A mathematical model and analytical solution for buckling of inclined beam-columns

Sampaio, Jorge H.B.; Hundhausen, Joan R.

doi:10.1016/s0307-904x(98)10014-8

Cited by 34 publications

(15 citation statements)

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“…Moreover, the analytical solutions of a multi-step bar with varying cross section were obtained by Li et al [18,19] and papers cited therein. The energy method was used by Sampaio et al [22] to find the solution for the problem of buckling behaviour of inclined beam-column. Some of the important researchers who studied the mechanical behavior of beams/columns are Keller [15], Tadjbakhsh and Keller [27] and Taylor [28].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Tilt‐buckling of Euler Columns With Varying Flexural Stiffness Using Homotopy Perturbation Method

Coşkun

2010

Mathematical Modelling and Analysis

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Abstract. In this paper, the Homotopy Perturbation Method (HPM), is introduced for elastic stability analysis of tilt-buckled columns with variable flexural stiffness. Buckling loads and corresponding mode shapes are determined considering different types of variations in flexural stiffness of columns. The proposed approach is an efficient technique for the elastic stability analysis of specified problems.

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Section: Introductionmentioning

confidence: 99%

Analysis of Tilt‐buckling of Euler Columns With Varying Flexural Stiffness Using Homotopy Perturbation Method

Coşkun

2010

Mathematical Modelling and Analysis

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“…(1) for the clamped prismatic rod with a free end and length l loaded by selfweight ( Fig. 1) can be, according to the literature [7], written in the form where the following boundary condition is applied Figure 1 Buckling under self-weight where x is a distance along the rod length, w(x) is the lateral displacement, γ is the gravity force per length unit and EJ is the rod stiffness. A trivial solution to Eq.…”

Section: Exact Solution To the Problemmentioning

confidence: 99%

“…(1) equals zero. A non-trivial solution is a problem of the own numbers, which is presented by Love in the form [7] ( ) …”

Section: Exact Solution To the Problemmentioning

confidence: 99%

An approximation of deflection line function at the rod loaded by buckling under self-weight

et al. 2016

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Preliminary notesThe paper deals with an approximation of the exact deflection line function at a rod loaded by self-weight buckling via the function, which is bestpresented by the exact shape of this rod. In this paper, we suggest the methods of derivation of the critical buckling length by the exact solution and by the energy method. For the substitute functions of deflection line, the variants of goniometric functions and polynomials are chosen. Individual coefficients of the functions are chosen on the basis of existing boundary conditions and in the case of their insufficient count, they are chosen in order to express the exact rod deflection line shape in the most suitable way, which was transposed from the concrete example solution by SolidWorks Simulation software. The paper shows the errors of critical buckling length calculation against the exact solution, as well as the maximum absolute and relative deviations in the lateral displacement for the chosen function. From the individual substitute functions, one function that meets the condition for general use and has the lowest deviations from the exact solution, is subsequently chosen. Keywords: approximation of function; buckling; polynomials; self-weight Aproksimacija funkcije linije otklona za štap opterećen izvijanjem pod vlastitom težinomPrethodno priopćenje Rad se bavi aproksimacijom točne funkcije linije otklona za štap opterećen izvijanjem zbog vlastite težine pomoću funkcije, što je najbolje prikazano točnim oblikom ovog štapa. U ovom radu predlažemo metode derivacije kritične duljine izvijanja pomoću točnog rješenja i pomoću metode energije. Za zamjenske funkcije linije otklona su izabrane varijante goniometrijskih funkcija i polinomi. Pojedinačni koeficijenti funkcija su izabrani na temelju postojećih rubnih uvjeta i u slučaju nedovoljnog broja, oni su izabrani kako bi se izrazio točan oblik linije otklona štapa na najprikladniji način, koji je prenesen iz konkretnog primjera rješenja pomoću softvera SolidWorks. Rad prikazuje pogreške kritičnog izračuna duljine izvijanja nasuprot točnom rješenju, kao i maksimalna apsolutna i relativna odstupanja kod bočnog pomicanja za odabranu funkciju. Od pojedinačnih zamjenskih funkcija je naknadno izabrana ona koja ispunjava uvjet za opće korištenje i ima najmanja odstupanja od točnog rješenja.

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“…Moreover, the analytical solutions of a multi-step bar with varying cross section were obtained by Li et al [16][17][18]. The energy method was used by Sampaio et al [19] to find the solution for the problem of buckling behavior of inclined beamcolumn. Some of the important researchers who studied the mechanical behavior of beamcolumns are Keller [20], Tadjbakhsh and Keller [21] and Taylor [22].…”

Section: Introductionmentioning

confidence: 99%

Elastic Stability Analysis of Euler Columns Using Analytical Approximate Techniques

Coşkun¹,

Öztürk²

2012

Advances in Computational Stability Analysis

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A mathematical model and analytical solution for buckling of inclined beam-columns

Cited by 34 publications

References 1 publication

Analysis of Tilt‐buckling of Euler Columns With Varying Flexural Stiffness Using Homotopy Perturbation Method

Analysis of Tilt‐buckling of Euler Columns With Varying Flexural Stiffness Using Homotopy Perturbation Method

An approximation of deflection line function at the rod loaded by buckling under self-weight

Elastic Stability Analysis of Euler Columns Using Analytical Approximate Techniques

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