Trefftz Method of Solving a 1D Coupled Thermoelasticity Problem for One- and Two-Layered Media

Artur Maciąg and Krzysztof Grysa
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Artur Maciąg: Faculty of Management and Computer Modeling, Kielce University of Technology, 25-314 Kielce, Poland
Krzysztof Grysa: Faculty of Management and Computer Modeling, Kielce University of Technology, 25-314 Kielce, Poland

Energies, 2021, vol. 14, issue 12, 1-16

Abstract: This paper discusses a 1D one-dimensional mathematical model for the thermoelasticity problem in a two-layer plate. Basic equations in dimensionless form contain both temperature and displacement. General solutions of homogeneous equations (displacement and temperature equations) are assumed to be a linear combination of Trefftz functions. Particular solutions of these equations are then expressed with appropriately constructed sums of derivatives of general solutions. Next, the inverse operators to those appearing in homogeneous equations are defined and applied to the right-hand sides of inhomogeneous equations. Thus, two systems of functions are obtained, satisfying strictly a fully coupled system of equations. To determine the unknown coefficients of these linear combinations, a functional is constructed that describes the error of meeting the initial and boundary conditions by approximate solutions. The minimization of the functional leads to an approximate solution to the problem under consideration. The solutions for one layer and for a two-layer plate are graphically presented and analyzed, illustrating the possible application of the method. Our results show that increasing the number of Trefftz functions leads to the reduction of differences between successive approximations.

Keywords: thermoelasticity; composite materials; Trefftz method; inverse operator (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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