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Information × Registration Number 0200U004003, 0198U004857 , R & D reports Title Mathematical modeling of processes of evolutionary interaction of physic-mechanical fields popup.stage_title Head Shynkarenko Georgij Andrijovych, Registration Date 08-10-2001 Organization Ivan Franko National University of Lviv popup.description2 The mathematical models of non-stationary acoustic interaction of elastic bodies and shells with liquids, nonlinear behaviour flexible multilayered elastic shells and quasistatic thermoelasticity for geometrical-nonlinear thin shells, spreading of waves in piezoelectricity are developed. The mathematical models are formulated as initial boundary-value problems in the terms of a vector of displacement of an elastic body and potential of speeds of a liquid, vector of elastic displacement piezoelectricity and his electrical potential. Proceeding from a principle of virtual works the respective variational problems are constructed. In a basis of researches lays the single energetic approach, which allows to investigate a correctness of variational problem and convergence of the numerical schemes of their solutions. The constructive method on the basis of boundary transition from a sequence of the approached solutions behind procedure semidiscretization Galercin with attraction of approximations of a finit e elements method (FEM) for spatial variable proves existence of the generalized solution of variational problems. Are developed projective - сеточные schemes for the solutions of the listed classes of problems with use of approximations FEM for spatial variable and one-step recurrent time integration scheme. The conditions of stability are established and the estimations of speed of convergence offered schemes are constructed. The received estimations allow with confidence to apply numerical schemes to the solution of complex problems connected to needs of practice. The program realization these schemes for the solution of problems of interaction of elastic bodies and environments with liquids, interaction of electromagnetic and mechanical fields in пьезоэлектриках and problems connected generalized термоупругости is carried out. The analysis of the solutions of some model and applied tasks is carried out. Product Description popup.authors popup.nrat_date 2020-04-02 Close