On the theory of loaded general cylindrical Cosserat elastic shells

Bîrsan, Mircea

doi:10.1016/j.ijsolstr.2007.04.016

Cited by 6 publications

(1 citation statement)

References 11 publications

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“…Robert and Keer [1], Stephen and Wang [2] studied the semi-infinite circular cylinder and boundary conditions under a general load. Birsan [3,4] studied cylindrical Cosserat elastic shells and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions for an axisymmetric circular cylinder

Zhao

Gao

Zhao

et al. 2010

Comptes Rendus. Mécanique

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Through generalizing the method of a decay analysis technique determining the interior solution developed by Gregory and Wan, two necessary conditions on the edge-data of an axisymmetric circular cylinder for the existence of a rapidly decaying solution are established. By accurate solutions for auxiliary regular state, and using the reciprocal theorem and Boussinesq solution, these necessary conditions for the edge-data to induce only a decaying elastostatic state will be translated into appropriate boundary conditions for the circular cylinder with axisymmetric deformations. The results of the present Note extend the known results to circular cylinder's deformation problems, which enable us to establish two correct boundary conditions with stress and mixed edge-data. For the stress data, our boundary conditions coincide with those obtained in conventional forms of elastic theories. More importantly, the appropriate boundary condition with mixed edge-data is obtained for the first time.

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Section: Introductionmentioning

confidence: 99%

Boundary conditions for an axisymmetric circular cylinder

Zhao

Gao

Zhao

et al. 2010

Comptes Rendus. Mécanique

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Large bending deformations of a cylindrical membrane with internal pressure

Kolesnikov

Зубов

2009

Z Angew Math Mech

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We consider the large bending of a thin‐walled cylinder made of a rubberlike material. It is loaded by internal pressure and bending moments at the ends. The exact formulation of the problem is given within the framework of the nonlinear membrane theory taking into account large strains of the cylinder. Using the special substitution describing the pure bending of the cylinder, the problem is reduced to the system of nonlinear ordinary differential equations. The latter is solved numerically. We establish that there exists the limit value of the bending moment, which depends essentially upon the internal pressure. As an example, the Mooney–Rivlin material is considered. On the base of the calculations we propose the approximate formulae describing the bending moment dependence on the axis curvature of the cylinder and the ultimate bending moment dependence on the internal pressure.

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