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Constructing solutions for two-dimensional quasi-static problems of thermomechanics in terms of stresses for bodies with plane-parallel boundaries

A methodology to construct solutions for two-dimensional quasi-static thermomechanical problems for bodies with plane-parallel boundaries (2D-QS thermomechanical problems) is proposed.  This approach begins with selecting equations for the plane quasi-static thermoelasticity problem in terms of stresses.  The methodology approximates the distribution of non-zero stress tensor components through the body's thickness using cubic polynomials, with coefficients expressed in terms of integral characteristics of the stress tensor components over the thickness variable and the

Generalization and application of the Cauchy-Poisson method to elastodynamics of a layer and the Timoshenko equation

The Cauchy-Poisson method is extended to n-dimensional Euclidean space so that to obtain partial differential equations (PDEs) of a higher order.   The application in the construction of hyperbolic approximations is presented, generalizing and supplementing the previous investigations.   Restrictions on derivatives in Euclidean space are introduced.  The hyperbolic degeneracy by parameters and its realization in the form of necessary and sufficient conditions are considered.  As a particular case of 4-dimensional Euclidean space, keeping operators up to the 6th order, we obtain a generalize