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 variable: radial displacement u, axial displacement w, angular, deflection of tangent in the meridian X, radial stress resultant H and meridional bending moment Ms, 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 efficientlky 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.
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Chien, H. On the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections. Appl Math Mech 7, 125–137 (1986). https://doi.org/10.1007/BF01897055
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DOI: https://doi.org/10.1007/BF01897055