Buckling of Euler Columns with a Continuous Elastic Restraint via Homotopy Analysis Method

Eryılmaz, Aytekin; Atay, Mehmet Tarık; Coşkun, Safa Bozkurt; Başbük, Musa

doi:10.1155/2013/341063

Cited by 13 publications

(11 citation statements)

References 36 publications

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“…In the case where the piezoceramic patches length is equal to zero (prismatic beam), the obtained numerical results can be compared with those presented in [7].…”

Section: The Influence Of Geometry On the Critical Buckling Loadmentioning

confidence: 99%

“…The role of elastic foundation modulus, ratio of the lumped mass to the column's mass, position of the lumped mass and four different types of load distribution have been examined. Eryilmaz et al [7] have presented a study in the buckling instability for Euler columns with continuous elastic restraint on the basis of homotopy analysis method (HAM). Results concerned the effect of five different ways of beam support and the effect of the elastic restraint coefficient on the first and second modes of buckling.…”

Section: Introductionmentioning

confidence: 99%

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Buckling of stepped beams resting on an elastic foundation

Kuliński

Przybylski

2015

J. Appl. Math. Comput. Mech.

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Abstract. The influence of structural parameters of a stepped beam with two ends fixed and resting on Winkler foundation on its buckling critical force has been discussed in this paper. The structure inhomogeneity results from two piezoceramic plates perfectly bonded at the top and bottom surface of the beam. For the performed analysis five different supports of beam ends which prevent longitudinal displacements have been adopted. Numerical analysis has been divided into two parts. The first part concerns the influence of the system geometry on its critical force, whereas in the second part, a modification of the buckling load resulting from the electric field applied to the piezosegment has been investigated.

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“…In the case where the piezoceramic patches length is equal to zero (prismatic beam), the obtained numerical results can be compared with those presented in [7].…”

Section: The Influence Of Geometry On the Critical Buckling Loadmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buckling of stepped beams resting on an elastic foundation

Kuliński

Przybylski

2015

J. Appl. Math. Comput. Mech.

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“…On the other hand, the closed-form solution of the 4 th order differential equation governing for the buckling or vibration behavior of columns or beams with arbitrary distributions of flexural stiffness and different end conditions is very difficult to determine in most of the cases and exists only for limited cases. In addition to this research field, several researchers presented some exact solutions to study the buckling of nonuniform columns, in terms of logarithmic and trigonometric functions, Bessel functions, Lommel functions, and in terms of series representation shown by Eryılmaz et al [6]. During the last decades, the columns' buckling has become the center point of study for many researchers.…”

Section: Introductionmentioning

confidence: 99%

Joint Effect of the Nonlinearity of Elastic Foundations and the Variation of the Inertia Ratio on Buckling Behavior of Prismatic and Nonprismatic Columns Using a GDQ Method

Abumandour

Abdelmgeed

Elrefaey

2020

Mathematical Problems in Engineering

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In this paper, we present a simple, powerful, yet efficient and easily applicable technique based on the GDQ method for solving nonlinear problems. The proposed technique is implemented to some nonlinear engineering problems in structure analysis. The results reveal that the proposed technique is effective. Then, the proposed technique is used to explain the effects of the variation of cross section area on the nondimensional critical buckling loads for columns with and without elastic foundation for three sets of boundary conditions. Finally, the proposed technique is used to investigate the effect of the nonlinearity term of Winkler elastic foundation on the nondimensional critical buckling loads of nonuniform columns resting on elastic foundations. The effectiveness of the proposed technique is validated through comparing the present results with exact solutions and other numerical results available in references. The proposed method benefits the optimum design of columns against buckling in engineering applications. The most important conclusions from this paper can be summarized as follows. When the inertia ratio varies parabolically, the nondimensional critical buckling loads increase in comparison with varying linearly. Moreover, the nondimensional critical buckling loads increase in the presence of the elastic foundation.

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“…Therefore, the knowledge of stability analyses in the theoretical and computational branch is required in more detail today [1,2]. At present, when the effort about design of the construction with a low mass dominates, the rods with a high slenderness, which have a tendency to succumb in stability loss, often appear in practice.…”

Section: Introductionmentioning

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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Buckling of Euler Columns with a Continuous Elastic Restraint via Homotopy Analysis Method

Cited by 13 publications

References 36 publications

Buckling of stepped beams resting on an elastic foundation

Buckling of stepped beams resting on an elastic foundation

Joint Effect of the Nonlinearity of Elastic Foundations and the Variation of the Inertia Ratio on Buckling Behavior of Prismatic and Nonprismatic Columns Using a GDQ Method

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

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