On shells of revolution with the Love-Kirchhoff hypotheses
type: Item
instance of: scholarly article
title: On shells of revolution with the Love-Kirchhoff hypotheses
zbMATH Open document ID: 0668.73035
DOI: 10.1007/BF00058512
published in: Journal of Engineering Mathematics
publication date: 1988-01-01T00:00:00Z
review text: On the occasion of the 100th anniversary of A. E. H. Love's fundamental paper on thin elastic shell theory, the present article summarizes a line of developments on shells of revolution related to the Love-Kirchhoff hypotheses which form the basis of Love's theory. The summary begins with the Günther-Reissner formulation of the linear theory which is shown to contain the classical first approximation shell theory as a special case. The static-geometric duality is deduced as a natural and immediate consequence of the more general theory. The repeated applications of this duality greatly simplify the solution process for boundary-value problems in shell theory, including the classical reduction of the axisymmetric bending problem and related recent reductions of shell equations for more general loadings to two simultaneous equations for a stress function and a displacement variable. In the nonlinear range, the article confines itself to Reissner's geometrically nonlinear theory of axisymmetric deformation of shells of revolution and Marguerre's shallow shell theory with special emphasis on recent results for elastic membranes, buckling of shells of revolution and applications of asymptotic methods.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 4094945
zbMATH Keywords: review article
zbMATH Keywords: Günther-Reissner formulation of the linear theory
zbMATH Keywords: static-geometric duality
zbMATH Keywords: Reissner's geometrically nonlinear theory
zbMATH Keywords: Marguerre's shallow shell theory
author: F. Y. M. Wan
author: Hubertus J. Weinitschke
MaRDI profile type: Publication
cites work: Non-linear bending of a circular plate under normal pressure
cites work: Non-linear theory of curved elastic sheets
cites work: Non-linear boundary values problems for the circular membrane
cites work: Membrane buckling: A study of solution multiplicity
cites work: Unsymmetric wrinkling of circular plates
cites work: On the system of differential equations of equilibrium of shells of revolution under bending loads
cites work: On the Theory of Thin Elastic Toroidal Shells
cites work: The plane circular elastic surface under normal pressure
cites work: Nonlinear Bending of Circular Plates
cites work: On the imperfection sensitivity of complete spherical shells
cites work: Asymptotic Solutions of the Von Karman Equations for a Circular Plate Under a Concentrated Load
cites work: A boundary-layer theory for elastic plates
cites work: The Non-Linear Boundary Value Problem of the Buckled Plate
cites work: Q5522839
cites work: Nonlinear boundary value problems for the annular membrane: A note on uniqueness of positive solutions
cites work: Non-linear boundary value problems for the annular membrane: New results on existence of positive solutions
cites work: Positive Solutions of Annular Elastic Membrane Problems with Finite Rotations
cites work: Existence theorems for some boundary value problems in the nonlinear theory of annular elastic membranes
cites work: Finite displacements of annular elastic membranes
cites work: An investigation of the complete post-buckling behavior of axisymmetric spherical shells
cites work: A Note on Multiple Asymptotic Series
cites work: Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory
cites work: On plate theories and Saint-Venant's principle
cites work: Q3757457
cites work: The Interior Solution for Linear Problems of Elastic Plates
cites work: Analoge Systeme von Schalengleichungen
cites work: Q5802855
cites work: Imperfection Sensitivity of Externally Pressurized Spherical Shells
cites work: A Boundary Layer Theory for Unsymmetric Deformations of Circular Cylindrical Elastic Shells
cites work: On the Foundations of the Theory of Thin Elastic Shells
cites work: Large deflections of axisymmetric circular membranes
cites work: Iterative solutions for the non-linear bending of circular plates
cites work: Q3850645
cites work: Q5594409
cites work: Q3908560
cites work: On large axisymmetrical deflection states of spherical shells
cites work: The axisymmetric branching behavior of complete spherical shells
cites work: Nonlinear Elastic Shell Theory
cites work: Q4039740
cites work: Asymptotic solutions of steadily spinning shallow shells of revolution under uniform pressure
cites work: The effect of transverse shear deformation on the bending of elastic shells of revolution
cites work: On the nonlinear theory of elastic shells under the Kirchhoff hypothesis
cites work: Finite Polar Dimpling of Shallow Caps Under Sub-Buckling Axisymmetric Pressure Distributions
cites work: A UNIQUENESS THEOREM FOR THE NONLINEAR AXISYMMETRIC BENDING OF CIRCULAR PLATES
cites work: Q5800230
cites work: Q5802854
cites work: The edge effect in symmetric bending of shallow shells of revolution
cites work: On torsion of thin cylindrical shells
cites work: On Finite Symmetrical Deflections of Thin Shells of Revolution
cites work: On the Derivation of Two‐Dimensional Shell Equations from Three‐Dimensional Elasticity Theory
cites work: On consistent first approximations in the general linear theory of thin elastic shells
cites work: A note on stress strain relations of the linear theory of shells
cites work: Rotationally Symmetric Stress and Strain in Shells of Revolution
cites work: Die Analogie zwischen den Verschiebungen und den Spannungsfunktionen in der Biegetheorie der Kreiszylinderschale
cites work: Lateral Bending and Twisting of Thin‐Walled Curved Tubes
cites work: Rigorous expunction of Poisson's ratio from the Reissner-Meissner equations
cites work: Q5615318
cites work: Nonlinear Shell Theory With Finite Rotation and Stress-Function Vectors
cites work: Asymptotic forms of a simplified version of the nonlinear Reissner equations for clamped elastic spherical caps under outward pressure

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cites work: Exact Reductions of the Equations of Linear Theory of Shells of Revolution

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cites work: Laterally loaded elastic shells of revolution

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cites work: Q3901090

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cites work: Stable and Unstable Axisymmetric Solutions for Membranes of Revolution

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cites work: Asymptotic solutions for finite deformation of thin shells of revolution with a small circular hole

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cites work: Existence of buckled states of circular plates

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