A fast meshfree technique for the coupled thermoelasticity problem

2018 ◽  
Vol 229 (6) ◽  
pp. 2657-2673 ◽  
Author(s):  
Kourosh Hasanpour ◽  
Davoud Mirzaei
Keyword(s):  
Thermoelasticity Problem ◽  
Coupled Thermoelasticity

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

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3637
Author(s):  
Artur Maciąg ◽  
Krzysztof Grysa
Keyword(s):  
Coupled System ◽  
Approximate Solutions ◽  
Thermoelasticity Problem ◽  
Successive Approximations ◽  
Trefftz Method ◽  
Coupled Thermoelasticity ◽  
General Solutions ◽  
Basic Equations ◽  
The Right ◽  
Derivatives Of

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.

The coupled thermoelasticity problem for thin plates

1992 ◽  
Vol 62 (1) ◽  
pp. 2489-2493
Author(s):  
Ya. S. Podstrigach ◽  
Yu. A. Chernukha
Keyword(s):  
Thermoelasticity Problem ◽  
Thin Plates ◽  
Coupled Thermoelasticity
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