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Title:Successive approximations in nonlinear thermoelasticity
Author(s):Yarrington, Paul; Carlson, Donald E.
Mechanical Loading
Thermal Loading
Linear Heat Conduction
Abstract:Starting with the basic equations of finite thermoelasticity for an incompressible, isotropic, homogeneous body, the usual method of successive approximations is generalized by expanding the relevant fields in terms of two parameters. These parameters separately characterize the mechanical and thermal loading on the body. The successive equations are derived, and it is seen that at each order the basic equations are linear and completely uncoupled. The displacement is determined by the equations of linear isothermal elasticity, while the temperature field is determined by the equation of linear heat conduction. Solutions, through second-order terms, are found for the following problems: annular cylinder with axial mechanical loading and radial thermal loading, torsion of an axial heat conductor, sperical shell with radial mechanical and thermal loading, solid cylinder with axial mechanical and thermal loading, constrained annular cylinder with internal pressure and radial thermal loading.
Issue Date:1974-02
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 381
Genre:Technical Report
Sponsor:National Science Foundation, 74/02
Rights Information:Copyright 1974 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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