%

Geometric nonlinear thermoelasticity and the time evolution of thermal stresses

Sadik

Yavari

2015

Mathematics and Mechanics of Solids

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“…The thermoelasticity has been used in several areas, especially for the application of static problems (Copetti, 1999;Shahani and Nabavi, 2007) and dynamic problems (Chen and Dargush, 1995;Norris, 2006;Shahani and Bashusqeh, 2014). Other analysis methods have been adopted to deal with coupled thermoelastic problems.…”

Section: The Coupled Thermomechanicalmentioning

confidence: 99%

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

Cavalcante

Maciel

Greco

et al. 2017

Lat. Am. j. solids struct.

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The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.

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