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CivilComp Proceedings
ISSN 17593433 CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 100
Coupled ThermoElastic Nonlinear Finite Element Analysis of Thinwalled Structures H. Bossong, S. Lentzen and R. Schmidt
Institute of General Mechanics, RWTH Aachen University, Germany H. Bossong, S. Lentzen, R. Schmidt, "Coupled ThermoElastic Nonlinear Finite Element Analysis of Thinwalled Structures", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 100, 2007. doi:10.4203/ccp.86.100
Keywords: nonlinear thermoelasticity, thermomechanical coupling, firstorder shear deformation theory, finite elements, nonlinear shell theory.
Summary
Due to thermoelastic coupling solids and structures exhibit nonclassical physical effects, like e.g. strain rate dependent cooling or heating due to the action of tensile or compressive stresses, respectively, or damping of vibrations due to heat loss. These effects cannot be modelled by merely accounting for the effect of temperature changes on the strains in the constitutive equations. The truly thermomechanically coupled analysis of solids and structures is based on coupling of the thermal and mechanical quantities in the field equations.
Thermodynamically consistent theories of threedimensional thermoelasticity that account for the thermomechanical coupling have been developed in the early works of Biot [1], Boley [2], Nowacki [3,4,5]. Tauchert [6] presents the coupled equations of motion and heat transfer governing small displacements and temperature changes in thin isotropic plates. In the present paper, a thermodynamically consistent continuum mechanics based framework of thermoelasticity in convective coordinates is used as described in [7]. It includes the conservation laws of mass, linear and angular momentum, and energy in a geometrically and thermally nonlinear approach. The second principle of thermodynamics is used to derive the restrictions for the constitutive equations. On this basis weak formulations of the conditions of equilibrium and conservation of energy are derived that serve as a starting point for the nonlinear finite element analysis of structures. For the transition to twodimensional plate and shell theory, the firstorder shear deformation (ReissnerMindlin) hypothesis is used along with the hypothesis of a cubic throughthickness distribution of the temperature field. Two examples are computed, where in the first example heating of a rod due to compression is analysed and the numerical results are compared with experimental results available in literature. The second example deals with damping effects on thermally induced vibrations of a hinged square plate subject to a sudden change of temperature on one bounding surface. References
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