Buckling analysis of thin-walled open members—A complementary energy variational principle

Erkmen, R. Emre; Mohareb, Magdi

doi:10.1016/j.tws.2008.01.001

Cited by 27 publications

(10 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This includes the work of Erkmen and Mohareb [39] who developed a complementary energy variational principle and formulated a finite element (Erkmen and Mohareb [40]) for thin-walled members with open cross-sections. In a subsequent study, focused on torsional buckling of columns, Erkmen et al [41] demonstrated that the elastic torsional buckling of columns can be guaranteed to converge from below.…”

Section: Buckling Solutions Under Shear Deformable Theoriesmentioning

confidence: 99%

Finite element formulation for lateral torsional buckling analysis of shear deformable mono-symmetric thin-walled members

Sahraei

Li-ping²,

Mohareb

2015

Thin-Walled Structures

Self Cite

View full text Add to dashboard Cite

Section: Buckling Solutions Under Shear Deformable Theoriesmentioning

confidence: 99%

Finite element formulation for lateral torsional buckling analysis of shear deformable mono-symmetric thin-walled members

Sahraei

Li-ping²,

Mohareb

2015

Thin-Walled Structures

Self Cite

View full text Add to dashboard Cite

“…Possible advantages of using complementary energy principles in structural stability problems were later pointed out by Oran [81,82], Schreyer and Shih [126], Popelar [97,98], Masur and Popelar [70], Koiter [62] and Tabarrok and Yuexi [136]. Recently, Erkmen and Mohareh [27,28] proposed a complementary energy method for the buckling analysis of thin-walled beams with open cross-sections. Also a complementary-energy method for the stability and post-buckling analysis of geometrically exact frames modeled using a Reissner-Simo beam theory has recently been proposed by Santos [118].…”

Section: Complementary-energy Based Principles For Non-linear Elasticmentioning

confidence: 99%

“…The true complementary energy (27) differs from the conjugate energy (29) on the following integral term…”

Section: Conjugate Energy and The Gap Functionalmentioning

confidence: 99%

Complementary-Energy Methods for Geometrically Non-linear Structural Models: An Overview and Recent Developments in the Analysis of Frames

Santos

2011

Arch Computat Methods Eng

View full text Add to dashboard Cite

Boundary-value problems in solid mechanics are often addressed, from both theoretical and numerical points of view, by resorting to displacement/rotation-based variational formulations. For conservative problems, such formulations may be constructed on the basis of the Principle of Stationary Total Potential Energy. Small deformation problems have a unique solution and, as a consequence, their corresponding total potential energies are globally convex. In this case, under the so-called Legendre transform, the total potential energy can be transformed into a globally concave total complementary energy only expressed in terms of stress variables. However, large deformation problems have, in general, for the same boundary conditions, multiple solutions. As a result, their associated total potential energies are globally non-convex. Notwithstanding, the Principle of Stationary Total Potential Energy can still be regarded as a minimum principle, only involving displacement/rotation fields. The existence of a maximum complementary energy principle defined in a truly dual form has been subject of discussion since the first contribution made by Hellinger in 1914. This paper provides a survey of the complementary energy principles and also accounts for the evolution of the complementary-energy based finite element models for geometrically non-linear solid/structural models proposed in the literature over the last 60 years, giving special emphasis to the complementary-energy based methods developed within the framework of the geometrically exact ReissnerSimo beam theory for the analysis of structural frames.

show abstract

“…The lateral buckling, as a type of overall buckling, may dominate a slender H-section beam. To propose approximate equations for the elastic critical bending value of an H-section steel member, Numerous analytical and experimental studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have been reported. Yet to the writer's knowledge, accurate closed-form equations have been rarely formed.…”

Section: Introductionmentioning

confidence: 99%

Overall Buckling and Ultimate Load of an H-Section Steel Member Under Combined Compression and Bending

Wang

2018

Journal of Asian Architecture and Building Engineering

View full text Add to dashboard Cite

This paper presents a theoretical method and FEM to study the overall buckling of an H-section steel member with narrow flanges. The theoretical study aims to elaborate the significant parameters involved. Based on the theoretical analysis, a parametric study is performed to identify the adequate coefficients for the design of an efficient and general evaluation technique to form the equation. As a result, the approximate closed-form equations are successfully proposed for the elastic critical moment of the H-section beam. Besides, the numerical analysis by FEM is performed to investigate the ultimate load, and the design equation for the ultimate load of an H-section column under combined compression and bending is recommended.

show abstract

Buckling analysis of thin-walled open members—A complementary energy variational principle

Cited by 27 publications

References 43 publications

Finite element formulation for lateral torsional buckling analysis of shear deformable mono-symmetric thin-walled members

Finite element formulation for lateral torsional buckling analysis of shear deformable mono-symmetric thin-walled members

Complementary-Energy Methods for Geometrically Non-linear Structural Models: An Overview and Recent Developments in the Analysis of Frames

Overall Buckling and Ultimate Load of an H-Section Steel Member Under Combined Compression and Bending

Contact Info

Product

Resources

About