Asymptotic decomposition in the problem of joined elastic plates

TL;DR

This paper introduces an asymptotic decomposition method for analyzing the elasticity problem in connected thin plates, separating it into simpler two-dimensional and local three-dimensional problems.

Contribution

It extends a local perturbation technique to connected thin plates, enabling complete problem decomposition into manageable subproblems.

Findings

Decomposition separates 2D plate theory from local 3D stress analysis.

Local problems can be solved numerically for detailed stress-strain states.

Method facilitates analysis of complex connected plate structures.

Abstract

In this paper, a method of local perturbations, previously successfully applied to decompose the problem of elasticity in the system of connected thin rods and beams [Kolpakov and Andrianov, 2013], is used to study the asymptotic behaviour of the elasticity problem in connected thin plates. A complete decomposition of the problem, i.e. the separation of the original problem in to the two-dimensional problem of the theory of plates and local problems is proposed. The local problems describe the three-dimensional stress-strain state in the connected plates and can be solved by numerical methods.