Mathematical modelling of multilayer thin body deformation

Abstract

We construct a theory of multilayer thin bodies within the framework of the threedimensional moment theory by using an efficient parametrization of a multilayer thin domain; in contrast to classic approaches, several base surfaces and an analytic method with Legendre and Chebyshev polynomial systems are used. Geometric characteristics typical for the proposed parametrizations are introduced into consideration. A fundamental theorem for a multilayer thin domain is formulated. Various representations of the equations of motion, the heat influx, and the constitutive relations of physical and heat content are presented for the new body domain parametrization. The definition of the kth order moment of a certain quantity with respect to an orthonormal system of second-kind Chebyshev polynomials is given. The expressions of moments of first- and second-order partial derivatives of a certain tensor field are obtained, and this is also done for some important expressions required for constructing different variants of the thin body theory. Various variants of the equations of motion in moments with respect to Legendre and Chebyshev polynomial systems are also obtained. The interlayer conditions are written down under various connections of adjacent layers of a multilayer body.