Engineering Transactions, 65, 3, pp. 423–445, 2017

Analysis of Euler-Bernoulli Beams with Arbitrary Boundary Conditions on Winkler Foundation Using a B-Spline Collocation Method

University of Mohaghegh Ardabili
Iran, Islamic Republic of

University of Mohaghegh Ardabili
Iran, Islamic Republic of

Structural beams are important parts of engineering projects. The structural analysis of beams is required to ensure that they provide the specifics needed to prevent and withstand failure. Therefore, the numerical solution to analyze an Euler-Bernoulli beam with arbitrary boundary conditions using sextic B-spline method is presented in this paper. A direct modeling technique is applied for modeling the Euler-Bernoulli beam with arbitrary boundary conditions on an elastic Winkler foundation. For this purpose, the effect of the translational along with rotational support, the type of beam supports and the elastic coefficient of Winkler foundation are assessed. Finally, some numerical examples are shown to present the efficiency of the sextic B-spline collocation method. To validate the analysis of the Euler-Bernoulli beam with the presented method, the results of B-spline collocation method are compared with the results of the analytical method and the integrated finite element analysis of structures (SAP2000).
Keywords: Euler–Bernoulli Beam; arbitrary boundary conditions; Winkler foundation; B-spline collocation method;
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Ghannadiasl A., Mofid M., An analytical solution for free vibration of elastically restrained Timoshenko beam on an arbitrary variable Winkler foundation and under axial load, Latin American Journal of Solids and Structures, an ABCM Journal, 12(13): 2417–2438, 2015.

Binesh S., Analysis of beam on elastic foundation using the radial point interpolation method, Scientia Iranica, 19(3): 403–409, 2012.

Ghannadiasl A., Mofid M., Free vibration analysis of general stepped circular plates with internal elastic ring support resting on Winkler foundation by Green function method, Mechanics Based Design of Structures and Machines, 44(3): 212–230, 2016.

Wang C., Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions, Journal of Engineering Mechanics, 121(6): 763–765, 1995.

Hamid N.N.A., Majid A.A., Ismail A.I.M., Quartic B-spline interpolation method for linear two-point boundary value problem,World Applied Sciences Journal, 17: 39–43, 2012.

Rashidinia J. et al., Sextic spline method for the solution of a system of obstacle problems, Applied Mathematics and Computation, 190(2): 1669–1674, 2007.

Ramadan M., Lashien I., Zahra W., Quintic nonpolynomial spline solutions for fourth order two-point boundary value problem, Communications in Nonlinear Science and Numerical Simulation, 14(4): 1105–1114, 2009.

Hsu M.-H., Vibration analysis of non-uniform beams resting on elastic foundations using the spline collocation method, Tamkang Journal of Science and Engineering, 12(2): 113–122, 2009.

Zarebnia M., Parvaz R., Septic B-spline collocation method for numerical solution of the Kuramoto-Sivashinsky equation, Communications in Nonlinear Science and Numerical Simulation, 7(3): 354–358, 2013.

Zarebnia M., Parvaz R., B-spline collocation method for numerical solution of the nonlinear two-point boundary value problems with applications to chemical reactor theory, International Journal of Mathematical Engineering and Science, 3(3): 6–10, 2014.

Mohammadi R., Sextic B-spline collocation method for solving Euler-Bernoulli beam models, Applied Mathematics and Computation, 241: 151–166, 2014.

Reali A., Gomez H., An isogeometric collocation approach for Bernoulli-Euler beams and Kirchhoff plates, Computer Methods in Applied Mechanics and Engineering, 284: 623–636, 2015.

Akram G., Solution of the system of fifth order boundary value problem using sextic spline, Journal of the Egyptian Mathematical Society, 23(2): 406–409, 2015.

Prochazkova J., Derivative of B-spline function, [In:] Proceedings of the 25th Conference on Geometry and Computer Graphics, Prague, Czech Republic, 2005.

Wilson E.L., Habibullah A., SAP2000: integrated finite element analysis and design of structures, Computers and Structures, Berkeley, California, 1997.

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