Journal ArticleDOI
Boundary layer solutions for some nonlinear elastic membrane problems
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In this paper, the matched asymptotic expansions were used to describe finite axisymmetric deformations of two thin elastic membrane problems: a circular membrane with small radial traction at the edge, an annular membrane with a small circular hole at the center.Abstract:
The method of matched asymptotic expansions is used to describe finite axisymmetric deformations of two thin elastic membrane problems: a circular membrane with a small radial traction at the edge, an annular membrane with a small circular hole at the center. In both problems, the surface load is assumed to be an axial pressure. There is a boundary layer at the outer edge in the first problem, and at the hole in the second problem.read more
Citations
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Journal ArticleDOI
Sensitivity Study of Precision Pressurized Membrane Reflector Deformations
TL;DR: In this article, the sensitivity of membrane shapes to selected environmental effects and physical assumptions used in numerical modeling is illustrated, including film thickness and material property variations, thermal effects and support perturbations, and the modeling of wrinkling.
Journal ArticleDOI
On finite displacements of circular elastic membranes
H. J. Weinitschke,E. Meister +1 more
Journal ArticleDOI
Finite displacements of annular elastic membranes
TL;DR: In this paper, the tensile tensile solution of the annular membrane problem is proved, including a rigorous derivation of a stress concentration factor originally found by Schwerin by formal methods.
Journal ArticleDOI
On shells of revolution with the Love-Kirchhoff hypotheses
F. Y. M. Wan,H. J. Weinitschke +1 more
TL;DR: In this article, a line of developments on thin elastic shell theory related to the Love-Kirchhoff hypotheses which form the basis of Love's theory is summarized, with special emphasis on recent results for elastic membranes, buckling of shells of revolution and applications of asymptotic methods.
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On the nonlinear membrane approximation and edge-wrinkling
TL;DR: In this paper, the wrinkling of a uniformly stretched thin elastic plate subjected to a pressure acting perpendicular to its surface is re-visited under the assumption that the basic state can be adequately described by an appropriate nonlinear membrane analysis.
References
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Book
Perturbation Methods in Applied Mathematics
TL;DR: In this paper, limit process expansions applied to Ordinary Differential Equations (ODE) are applied to partial differential equations (PDE) in the context of Fluid Mechanics.
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A collocation solver for mixed order systems of boundary value problems
TL;DR: Implementation of a spline collocation method for solving boundary value problems for mixed order systems of ordinary differential equations is discussed and the resulting general purpose code, COLSYS, is tested on a number of examples to demonstrate its stability, efficiency and flexibility.
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Vorlesungen über technische Mechanik: O. Föppl, III. Bd.: Festigkeitslehre. 10. Aufl. 1927, Teubner, Leipzig, Berlin. Geb. M 16·60
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Non-linear theory of curved elastic sheets
E. Bromberg,J. J. Stoker +1 more
TL;DR: The membrane theory of shells as discussed by the authors is a generalization of the general theory of elasticity, and it has been used for many applications in the field of computer vision and artificial intelligence.