ON THE PROBLEM OF AXISYMMETRICALLY LOADED SHELLS OF REVOLUTION WITH SMALL ELASTIC STRAINS AND ARBITRARILY LARGE AXIAL DEFLECTIONS

Applied Mathematics and Mechanics (English Edition) ›› 1986, Vol. 7 ›› Issue (2): 125-137.

ON THE PROBLEM OF AXISYMMETRICALLY LOADED SHELLS OF REVOLUTION WITH SMALL ELASTIC STRAINS AND ARBITRARILY LARGE AXIAL DEFLECTIONS

黄黔

Shanghai University of Technology, Shanghai

收稿日期:1984-10-01 出版日期:1986-02-18 发布日期:1986-02-18

ON THE PROBLEM OF AXISYMMETRICALLY LOADED SHELLS OF REVOLUTION WITH SMALL ELASTIC STRAINS AND ARBITRARILY LARGE AXIAL DEFLECTIONS

Hwang Chien

Shanghai University of Technology, Shanghai

Received:1984-10-01 Online:1986-02-18 Published:1986-02-18

摘要/Abstract

摘要： For the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections, this paper suggests a group of state variables: radial displacement u, axial displacement w, angular deflection of tangent in the meridian X. radial stress resultant H and meridional bending moment M₄. and derives a System of First-order Nonlinear Differential Equations under global coordinate system with these variables. The Principle of Minimum Potential Energy for the problem is obtained by means of weighted residual method, and its Generalized Variational Principle by means of identified Lagrange multiplier method.This paper also presents a Method of Variable-characteristic Nondimensionization with a scale of load parameter, which may efficiently raise the probability of success for nonlinearity calculation. The obtained Nondimensional System of Differential Equations and Nondimensional Principle of Minimum Potential Energy could be taken as the theoretical basis for the numerical computation of axisymmetrical shells with arbitrarily large deflections.

关键词: paradox, symplectic space, Jordan form, elastic wedge

Abstract: For the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections, this paper suggests a group of state variables: radial displacement u, axial displacement w, angular deflection of tangent in the meridian X. radial stress resultant H and meridional bending moment M₄. and derives a System of First-order Nonlinear Differential Equations under global coordinate system with these variables. The Principle of Minimum Potential Energy for the problem is obtained by means of weighted residual method, and its Generalized Variational Principle by means of identified Lagrange multiplier method.This paper also presents a Method of Variable-characteristic Nondimensionization with a scale of load parameter, which may efficiently raise the probability of success for nonlinearity calculation. The obtained Nondimensional System of Differential Equations and Nondimensional Principle of Minimum Potential Energy could be taken as the theoretical basis for the numerical computation of axisymmetrical shells with arbitrarily large deflections.

Key words: paradox, symplectic space, Jordan form, elastic wedge

黄黔. ON THE PROBLEM OF AXISYMMETRICALLY LOADED SHELLS OF REVOLUTION WITH SMALL ELASTIC STRAINS AND ARBITRARILY LARGE AXIAL DEFLECTIONS[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(2): 125-137.

Hwang Chien . ON THE PROBLEM OF AXISYMMETRICALLY LOADED SHELLS OF REVOLUTION WITH SMALL ELASTIC STRAINS AND ARBITRARILY LARGE AXIAL DEFLECTIONS[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(2): 125-137.

参考文献

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[3] Reissner,E.,On the theory of thin elastic shells,H.Reissner Anniversary Volume,J.W.Edwards,Ann Arbor,Michigan(1949),231-247.
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ON THE PROBLEM OF AXISYMMETRICALLY LOADED SHELLS OF REVOLUTION WITH SMALL ELASTIC STRAINS AND ARBITRARILY LARGE AXIAL DEFLECTIONS

ON THE PROBLEM OF AXISYMMETRICALLY LOADED SHELLS OF REVOLUTION WITH SMALL ELASTIC STRAINS AND ARBITRARILY LARGE AXIAL DEFLECTIONS

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