Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Euler-Bernoulli beam Related Abstracts

3 Thermal Buckling Analysis of Functionally Graded Beams with Various Boundary Conditions

Authors: Gholamreza Koochaki

Abstract:

This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.

Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam

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2 Nonlinear Analysis of Shear Deformable Deep Beam Resting on Nonlinear Two-Parameter Random Soil

Authors: M. Seguini, D. Nedjar

Abstract:

In this paper, the nonlinear analysis of Timoshenko beam undergoing moderate large deflections and resting on nonlinear two-parameter random foundation is presented, taking into account the effects of shear deformation, beam’s properties variation and the spatial variability of soil characteristics. The finite element probabilistic analysis has been performed by using Timoshenko beam theory with the Von Kàrmàn nonlinear strain-displacement relationships combined to Vanmarcke theory and Monte Carlo simulations, which is implemented in a Matlab program. Numerical examples of the newly developed model is conducted to confirm the efficiency and accuracy of this later and the importance of accounting for the foundation second parameter (Winkler-Pasternak). Thus, the results obtained from the developed model are presented and compared with those available in the literature to examine how the consideration of the shear and spatial variability of soil’s characteristics affects the response of the system.

Keywords: Nonlinear Analysis, Soil-Structure Interaction, timoshenko beam, Winkler foundation, spatial variability, Pasternak foundation, Euler-Bernoulli beam, large deflection

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1 Mathematical Analysis of Simple Supported Euler-Bernoulli Beam on a Variable Elastic Foundation under a Partially Distributed Moving Load

Authors: I. A. Idowu, A. A. Owolabi, S. O. Sogunro, F. O. Akinpelu

Abstract:

The dynamic responses of an elastically supported Euler- Bernoulli beam on variable elastic foundation under partially distributed moving loads were investigated. The governing equation is fourth order partial differential equation, which was reduced to second order ordinary differential equation by using the analytical method in terms of series solution and solved by a numerical method using mathematical software (Maple). The numerical analysis shows that the response amplitude of the moving mass and moving force for variable pre-stressed increase as mass of the load M increases. It was found that the response displacement of the beam decreases as the value of the elastic foundation K increases. Also, the response displacement of the beam decreases as the value of the pre-stressed N increase. Comparison of moving mass and moving force shown that moving mass is greater than that of moving force.

Keywords: moving load, elastic foundation, Euler-Bernoulli beam, Variable pre-stressed, partially distributed, moving force

Procedia PDF Downloads 106