Elastica and buckling loads of nonlinear elastic tapered cantilever columns

Lee, Joon Kyu; Lee, Byoung Koo

doi:10.5267/j.esm.2017.11.001

Cited by 12 publications

(5 citation statements)

References 15 publications

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“…These kinds of solution methods for the boundary and eigenvalue problems like Eq. (14) are described in detail in references (Lee & Lee, 2018. In this study, the lowest, i.e., first, value of is computed.…”

Section: Solution Methodsmentioning

confidence: 99%

Buckling lengths of heavy column with various end conditions

Lee¹,

Lee²

2020

10.5267/j.esm

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This paper deals with buckling lengths of the heavy column with various end conditions, where both top and bottom ends are either free or hinged or clamped. Based on equilibrium equations of the buckled column element, the differential equation governing the buckled mode shape is derived. For solving the buckling length, the differential equation is integrated by the direct integration method and the buckling length is calculated by the determinant search method. The buckling lengths of this study agree well with those of references. The buckling lengths with various end conditions, buckled mode shapes and buckling stresses are presented.

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Section: Solution Methodsmentioning

confidence: 99%

Buckling lengths of heavy column with various end conditions

Lee¹,

Lee²

2020

10.5267/j.esm

Self Cite

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“…There are several works focused on the study of the buckling behavior of nonlinear elastic columns but the number of works using green composites is quite reduced. Most of them are theoretical works that assume a nonlinear elastic behavior following the Ludwick law as in [ 23 ]. Lee and Lee [ 23 ] analyzed the buckling response of tapered rectangular columns that obey the Ludwick-type material behavior.…”

Section: Introductionmentioning

confidence: 99%

“…Most of them are theoretical works that assume a nonlinear elastic behavior following the Ludwick law as in [ 23 ]. Lee and Lee [ 23 ] analyzed the buckling response of tapered rectangular columns that obey the Ludwick-type material behavior. They developed a mathematical model and solved it with two FORTRAN computer programs.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Critical Buckling Load on Open Cross-Section Columns of Flax/PLA Green Composites

et al. 2022

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The present work aims to analyze the buckling behavior of nonlinear elastic columns with different open cross-sections and slenderness ratios to verify the limits of the modified Ludwick law to predict the critical buckling load. The results of the analytical formulation based on the modified Ludwick law are compared with a FEM numerical model using the Marlow hyperelastic behavior and experimental results conducted on flax/PLA specimens with three different open cross-sections. The comparative results show that the numerical predictions agree with the experimental results in all the cases. The FEM model can exactly reproduce the buckling behavior of the C-section columns. However, the prediction errors for the C90 and C180 columns are higher than for the C60 columns. Moreover, the theoretical estimations indicate that the C90 cross-section column is the limit of application of the modified Ludwick law to predict the critical buckling load of nonlinear elastic columns with open cross-sections, and the C180 column is out of the prediction limits. Generally, the numerical and theoretical models underestimated the scattering effects of the predictions because more experimental variables were not considered by the models.

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“…A commonly adopted alternative to those methods, as recommended by design codes, is the use of advanced (physically and geometrically nonlinear) finite element analysis (FEA), which is obviously unfeasible in current design practice due to their time and know-how requirements (besides involving expensive FEA software). Although the large amount of research performed in the last few decades, either concerning i) numerical/analytical formulations (Asgarian and Soltani 2011, Trahair 2014, Mohri et al 2015, Ghadban et al 2017, Kim and Jang 2017, Balduzzi et al 2017, Lee and Lee 2018, or ii) design methods (Marques et al 2012, Zhang et al 2013, Papp 2016, it is still imperative the development of groundbreaking (i.e., simultaneously accurate, easy-to-use, versatile, efficient and affordable) design rules/tools for tapered steel members.…”

Section: Introductionmentioning

confidence: 99%