@Article{JMS-51-4,
author = {Li, Kaitai and Xiaoqin, Shen},
title = {A Dimensional Splitting Method for 3D Elastic Shell with Mixed Tensor Analysis on a 2D Manifold Embedded into a Higher Dimensional Riemannian Space},
journal = {Journal of Mathematical Study},
year = {2018},
volume = {51},
number = {4},
pages = {377--458},
abstract = {<p style="text-align: justify;">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&nbsp;$\vec{\eta}$ 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.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v51n4.18.02},
url = {https://global-sci.com/article/87759/a-dimensional-splitting-method-for-3d-elastic-shell-with-mixed-tensor-analysis-on-a-2d-manifold-embedded-into-a-higher-dimensional-riemannian-space}
}