On Lagrange Theory of Shells of Revolution

TL;DR

This paper introduces a new linear elastic shell theory that addresses logical flaws in previous models, derives equations for shells of revolution, and compares them with existing theories and 3D elasticity equations.

Contribution

It presents a novel, logically consistent linear shell theory and formulates equations for shells of revolution, improving upon prior approaches.

Findings

Derived equations for shells of revolution

Compared shell equations with existing models and 3D elasticity

Identified key quality decisions in shell modeling

Abstract

The new linear theory of elastic shells is presented in this paper. This theory is free from various logical imperfections, that may be found in the approaches of earlier researchers. On the base of this theory the equations of shells of revolution are built. The equations of cylindrical shell are compared by a number of properties with the equations of other researchers and with elasticity equations of 3-dimensional tube. Important quality decisions are stated.