Refined Equations of the Sandwich Shells Theory with Composite External Layers and a Transverse Soft Core at Average Bending

• Published in: Lobachevskii journal of mathematics Vol. 40; no. 11; pp. 1904 - 1914
• Main Authors: Badriev, I. B., Paimushin, V. N., Shihov, M. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.11.2019; Springer Nature B.V
• Subjects: Algebra; Analysis; Bending; Compressive properties; Deformation; Elasticity; Equilibrium equations; Geometry; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Nonlinear equations; Probability Theory and Stochastic Processes; Product design; Shear stress; Strain; Stress-strain relationships; Stresses; Thickness; Variational principles; stress-strain state; carrier composite layer; transversally soft core; motion equation; sandwich shell; average bending; equilibrium equation; buckling form; sandwich plate; variability of a function
• DOI: 10.1134/S1995080219110076
• ISSN: 1995-0802

In the development of previously obtained results for the case of average bending, a refined geometrically nonlinear theory of static and dynamic deformation of sandwich plates and shells with a transversely soft core and external composite layers with low rigidity for transverse shears and transverse compression was constructed. It is based on the use of the refined Tymoshenko’s shear model for the carrier layers, taking into account lateral reduction, and for the transversally soft core, the simplified three-dimensional equations of the elasticity theory, which can be integrated along the transverse coordinate. The hypothesis of the similarity of the change laws of displacements across the thickness of the core during its static and dynamic deformation processes was adopted. When integrating the compiled equations of the elasticity theory to describe the stress-strain state, the two two-dimensional unknown functions are introduced that represent transverse shear stresses that are constant in thickness. Based on the generalized Lagrange and Ostrogradsky Hamilton variational principles for describing static and dynamic deformation processes with large indicators of the variability of the stress-strain state parameters, two-dimensional geometrically nonlinear equilibrium equations and general movements are constructed, which allow to reveal purely shear of buckling forms of the carrier layers during formation normal compressive stresses.