Infinitesimal deformations of surfaces and the stress distribution on some membranes under constant inner pressure

Soyuçok, Ziya

doi:10.1016/0020-7225(95)00142-5

Cited by 4 publications

(2 citation statements)

References 1 publication

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“…The equilibrium under constant inner pressure of membranes with canal surface geometry has been investigated by Soyu» cok (1996). In order to reveal their significance in connection with theorem 4.3, it is required to show that the equilibrium equations (2.6) may be satis¯ed for any given canal surface.…”

Section: Particular Membrane Geometries Canal Surfaces and Dupin Cyclidesmentioning

confidence: 99%

On the equilibrium of shell membranes under normal loading. Hidden integrability

Rogers

Schief

2003

Proc. R. Soc. Lond. A

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It is established that a well-known system of classical shell theory descriptive of membranes in equilibrium is, in fact, integrable. The membranes are shown to have geometries within the integrable class of so-called O surfaces. The membrane O surfaces include inter alia minimal, constant mean curvature, constant Gaussian curvature and, more generally, linear Weingarten surfaces, as well as canal surfaces and Dupin cyclides.

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Section: Particular Membrane Geometries Canal Surfaces and Dupin Cyclidesmentioning

confidence: 99%

On the equilibrium of shell membranes under normal loading. Hidden integrability

Rogers

Schief

2003

Proc. R. Soc. Lond. A

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“…Practically, the minimisation is here done by the means of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. was also proven for canal surfaces before in [33]. in Figure 8 and it will be shown that it admits a one pa- surface.…”

Section: Input For Design With Super-canal Surfacesmentioning

confidence: 60%

Morphogenesis of surfaces with planar lines of curvature and application to architectural design

Mesnil

Douthe

Baverel

et al. 2018

Automation in Construction

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This article presents a methodology to generate surfaces with planar lines of curvature from two or three curves and tailored for architectural design. Meshing with planar quadrilateral facets and optimal offset properties for the structural layout are guaranteed. The methodology relies on the invariance of circular meshes by spherical inversion and discrete Combescure transformations, and uses parametrisation of surfaces with cyclidic patches. The shapes resulting from our methodology are called super-canal surfaces by the authors, as they are an extension of canal surfaces. An interesting connection to shell theory is recalled, as the shapes proposed in this paper are at equilibrium under uniform normal loading. Some applications of these shapes to architecture are shown.

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Novel integrable reductions in nonlinear continuum mechanics via geometric constraints

Rogers

Schief

2003

Journal of Mathematical Physics

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Integrability of nonlinear wave equations and solvability of their initial value problem J. Math. Phys. 53, 043701 (2012); 10.1063/1.3699358 Fractional curve flows and solitonic hierarchies in gravity and geometric mechanicsThe nonlinear equations that describe solitonic behavior in physical systems have, to-date, typically been derived by approximation or expansion methods. Here, by contrast, hidden integrable structure is revealed in diverse areas of nonlinear continuum mechanics through natural geometric constraints.This constitutes an overdetermined system of linear equations for the velocity components v s , v n , and v b with compatibility condition 3352

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Infinitesimal deformations of surfaces and the stress distribution on some membranes under constant inner pressure

Cited by 4 publications

References 1 publication

On the equilibrium of shell membranes under normal loading. Hidden integrability

On the equilibrium of shell membranes under normal loading. Hidden integrability

Morphogenesis of surfaces with planar lines of curvature and application to architectural design

Novel integrable reductions in nonlinear continuum mechanics via geometric constraints

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