Three-dimensional bending stress-strain state of rectangular variable-thickness orthotropic plates

Abstract

A review of studies on the stress-strain state during bending of a refined two-dimensional theories of various order is given. A solution of the problem of bending of a rectangular orthotropic plate of constant thickness within the framework of the three-dimensional theory of elasticity was given. Bending of variable-thickness orthotropic plates was considered. Using the theory of thin plates, Sarkisyan obtained solutions for a freely supported thin plate with a thickness that varies according to a power law and a tightly clamped plate, with a gradually changing thickness under a sinusoidal load and a uniformly distributed load, respectively. Khoma and Chernopiskii studied the bending of freely supported and tightly clamped plates, whose thickness varied linearly in one direction; to obtain the solution they reduced the three-dimensional problem to a two-dimensional problem by expanding the desired function in a Fourier-Legendre series. In this study we consider a three-dimensional boundary-value problem of the bending of a variable-thickness orthotropic plate, with nonplanar faces perpendicular to the load, which admits representation by a double trigonometric series. The method of perturbation of the shape of the boundary for surfaces close to the coordinate planes is used to solve the problem. On the basis of themore » solution built we examine the laws governing the stress-strain state of orthotropic plates with surfaces that periodically curve in one direction as they are bent by localized loads, depending on the amplitude and frequency of the undulation of the curvatures and the degree of load localization.« less