About lithospheric plates made of multicomponent materials
UDC
539.3DOI:
https://doi.org/10.31429/vestnik-19-1-65-69Abstract
Earlier in the works of the authors, a series of models of lithospheric plates on deformable bases that interact with their ends, causing starting earthquakes was built. Kirchhoff plates were taken as lithospheric plates. The question of the behavior of lithospheric plates, simulated materials of other rheologies, in particular, multicomponent ones, were solved by considering models of the linear theory of elasticity. However, it was possible to consider only boundary value problems for anti-plane tasks. And only recently it has been possible to develop a universal modeling method that made it possible to present solutions of boundary value problems for multicomponent materials described by systems of partial differential equations in the form of decompositions for solutions of simpler boundary value problems. Thus, the advantage of the method is the possibility of avoiding the need to solve complex boundary value problems for systems of partial differential equations by replacing them with separate differential equations, among which the Helmholtz equations are the simplest. Namely, with the help of combinations of solutions of boundary value problems for this equation, it is possible to describe the behavior of complex solutions of multicomponent boundary value problems. In this paper, the derivation of integral equations arising in the boundary problem under consideration and the method of their solution with the prospect of their application in problems of multicomponent materials is given.
Keywords:
lithospheric plates, block elements, vector boundary value problems, integral equationsAcknowledgement
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Copyright (c) 2022 Evdokimova O.V., Babeshko O.M., Babeshko V.A., Telyatnikov I.S., Khripkov D.A., Uafa G.N., Mukhin A.S.
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