Abstract
Proceeding from three-dimensional formulations of initial boundary value problems of the three-dimensional linear micropolar theory of thermoelasticity, similar formulations of initial boundary value problems for the theory of multilayer thermoelastic thin bodies are obtained. The initial boundary value problems for thin bodies are also obtained in the moments with respect to systems of orthogonal polynomials. We consider some particular cases of formulations of initial boundary value problems. In particular, the statements of the initial-boundary value problems of the micropolar theory of K-layer thin prismatic bodies are considered. From here, we can easily get the statements of the initial-boundary value problems for the five-layer thin prismatic bodies.
Highlights
Any problem of the theory of a thin body can be considered in a three-dimensional formulation, which is more accurate than a two-dimensional one
The new parameterization in the case of a one-layered thin body is described in detail in [3,4]
As is seen from Equation (20), the quantities in Equations (15) and (16) introduced above represent the components of the second rank unit tensor for a multilayer thin domain of the three-dimensional Euclidean space. It is seen from the material presented above that, in the parameterization of the multilayer domain considered, for each layer, all the corresponding relations for a one-layered thin body under a new parameterization in [3,4], as well as for other parameterizations considered in [3,5,22], hold under the condition that the root letters of quantities entering these relations must be equipped with the bottom index, which denotes the number of the layer considered
Summary
Any problem of the theory of a thin body can be considered in a three-dimensional formulation, which is more accurate than a two-dimensional one. It should be noted that the analytic method with the use of the Legendre polynomial system in constructing the one-layer thin body theory [5,6,7,8,9,10,11,12,13,14] and multilayer thin body theory [15,16] was applied by other authors In this direction, the authors published many papers (e.g., [1,2,3,17,18,19,20,21]) with the application of Legendre and Chebyshev polynomial systems. Classical theories, especially micropolar theories and theories of other rheologies, constructed by this method, are far from perfection
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