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Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam

Acta Mechanica Sinica 2007年第3期23卷 287-296页

作者： BoonchaiPhungpaingam SomchaiChucheepsakul Department of Civil Engineering Faculty of EngineeringKing Mongkut's University of Technology ThonburiPracha-utid RdBangmodToongkruBangkok10140Thailand

This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The non-linear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge-Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance （10^-5）. The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.

关键词： Postbuckling Elastica Concentrated moment elliptic integral Shooting method

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Tangential Developable Surfaces as Bonnet Surfaces

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Acta Mathematica Sinica,English Series 1999年第2期15卷 269-276页

作者： Ioannis M. Roussos, Department of Mathematics, Hamline University, Saint Paul, MN 55104-1284, U. S. AE-mail: iroussos@seq.hamline, edu Department of Mathematics Hamline University Saint Paul U. S. A.

We study the real Bonnet surfaces which accept one unique nontrivial isometry that preserves the mean curvature, in the three-dimensional Euclidean space. We give a general criterion for these surfaces and use it to determine the tangential developable surfaces of this kind. They are determined implicitly by elliptic integrals of the third kind. Only the tangential developable surfaces of circular helices are explicit examples for which we completely determine the above unique nontrivial isometry.

关键词： Bonnet surface Mean curvature Isometry Tangential developable elliptic integral Circular helix

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Identities for Catalan’s Constant Arising from integrals Depending on a Parameter

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Acta Mathematica Sinica,English Series 2020年第10期36卷 1083-1093页

作者： Feclerica FERRETTI Alessandro GAMBINI Daniele R.ITELLI Free University of Bozen Bressanone CampusViale Ratisbona 1639042 Bressanone(BZ) Sapienza Universiti di Roma Dipartirento di Matcatica"G.Castelruovo"Piazzale Aldo Moro 500185 Roma Urieersita di Bologna Dipartimento di Scienze StatisticheVia delle Bele Arti 4140126 Bologna

In this paper we provide some relationships between Catalan’s constant and the 3F2 and4F3 hypergeometric functions,deriving them from some parametric *** particular,using the complete elliptic integral of the first kind,we found an alternative proof of a result of Ramanujan for3F2,a second identity related to 4F3 and using the complete elliptic integral of the second kind we obtain an identity by Adamchik.

关键词： Catalan constant elliptic integral hypergeometric functions

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Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire

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Advances in Applied Mathematics and Mechanics 2011年第6期3卷 689-701页

作者： Malik Mamode Department of Physics Laboratoire PIMENTEquipe MASCUniversity of La Reunion97400 Saint-DenisFrance

The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential,is *** an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic *** result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

关键词： Nonlinear oscillator exact period elliptic integral

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