Wrinkle-free solutions in the theory of annular elastic membranes

DOI10.1007/BF00944773zbMath0742.73010OpenAlexW1679340054MaRDI QIDQ1180669

Hans Grabmüller

Publication date: 27 June 1992

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00944773

zbMATH Keywords

monotonicityconcavityexistenceuniquenessnonlinear boundary conditionnonlinear two-point boundary value problemaxisymmetric deformationssuperfunctionsconcept of switch pointrotationally symmetric deformations

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Plates (74K20) Maximum principles in context of PDEs (35B50) Stability theory for ordinary differential equations (34D99)

Related Items (5)

Existence theorems for some boundary value problems in the nonlinear theory of annular elastic membranes ⋮ Closed-form solution of well-known Hencky problem without small-rotation-angle assumption ⋮ Closed-form solution of a peripherally fixed circular membrane under uniformly distributed transverse loads and deflection restrictions ⋮ Recent mathematical results in the nonlinear theory of flat and curved elastic membranes of revolution ⋮ Wrinkle-free solutions of circular membrane problems

Cites Work

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• Finite displacements of annular elastic membranes
• A simplified version of Reissner's nonlinear equations for a first- approximation theory of shells of revolution
• Nonlinear boundary value problems for the annular membrane: A note on uniqueness of positive solutions
• Membrane caps
• Non-linear boundary value problems for the annular membrane: New results on existence of positive solutions
• Existence theorems for some boundary value problems in the nonlinear theory of annular elastic membranes
• Stable and Unstable Axisymmetric Solutions for Membranes of Revolution

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