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A mathematical model of buckling of three-dimensional structures is considered, considering the thermal effect on them. The proposed methodology for studying stability consists in solving a system of three problems: thermal conductivity, quasi-static linear thermoelasticity, and, in fact, the problem of buckling theory. The first two tasks correspond to the basic state of the structure, and the third to the varied one, which occurs when the structure loses its stability. The approach described in the work allows considering the influence on the buckling of the structure not only of three-dimensional phenomena (holes, joined local element etc.) but also the influence of thermal stresses. In the study, an algorithm for solving the buckling problem is considered and a variational statement is formulated. The presented model was tested on the rod buckling problem, which showed good agreement with the results obtained in CAE ANSYS software. The modelling presented was carried out in the SMCM software, developed by SIMPLEX Scientific and Educational Centre of Bauman Moscow State Technical University.

Mathematical and numerical models of buckling of three-dimensional structures taking into account the thermal effect