Refined Equations of the Theory of Composite Multilayered Shells with Transversally Soft Core under Medium Bending

In development of the results obtained earlier, an improved two-dimensional mathematical model of static and dynamic deformation of composite multilayer plates and shells with transversely soft core was constructed. Theory based on the use of the refined shear model of S.P. Timoshenko for bearing layers and the hypothesis about the similarity of the displacements laws through the thickness of the core both under static and dynamic loading processes was constructed. Based on this hypothesis, simplified quasi-static equations of the theory of elasticity were derived for a transversally soft core, which allow integration through thickness coordinate. When integrating them to describe the stress-strain state, two two-dimensional unknown functions are introduced into consideration, as in static problems, which are transverse shear stresses that are constant over the thickness. Based on the generalized variational principles of Lagrange and Ostrogradsky-Hamilton to describe static and dynamic deformation processeswith large variability of stress-strain parameters, two-dimensional equations of equilibriumand motion of a general form are constructed. Simplification of the constructed equations for the case of low variability of stress-strain parameters is carried out.