COMPOUND BENDING OF INHOMOGENEOUS THIN PLATES IN NONUNIFORM TEMPERATURE FIELD

Abstract

ABSTRACTThe particular interest in the mechanics of deformable solid are the problemsassociated with the bends of flexible plates and various flexible shells working innon-uniform temperature field. Such problems are commonly encountered in appliedproblems of the construction, oil-field, mechanical engineering, water and airtransport. During mathematical review of such kind of problems you have to dealwith systems of linear differential equations with variable coefficients and nonlineardifferential equations, and making analytical solution of which representsconsiderable mathematical difficulties. Analytical solutions of such problems can bemade by the method of partial discretization, the method that has been derived byone of the authors of this article based on the theory of generalized functions.The paper considers the problem of thermoelasticity of inhomogeneous circularflexible plate in the axially symmetric temperature field by taking into account theinfluence of bending tension and change of elastic properties of plate material alongits thickness. The problem of compound bending of inhomogeneous circular plateexposed to the action of lateral load, under temperature changes in thickness of theplate with the influence of bending tension come to the investigation of decoupledsystem of differential equations, obtaining of analytical solution of which using theexisting mathematical apparatus was not possible.