![](/images/graphics-bg.png)
Some Differential Geometric Relations in the Elastic Shell
Joint Authors
Cao, Xiaoshan
Shen, Xiaoqin
Li, Haoming
Li, Kaitai
Yang, Qian
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-12-15
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Shen, Xiaoqin& Li, Haoming& Li, Kaitai& Cao, Xiaoshan& Yang, Qian. 2016. Some Differential Geometric Relations in the Elastic Shell. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1111721
Modern Language Association (MLA)
Shen, Xiaoqin…[et al.]. Some Differential Geometric Relations in the Elastic Shell. Mathematical Problems in Engineering No. 2016 (2016), pp.1-9.
https://search.emarefa.net/detail/BIM-1111721
American Medical Association (AMA)
Shen, Xiaoqin& Li, Haoming& Li, Kaitai& Cao, Xiaoshan& Yang, Qian. Some Differential Geometric Relations in the Elastic Shell. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1111721
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1111721