Metric Tensor and Curvature Tensor in Deformed Shell Middle Surface

沈晓芹; 李开泰

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Metric Tensor and Curvature Tensor in Deformed Shell Middle Surface

更新时间：2025-12-08

- Metric Tensor and Curvature Tensor in Deformed Shell Middle Surface
- Vol. 41, Issue 12, Pages: 1483-1486(2007)
- 作者机构：
  
  西安交通大学理学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： O242
- Online First：10 December 2007，
  
  Published：2007
- 稿件说明：
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沈晓芹, 李开泰. Metric Tensor and Curvature Tensor in Deformed Shell Middle Surface[J]. 2007, 41(12): 1483-1486.
DOI：

沈晓芹, 李开泰. Metric Tensor and Curvature Tensor in Deformed Shell Middle Surface[J]. 2007, 41(12): 1483-1486. DOI：

摘要

为了从数学角度更好地描述壳体中性曲面如何变形

通过渐近分析和张量分析

给出了当壳体中性曲面发生形变时度量张量和曲率张量改变量的完整表达式.提出的度量张量的改变量与Ciarlet给出的一致

而曲率张量的改变量比Ciarlet给出的更精确.由于度量张量和曲率张量的改变量是构造Koiter型线性、非线性弹性壳体模型的重要组成部分

因此提出新的Koiter型非线性弹性壳体模型

理论上比Ciarlet的非线性模型误差更小.这为火箭、导弹、航天飞船等国防领域和火车、汽车等工业领域的研究提供了更好的数学基础.

Abstract

To mathematically characterize the deformation of the middle surface of a shell

the metric tensor and curvature tensor ought to be investigated in detail. Based on the definitions of metric tensor and curvature tensor

the full expressions of their changes are put forward with asymptotic analysis

where the metric tensor change expression coincides with Ciarlet's

and the curvature tensor change expression is described more accurately than Ciarlet's. Then a new nonlinear shell model of Koiter's type is constructed with smaller error than in Ciarlet's theory for the fields of national defense

such as rockets

missiles

aircrafts

and for the fields of industry

such as trains and cars.

关键词

Keywords

references

Ciarlet P G, Ciarlet P Jr. Another approach to linearized elasticity and a new proof of Korn's inequality[J]. Math Models Methods Appl Sci, 2005, 15: 259-271.

Ciarlet P G, Gratie L. Another approach to linear shell theory and a new proof of Korn's inequality on a surface[J]. C R Acad Sci Paris: I, 2005, 340: 471-478.

Ciarlet P G. A two-dimensional nonlinear shell model of Koiter's type[C]∥Jean Leray'99 Conference Proceedings. Dordrecht: Kluwer, 1999:437-449.

Koiter W T. On the foundations of the linear theory of thin elastic shells[C]∥Proc Kon Ned Akad Wetensch. Amsterdam:North-Holland Pub. Co., 1970: 169-195.

Koiter W T. A consistent first approximation in the general theory of thin elastic shells[C]∥IUTAM Symposium on the Theory of Thin Elastic Shells. Amsterdam: Delft, 1959:12-33.

Ciarlet P G. An introduction to differential geometry, with applications to elasticity[M]. Heidelberg: Springer-Verlag,2005.

Ciarlet P G, Gratie L. A new approach to linear shell theory[J]. Math Models Methods Appl Sci, 2005, 15(8):1181-1202.

李开泰,黄艾香. 张量分析及其应用[M]. 北京:科学出版社,2004: 62-111.

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