TY - JOUR
A2 - Merodio, Jose
AU - Shen, Xiaoqin
AU - Li, Haoming
AU - Li, Kaitai
AU - Cao, Xiaoshan
AU - Yang, Qian
PY - 2016
DA - 2016/12/15
TI - Some Differential Geometric Relations in the Elastic Shell
SP - 1463823
VL - 2016
AB - 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.
SN - 1024-123X
UR - https://doi.org/10.1155/2016/1463823
DO - 10.1155/2016/1463823
JF - Mathematical Problems in Engineering
PB - Hindawi Publishing Corporation
KW -
ER -