A Dimensional Splitting Method for 3D Elastic Shell with Mixed Tensor Analysis on a 2D Manifold Embedded into a Higher Dimensional Riemannian Space
Year: 2018
Author: Kaitai Li, Xiaoqin Shen
Journal of Mathematical Study, Vol. 51 (2018), Iss. 4 : pp. 377–458
Abstract
In this paper, a mixed tensor analysis for a two-dimensional (2D) manifold embedded into a three-dimensional (3D) Riemannian space is conducted and its applications to construct a dimensional splitting method for linear and nonlinear 3D elastic shells are provided. We establish a semi-geodesic coordinate system based on this 2D manifold, providing the relations between metrics tensors, Christoffel symbols, covariant derivatives and differential operators on the 2D manifold and 3D space, and establish the Gateaux derivatives of metric tensor, curvature tensor and normal vector and so on, with respect to the surface $\vec{\Theta}$ along any direction $\vec{\eta}$ when the deformation of the surface occurs. Under the assumption that the solution of 3D elastic equations can be expressed in a Taylor expansion with respect to transverse variable, the boundary value problems satisfied by the coefficients of the Taylor expansion are given.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v51n4.18.02
Journal of Mathematical Study, Vol. 51 (2018), Iss. 4 : pp. 377–458
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 82
Keywords: Dimensional splitting method linear elastic shell mixed tensor analysis nonlinear elastic shell.