Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law

Brojan, Miha; Videnic, T.; Kosel, Franc

doi:10.1007/s11012-009-9209-z

Cited by 40 publications

(17 citation statements)

References 20 publications

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“…The solution method is based on a simple formulation and is therefore easy to understand and use. Furthermore, it can be generalized to employ nonlinear material response or other physical behavior without major difficulties, [1,[25][26][27].…”

Section: Introductionmentioning

confidence: 99%

A simple method for determining large deflection states of arbitrarily curved planar elastica

2013

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The paper discusses a relatively simple method for determining large deflection states of arbitrarily curved planar elastica, which is modeled by a finite set of initially straight flexible segments. The basic equations are built using Euler-Bernoulli and large displacement theory. The problem is solved numerically using RungeKutta-Fehlberg integration method and Newton method for solving systems of nonlinear equations. This solution technique is tested on several numerical examples. From a comparison of the results obtained and those found in the literature, it can be concluded that the developed method is efficient and gives accurate results. The solution scheme displayed can serve as reference tool to test results obtained via more complex algorithms.

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Section: Introductionmentioning

confidence: 99%

A simple method for determining large deflection states of arbitrarily curved planar elastica

2013

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“…40 Secondly, works dealing with the elastica of the nonlinear elastic materials which obey the Ludwick type constitutive law directly related to the present study are very limited. For elastica problems of the nonlinear elastic beams, several works are shortly introduced: Monasa (1981, 1982) solved the large deflections of the prismatic beams subjected to the point load and tip couple, respectively; Lee (2002) studied the large deformed prismatic beams with both the tip point load and uniform load; Jung and Kang (2005) studied the large deflections of cantilever beams with the nonlinear elastic materials; Eren (2008) solved the large deflections of the rectangular combined loaded beams by means of different arc length assumptions; and Brojan et al (2009) investigated the large deflections of nonprismatic/tapered beams with the tip couple.…”

Section: Introductionmentioning

confidence: 99%

“…Typical works are shortly reviewed: Kounadis and Mallis (1978) presented the post-buckling response of a simply supported, axially compressed, uniform bar of nonlinearly elastic material, in which the bar axis shortening was taken into account; Haslach (1985) analyzed the post-buckling behavior of the column made of a material with cubic constitutive equation to discover the post-buckling load deflection relationship; Lee (2001) investigated the post-buckling tip responses of uniform column under a combined load consisting of a uniformly distributed axial load and concentrated load at the free end; Jung and Kang (2005) studied the large deflections of cantilever columns with the modified Ludwick nonlinear elastic materials; Brojan et al (2007Brojan et al ( , 2009 presented the buckling stability characteristics of nonlinear elastic column, depending upon the values of different material parameters; and Saetiew and Chucheepsakul (2012) studied the post-buckling behavior of the linearly tapered and simply supported column made of the nonlinear elastic materials.…”

Section: Introductionmentioning

confidence: 99%

Elastica and buckling loads of nonlinear elastic tapered cantilever columns

Lee¹,

Lee²

2018

10.5267/j.esm

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This paper deals with the elastica and buckling loads of the nonlinear elastic tapered cantilever columns subjected to an axial load at the free end. The column cross section is rectangular, where the width and depth vary linearly with the column axis. The column material is nonlinear elastic, which obeys the Ludwick's constitutive law. The ordinary differential equations governing the elastica of buckled column are derived and solved numerically for computing the elastica and buckling loads. Parametric studies for the annealed copper, N.P. 8 aluminum alloy and steel columns are conducted.

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“…A semi-exact solution was obtained by Solano-Carrillo [9] for large deflection of cantilever beams made of Ludwick type material subjected to a combined action of a uniformly distributed load and to a vertical concentrated force at the free end. Brojan et al [10] studied the large deflections of nonlinearly elastic non-prismatic cantilever beams made of materials obeying the generalized Ludwick constitutive law. Holden [11] obtained the numerical solution to the problem of finite deflection of linear elastic cantilever beam with uniformly distributed load using a fourth order Runge-Kutta method.…”

Section: Introductionmentioning

confidence: 99%

Large deflection of a non-linear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end

Borboni

Santis

2014

Meccanica

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The investigated cantilever beam is characterized by a constant rectangular cross-section and is subjected to a concentrated constant vertical load, to a concentrated constant horizontal load and to a concentrated constant bending torque at the free end. The same beam is made by an elastic non-linear asymmetric Ludwick type material with different behavior in tension and compression. Namely the constitutive law of the proposed material is characterized by two different elastic moduli and two different strain exponential coefficients. The aim of this study is to describe the deformation of the beam neutral surface and particularly the horizontal and vertical displacements of the free end cross-section. The analysis of large deflection is based on the Euler-Bernoulli bending beam theory, for which cross-sections, after the deformation, remain plain and perpendicular to the neutral surface; furthermore their shape and area do not change. On the stress viewpoint, the shear stress effect and the axial force effect are considered negligible in comparison with the bending effect. The mechanical model deduced from the identified hypotheses includes two kind of non-linearity: the first due to the material and the latter due to large deformations. The mathematical problem associated with the mechanical model, i.e. to compute the bending deformations, consists in solving a non-linear algebraic system and a non-liner second order ordinary differential equation. Thus a numerical algorithm is developed and some examples of specific results are shown in this paper.

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Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law

Cited by 40 publications

References 20 publications

A simple method for determining large deflection states of arbitrarily curved planar elastica

A simple method for determining large deflection states of arbitrarily curved planar elastica

Elastica and buckling loads of nonlinear elastic tapered cantilever columns

Large deflection of a non-linear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end

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