The Stress–Strain State of a Ribbed Cylindrical Shell Interacting with an Elastic Foundation Under Short-Term Loads

Abstract

A method for analyzing the stress-strain state of a ribbed cylindrical shell that interacts with an elastic foundation under dynamic axisymmetric loading is presented. The effect of the duration of loading and the parameters of the foundation on the deflection and bending moments of the shell is analyzed Introduction. The effect of the ambient medium on the vibrations, stability, and stress-strain state of shells under dynamic loading was addressed in many studies (5-17, 19, etc.). A literature review indicates that the dynamics of ribbed shells interacting with the ambient medium is of interest. In the present paper, we will use the Pasternak model (4) and the Winkler model to describe the ambient medium as an elastic foundation. 1. Problem Formulation. Basic Equations. Below, we will analyze the stress-strain state (SSS) of a ribbed closed cylindrical shell under short-term loads distributed over its surface. The shell interacts with an elastic foundation that prevents the normal displacements of the shell and the rotations of its mid-surface about a circumferential coordinate line. Let the longitudinal stiffening ribs (stringers) be arranged regularly and the shell be hinged at the ends. To solve the problem, we will use the classical theory of shells and rods (1) and the energy method. The total potential energy of the disturbed elastic system and the kinetic energy are given by