TY - JOUR
T1 - A Dimensional Splitting Method for 3D Elastic Shell with Mixed Tensor Analysis on a 2D Manifold Embedded into a Higher Dimensional Riemannian Space
AU - Li , Kaitai
AU - Shen , Xiaoqin
JO - Journal of Mathematical Study
VL - 4
SP - 377
EP - 458
PY - 2018
DA - 2018/12
SN - 51
DO - http://doi.org/10.4208/jms.v51n4.18.02
UR - https://global-sci.org/intro/article_detail/jms/12916.html
KW - Dimensional splitting method, linear elastic shell, mixed tensor analysis, nonlinear elastic shell.
AB - <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>