A peridynamic theory for linear elastic shells

TL;DR

This paper introduces a novel surface-based peridynamic model for linear elastic shells, capturing deformation with curved bonds and validated through numerical tests on various shell geometries.

Contribution

It presents the first general surface-based peridynamic formulation for shells, incorporating curved bonds to model force transfer in thin structures.

Findings

Accurately predicts static deformation of spherical shells

Successfully models cylindrical shell behavior

Validates approach with flat plate deformation analysis

Abstract

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one physical dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states beget the necessary force and deformation vectors governing the motion of the shell. Correctness of our proposal on the peridynamic shell theory is numerically assessed against static deformation of spherical and cylindrical shells and flat plates.