Some differential geometric relations in the elastic shell
type: Item
instance of: scholarly article
title: Some differential geometric relations in the elastic shell
zbMATH Open document ID: 1400.74072
DOI: 10.1155/2016/1463823
author: Xiaoqin Shen
author: Haoming Li
author: Xiaoshan Cao
author: Qian Yang
author: Kaitai Li
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: The theory of the elastic shells is one of the most important parts of the theory of solid mechanics. The elastic shell can be described with its middle surface; that is, the three-dimensional elastic shell with equal thickness comprises a series of overlying surfaces like middle surface. In this paper, the differential geometric relations between elastic shell and its middle surface are provided under the curvilinear coordinate systems, which are very important for forming two-dimensional linear and nonlinear elastic shell models. Concretely, the metric tensors, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the three-dimensional elasticity are expressed by those on the two-dimensional middle surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell. Thus, the novelty of this work is that we can further split three-dimensional mechanics equations into two-dimensional variation problems. Finally, two kinds of special shells, hemispherical shell and semicylindrical shell, are provided as the examples.
Mathematics Subject Classification ID: 74K25
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 53A45
zbMATH DE Number: 6952783
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/1463823
OpenAlex ID: W2561213571
Wikidata QID: Q59130959
cites work: Q5715116
cites work: Q4485429
cites work: Q4725258
cites work: Q3956025
cites work: On some problems of tensor calculus. I.
cites work: Q3848032
cites work: Q5615316
cites work: A dimensional splitting method for the linearly elastic shell
cites work: Discrete product integration methods for eigen-problems of a class of non-compact integral operators
cites work: Justification of two-dimensional nonlinear dynamic shell equations of Koiter's type
description: scientific article; zbMATH DE number 6952783