A Fundamental Surface Theory for Kinetic Analogy of Thin Elastic Shells

XUE Yun; CHEN Liqun

doi:10.21656/1000-0887.430222

Volume 44 Issue 5

May 2023

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XUE Yun, CHEN Liqun. A Fundamental Surface Theory for Kinetic Analogy of Thin Elastic Shells[J]. Applied Mathematics and Mechanics, 2023, 44(5): 489-498. doi: 10.21656/1000-0887.430222

Citation:

XUE Yun, CHEN Liqun. A Fundamental Surface Theory for Kinetic Analogy of Thin Elastic Shells[J]. Applied Mathematics and Mechanics, 2023, 44(5): 489-498. doi: 10.21656/1000-0887.430222

Citation:

XUE Yun, CHEN Liqun. A Fundamental Surface Theory for Kinetic Analogy of Thin Elastic Shells[J]. Applied Mathematics and Mechanics, 2023, 44(5): 489-498. doi: 10.21656/1000-0887.430222

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A Fundamental Surface Theory for Kinetic Analogy of Thin Elastic Shells

doi: 10.21656/1000-0887.430222

XUE Yun^1
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CHEN Liqun^{2
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1.
School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, P.R.China
2.
Department of Mechanics, School of Science, Harbin Institute of Technology, Shenzhen, Shenzhen, Guangdong 518055, P.R.China

Received Date: 2022-07-04
Rev Recd Date: 2022-08-06
Publish Date: 2023-05-01

Abstract

Abstract

The generalization of the Kirchhoff kinetic analogy from thin elastic rods to thin elastic shells, namely the generalized Kirchhoff kinetic analogy, needs a corresponding novel expression of the classical surface theory with its fundamental properties described by means of the concept and method of the rigid body dynamics. A rigid orthogonal-axis system and a curvature-twist vector were defined for the non-orthogonal meshing of a surface, and the Euler angles were used to express the attitude of the system and the partial differential geometric equation of the surface. The curvature-twist vector and the Lamé coefficient were applied to depict the 1st and the 2nd basic quadratic forms of the surface, obtain the normal curvature and calculate the principal curvature and the principal direction. The analysis demonstrates the consistency between the new and the classical expressions of the surface theory. The application example of the proposed method shows that, this method can reasonably express the Rodrigues equation, the Weingarten equation, the Gauss equation and the fundamental equations for the surface, and well describe the differential geometry of the surface. This method has the benefits of conciseness and directness, and lays a mathematical foundation for the generalized Kirchhoff kinetic analogy and its further developments.
- generalized Kirchhoff analogy,
- surface curvature-twist vector,
- surface 2nd fundamental quadratic,
- elastic thin shell,
- rigid body dynamics

Contributed by CHEN Liqun, M. AMM Editorial Board

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References(20)

References

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