|Mathematical Problems in Engineering||Volume 2016 ,2016-12-15|
|Some Differential Geometric Relations in the Elastic Shell|
|Xiaoqin Shen 1 Haoming Li 1 Kaitai Li 2 Xiaoshan Cao 1 , 3 Qian Yang 1|
|Received 2016-09-30, accepted for publication 2016-11-09, Published 2016-11-09|
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.
Copyright © 2016 Xiaoqin Shen et al. 2016
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Two-dimensional domain ω and surface S (cf. ).
The shell Ω^ε with middle surface S (cf. ).
Middle surface of hemispherical shell.
Middle surface of semicylindrical shell.
Xiaoqin Shen.School of Sciences, Xi’an University of Technology, Xi’an 710054, China, email@example.com
Xiaoqin Shen,Haoming Li,Kaitai Li,Xiaoshan Cao,Qian Yang. Some Differential Geometric Relations in the Elastic Shell. Mathematical Problems in Engineering ,Vol.2016(2016)
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