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Effect of higher order terms of Maclaurin expansion in nonlinear analysis of the Bernoulli beam by single finite element
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 Title & Authors
Effect of higher order terms of Maclaurin expansion in nonlinear analysis of the Bernoulli beam by single finite element
Zahrai, Seyed Mehdi; Mortezagholi, Mohamad Hosein; Mirsalehi, Maryam;
 Abstract
The second order analysis taking place due to non-linear behavior of the structures under the mechanical and geometric factors through implementing exact and approximate methods is an indispensible issue in the analysis of such structures. Among the exact methods is the slope-deflection method that due to its simplicity and efficiency of its relationships has always been in consideration. By solving the differential equations of the modified slope-deflection method in which the effect of axial compressive force is considered, the stiffness matrix including trigonometric entries would be obtained. The complexity of computations with trigonometric functions causes replacement with their Maclaurin expansion. In most cases only the first two terms of this expansion are used but to obtain more accurate results, more elements are needed. In this paper, the effect of utilizing higher order terms of Maclaurin expansion on reducing the number of required elements and attaining more rapid convergence with less error is investigated for the Bernoulli beam with various boundary conditions. The results indicate that when using only one element along the beam length, utilizing higher order terms in Maclaurin expansion would reduce the relative error in determining the critical buckling load and kinematic parameters in the second order analysis.
 Keywords
non-linear behavior;slope-deflection method;axial compressive force;Maclaurin expansion;critical load;kinematic parameters;
 Language
English
 Cited by
1.
Closed-form solutions for non-uniform axially loaded Rayleigh cantilever beams,;;;

Structural Engineering and Mechanics, 2016. vol.60. 3, pp.455-470 crossref(new window)
1.
Closed-form solutions for non-uniform axially loaded Rayleigh cantilever beams, Structural Engineering and Mechanics, 2016, 60, 3, 455  crossref(new windwow)
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