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CNAA / Theses / 2018 / July /

Integral solutions in uncoupled thermoelasticity

Author: Creţu Ion
Degree:doctor of engineering
Speciality: 01.04.27 - Mechanics of deformable solids
Scientific adviser: Victor Şeremeţ
doctor habilitat, professor
Institution: Technical University of Moldova


The thesis was presented on the 27 July, 2018
Approved by NCAA on the 23 November, 2018


Adobe PDF document3.98 Mb / in romanian


CZU 539.3:517.9(043.2)

Adobe PDF document 16.00 Mb / in romanian
142 pages


integral solutions, thermoelasticity, Green’s functions, influence functions, thermal displacements, thermal stresses, boundary conditions, volume dilatation


The thesis structure: introduction, three chapters, conclusions, 120 pages of basic text including 39 figures, bibliography containing 122 sources and 4 Annexes. Results are published in 10 articles.

The field of the investigation: theory of thermoelasticity. The thesis aim: obtaining integral solutions in uncoupled thermoelasticity by generalizing the harmonic integral representation method (HIRM), using the Maysel’s method (MM) and the GΘ convolution method (GΘ-CM) for new boundary value problems for various canonical domains.

The objectives: construction of Green’s functions; obtaining integral solutions for the temperature field based on Green’s functions; general integral representations of the main thermoelastic Green’s functions (MTGFs); determination of MTGFs based on general representations using HIRM for the Cartesian coordinate system and GΘ-CM for the spherical canonical domain; сalculating some surface and volume integrals to get the integral solutions; solving particular problems in uncoupled thermoelasticity based on integral solutions using HIRM, GΘ-CM and the methodology of application of the Maysel’s formula; plotting graphs using the Maple 18 program and their subsequent analysis for the MTGFs and analytical solutions for the temperature field, thermal displacements and stresses; validation of the results obtained.

Scientific novelty and originality of the results: to increase the arsenal with integral solutions obtained in solving boundary value problems by generalizing the HIRM for Cartesian canonical domains and the GΘ-CM for the spherical canonical domain and use of integral solutions to solve particular new boundary value problems of thermal elasticity.

The theoretical importance: developing the HIRM and the GΘ-CM for cartesian and spherical domains by obtaining integral solutions with the help of which problems of uncoupled thermoelasticity can be solved.

The applied value: HIRM and the GΘ-CM had a contribution to increase the arsenal of integral solutions in the field of solid body mechanics. These are of major importance due to the possibilities of solving other new boundary problems in the field, or can be used as test problems for validation classic methods.

The scientific results implementation. The results obtained can be applied to the determination of thermal displacements and stresses for domains that have the same shape as the calculated domain, including building elements, and not only (strip - building wall, half-strip - wall near the door or window, spherical wedge - welding seam etc.).