Membrane Theory for Layered Ellipsoidal Shells

1983 ◽  
Vol 105 (4) ◽  
pp. 356-362 ◽  
Author(s):  
D. L. Logan ◽  
M. Hourani
Keyword(s):  
Elastic Behavior ◽  
Pressure Loading ◽  
Membrane Theory ◽  
Shells Of Revolution ◽  
Ellipsoidal Shell ◽  
Closed Form Solutions ◽  
Membrane Shell ◽  
Epoxy Material ◽  
Specific Geometry ◽  
Membrane Shells

The stress analysis of a laminated anisotropic ellipsoidal membrane shell of revolution is considered. A system of equations which is appropriate to the elastic behavior of anisotropic membrane shells of revolution is used as a basis. These equations are applied to the specific geometry of an ellipsoidal shell to develop the particular equations used in the analysis. Closed-form solutions are derived for the stresses and displacements. Methods for determining the extremely cumbersome integrals in the equations for the displacements are discussed as well. To illustrate the equations, solutions are presented for an ellipsoidal shell simply supported on one edge and subjected to internal pressure loading. Numerical results are presented for glass-epoxy and boron-epoxy material systems.

Extension of Vlasov’s Semi-membrane Theory to Reinforced Composite Shells

1992 ◽  
Vol 59 (2) ◽  
pp. 462-464 ◽  
Author(s):  
V. Birman
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Membrane Theory ◽  
Composite Shells ◽  
Governing Equations ◽  
Closed Form Solutions ◽  
Membrane Shell ◽  
Reinforced Composite ◽  
Statics And Dynamics ◽  
Vibration Problems

Governing equations for the statics and dynamics of reinforced composite shells are developed based on Vlasov’s semi-membrane shell theory. These equations have closed-form solutions illustrated for buckling and free vibration problems. The buckling solution converges to the known result for unstiffened isotropic shells.

The Membrane Shell as an Underconstrained Structural System

1989 ◽  
Vol 56 (2) ◽  
pp. 387-390 ◽  
Author(s):  
E. N. Kuznetsov
Keyword(s):  
Cross Section ◽  
Arbitrary Cross Section ◽  
Structural Behavior ◽  
Structural System ◽  
Membrane Theory ◽  
Apparent Paradox ◽  
Membrane Shell ◽  
Membrane Shells ◽  
New Perspective ◽  
Peculiar Behavior

Statical-kinematic analysis is employed to provide a new perspective on the structural behavior of membrane shells and the related limitations of the linear membrane theory. The obtained results include a resolution of an apparent paradox in the statics of membranes, a description and explanation of the peculiar behavior of toroidal membranes with an arbitrary cross-section, and a stronger version of a central theorem in the membrane theory.

scholarly journals Numerical Solution of a Deep-Drawing Problem

1977 ◽  
Vol 99 (1) ◽  
pp. 206-209 ◽  
Author(s):  
E. I. Odell ◽  
W. E. Clausen
Keyword(s):  
Work Hardening ◽  
Deep Drawing ◽  
Numerical Technique ◽  
Strain Theory ◽  
Membrane Theory ◽  
Rigid Plastic ◽  
Normal Anisotropy ◽  
Membrane Shell ◽  
Plastic Analysis ◽  
Incremental Strain

A rigid-plastic analysis of the axisymmetric deep-drawing problem is made using a special numerical technique. The effects of work-hardening, friction, and normal anisotropy have been included. Incremental strain theory is used to obtain results for both bending and membrane shell theories. These results are then compared. The authors feel that membrane theory gives very good results and should be used in the future to analyze any relatively thin cups.

Membrane Theory for Anisotropic Laminated Shells of Revolution

1989 ◽  
Vol 111 (2) ◽  
pp. 130-135 ◽  
Author(s):  
D. L. Logan ◽  
G. E. O. Widera
Keyword(s):  
Asymptotic Expansion ◽  
Variational Principle ◽  
Practical Interest ◽  
Small Deformation ◽  
Membrane Theory ◽  
Shells Of Revolution ◽  
Laminated Shells ◽  
Expansion Technique ◽  
Laminated Shells Of Revolution ◽  
Anisotropic Elastic

The present paper discusses the derivation and application of the membrane theory equations governing the small deformation of laminated, anisotropic, elastic shells of revolution. The equations are derived by use of the Hellinger-Reissner variational principle in conjunction with the asymptotic expansion technique. They are then used to analyze specific shells under loadings of practical interest.

Nonlinear Analysis of Geometrically Imperfect Stiffened Shells of Revolution

1988 ◽  
Vol 32 (01) ◽  
pp. 29-36
Author(s):  
J. Subbiah
Keyword(s):  
Finite Element ◽  
Nonlinear Analysis ◽  
Large Deformation ◽  
Initial Imperfection ◽  
Element Formulation ◽  
Pressure Loading ◽  
Shells Of Revolution ◽  
Stiffened Shells ◽  
Displacement Behavior ◽  
Circumferential Pressure

A nonlinear, large-deformation, finite-element formulation is presented for the analysis of general instability of ring-stiffened shells of revolution subjected to combined end compression and circumferential pressure loading. The pressure loading is treated as a follower force. The effect of varying degrees of initial imperfection on the load displacement behavior is reported. A combined nonlinear and eigenvalue analysis is presented to determine critical pressures for initially imperfect, stiffened cylinders.

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