Geometrically nonlinear strain and buckling analysis of sandwich plates and shells reinforced on their edge

摘要

for sandwich plates and shells with transverse soft core and reinforcing columns on the outer contour for small strains and medium displacements the refined geometrically nonlinear theory has developed. It allows to describe prebuckling behaviour of sandwich plates and shells and reveal all possible buckling modes of external layers and reinforcing elements. It considers the interaction contact forces between external layers and core as indeterminate and interaction of external layers and core with reinforcing columns in all points of conjunction surfaces. In order to describe the mechanics of external layers strain state, the relations of classical nonlinear medium bending shell theory are used. For the core three-dimensional theory of elasticity relations simplified in accordance of transverse soft core model and integrated over the z-direction with satisfaction of conjugate of external layers and core in deflections are used. For the reinforcing columns simplified geometrically nonlinear theory of columns, based on S.P.Timoshenko shear model without compression strains in transverse directions is used. In order derive the basic equilibrium equations, static boundary conditions are applied for shell and reinforcing columns and for kinematic coupling conditions of external layers with core, external layers and core with reinforcing columns earlier proposed generalized Lagrange variational principle. Among the known variants of theories the proposed theory is characterized by a high degree of accuracy and intensionality when considering the minimum number of unknown two-dimensional functions for the shell, one-dimensional functions for reinforcing columns and two-dimensional and one-dimensional contact forces of structural elements interaction. The transverse-longitudinal bending problem of sandwich column in face loading applying through the perfectly rigid body with eccentricity was considered, numerical solving technique based of finite sum method was proposed, the analysis of pre- and postbuckling stress-strain state was carried out.