Methods of asymptotic synthesis and heat-and-pressure analogies in membrane shell theory

Abstract

The generation of analytical solutions for cylindrical and conical shells equations on the base of asymptotic synthesis methods (MAS) in the state of strain is considered. Various approximate equations for membrane theory (semi-membrane theory and boundary disturbance, Vlasov–Donnell, moment and tangential states) are applied and their asymptotic and true errors are analyzed in this paper. The differential equations of general theory of transversally isotropic shells being the synthesis of Vlasov’s equations are recorded here. Various approximate equations and numbers of coalescence modes for solutions during MAS application are given here as well. The correlations of mathematically based heat-and-pressure analogy that allow solving thermoelastic tasks instead of pressure ones are brough there. These tasks show the direct differential constraint between effects from pressure and temperature impact on shells.