ANALYTICAL METHOD OF SOLVING PROBLEMS OF THERMOELASTICITY WITH PERIODIC CONDITIONS FOR MULTILAYER FOUNDATION

VELICHKO Igor G., Cand. Phys.-Math. Sc., Associate Professor, Head of the Department "Higher Mathematics and Physics", e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., Tavria State Agrotechnological University, Melitopol, Ukraine

A method for solving the two-dimensional stationary problem of thermoelasticity for multilayer foundations. The upper boundary of the temperature and pressure are described by periodic functions. At the lower boundary temperature and displacement zero. On the common boundary layers of the conditions of continuity of the temperature field and the equality of heat fluxes. The desired function in each layer are written in the form of Fourier series. To ensure the fulfillment of the conditions at the common borders layers of a modification of the method of compliance matrices. An algorithm for solving the problem. It is shown that the method gives the exact solution of the problem for any finite number of layers. According to the results of theoretical studies, numerical experiments. Formulate conclusions concerning the identified thermoelastic effects.

multilayer foundation, thermoelasticity, recurrence relations, compliance matrix, Fourier series, Fourier law

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