Modified Fourier transform method and its application for solving the problem of large deformations of a beam

• Autorzy: Trajkovski D. , Cukic R. S.
• Konferencja: 8th International Conference on Numerical Methods in Continuum Mechanics (September 19-24, 2000 ; Liptovsky Ján, Low Tatras ; Slovakia)
• Języki publikacji: EN

Abstrakty

EN

A modification of the Fourier transform method, which makes feasible transforming products of two functions and/or their derivatives, is described. By application of this method, some kinds of nonlinear differential equations can be transformed and solved. In this paper, the solution of the problem of bending a beam with fixed supports, under continuous transversal loading is given. Equations of the large deformations theory are used. The mutual influence between the deflection and the axial force is taken into account. The problem is mathematically described by a system of three nonlinear differential equations, with the appropriate boundary conditions. The solution is obtained by making use of an iterative procedure, based on the modified Fourier transform method.

Słowa kluczowe

EN

Fourier transform; beam; large deformation

PL

transformacja Fouriera; belka

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2002
• Tom: Vol. 9, No. 4
• Strony: 583--595
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Trajkovski D.

• University "Sv. Kliment Ohridski", Faculty of Sciences, Ivo Ribar Lola bb, 7000 Bitola, Macedonia

autor

Cukic R. S.

• University of Belgrade, Faculty of Mechanical Engineering, 27 Marta 80, 11000, Belgrade, Yugoslavia

Bibliografia

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• [7] D. Trajkovski, R. Cukic. Fourier transform method in solving the nonlinear Karman's equations in the theory thermoplastic plates. Proceedings of the 16th Canadian Congress of Applied Mechanics CANCAM'97, Vol. 1, University Laval, Quebec City, 1997.
• [8] Z Turek. A new method of finding approximate solutions of the heat conduction equation. Engineering Trans., 295-301, 1996.
• [9] Z. Turek. A new method of finding strong approximation to solutions to some IBVPs. Arch. Mech., 49: 573-587, 1997.
• [10] Z. Turek. Application of the Fourier cosine series to continuous approximation to solutions of heterogeneous nonlinear thermal problems. Proc. of the 2nd Intl. Symp. on Thermal Stresses and Related Topics "Thermal Stresses '97", 611-614. Rochester Institute of Technology, 1997.