Abstract
The relevance of this paper is explained by a demand for the development of mechanical and mathematical models and methods for calculating the stress-strain state of the sandwich structural elements. The statement of the boundary value problem on the deformation of a circular sandwich plate with a central hole, connected to the soil foundation, was given. To describe the kinematics of an asymmetric plate pack, the broken line hypotheses are accepted. In a relatively thick lightweight core, the normal does not change its length, remains rectilinear, but rotates through some additional angle. Tuff, coarse grained soil, granite, and gneiss are accepted as the soil foundation. The bearing reaction is described by the Winkler model. The system of equilibrium equations is obtained by the variational method. Its solution is written in displacements through Kelvin functions. A numerical parametric analysis of displacements and stresses in the plate is carried out, their dependence on the type of soil foundation is shown.
Highlights
Rods, plates and shells with a layered structure are usually assembled from materials with significantly different physical and mechanical properties
The highest stresses are achieved on the outer planes of the plate, while they are equal in magnitude
Coarse-grained soil, and granite were assumed as the base. They showed that with an increase in the stiffness of the foundation, the maximum deflection and relative shear decrease significantly. The stresses reach their maximum on the inner contour, where they are 1.5 times the stresses on the outer contour
Summary
Rods, plates and shells with a layered structure are usually assembled from materials with significantly different physical and mechanical properties. Bonding layer – core (foams, corrugated cardboard, polymer materials) serves to form a monolithic structure. This combination of layers makes it possible to ensure reliable operation of systems in adverse environmental conditions, to create structures that combine high strength and rigidity with a relatively low weight. The solution to the problem of harmonic vibrations of a viscoelastoplastic sandwich cylindrical shell [1] was obtained using the expansion in a Fourier series and limiting only to its first term (monoharmonic approximation). Free and forced vibrations of sandwich cylindrical shells with elastic core were investigated in papers [2,3,4]. Nonstationary contact problems associated with spherical shells were considered in [6,7]
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