Complementary energy based formulation for torsional buckling of columns / Erkmen, R. Emre in Journal of engineering mechanics, Vol. 135 N° 12 (Décembre 2009)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 135 N° 12 (Décembre 2009) . - pp. 1420-1426 Titre : Complementary energy based formulation for torsional buckling of columns Type de document : texte imprimé Auteurs : Erkmen, R. Emre, Auteur ; Magdi Mohareb, Auteur ; Bradford, Mark A., Auteur Article en page(s) : pp. 1420-1426 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Buckling Torsion Convergence. Résumé : A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs' transformation. In contrast to flexural buckling analysis of columns, it is shown that when the principle of stationary complementary energy is used, the torsional buckling loads can be underpredicted. A mathematical proof is provided to elucidate this property. The convergence behavior of the approximate solutions is illustrated through numerical examples for several columns with different boundary conditions. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/vsearch/servlet/VerityServlet?KEY=JENMDT&smode=strres [...] [article] Complementary energy based formulation for torsional buckling of columns [texte imprimé] / Erkmen, R. Emre, Auteur ; Magdi Mohareb, Auteur ; Bradford, Mark A., Auteur . - pp. 1420-1426. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 135 N° 12 (Décembre 2009) . - pp. 1420-1426 Mots-clés : Buckling Torsion Convergence. Résumé : A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs' transformation. In contrast to flexural buckling analysis of columns, it is shown that when the principle of stationary complementary energy is used, the torsional buckling loads can be underpredicted. A mathematical proof is provided to elucidate this property. The convergence behavior of the approximate solutions is illustrated through numerical examples for several columns with different boundary conditions. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/vsearch/servlet/VerityServlet?KEY=JENMDT&smode=strres [...]

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Nonlinear inelastic dynamic analysis of i-beams curved in-plan / Erkmen, R. Emre in Journal of structural engineering, Vol. 137 N° 11 (Novembre 2011)  

Public ISBD [article]  inJournal of structural engineering > Vol. 137 N° 11 (Novembre 2011) . - pp. 1373-1380 Titre : Nonlinear inelastic dynamic analysis of i-beams curved in-plan Type de document : texte imprimé Auteurs : Erkmen, R. Emre, Auteur ; Bradford, Mark A., Auteur Année de publication : 2012 Article en page(s) : pp. 1373-1380 Note générale : Génie Civil Langues : Anglais (eng) Mots-clés : Curved beams Dynamic analysis Inelastic behavior Geometric nonlinearity Résumé : This paper presents a finite-element formulation for the dynamic analysis of I-beams curved in-plan, in which geometric nonlinearities owing to large deflections and inelastic material behavior are taken into account. The developed finite element is based on the total Lagrangian formulation. Wagner and warping effects are considered in the analysis. The nonlinear dynamic equilibrium equations are solved by using Newmark’s step by step numerical integration procedure. The von Mises associative isotropic hardening model is used to formulate the metal plasticity. The elastic predictor-radial corrector algorithm is used to consider gradual yielding on the cross section and along the beam. Simpler finite-element formulations are also developed by excluding the effects of geometric and material nonlinearities. Numerical examples are provided to illustrate the significance of the effects of geometric and material nonlinearities on the dynamic behavior of I-beams that are curved in-plan. DEWEY : 624.17 ISSN : 0733-9445 En ligne : http://ascelibrary.org/sto/resource/1/jsendh/v137/i11/p1373_s1?isAuthorized=no [article] Nonlinear inelastic dynamic analysis of i-beams curved in-plan [texte imprimé] / Erkmen, R. Emre, Auteur ; Bradford, Mark A., Auteur . - 2012 . - pp. 1373-1380. Génie Civil Langues : Anglais (eng) in Journal of structural engineering > Vol. 137 N° 11 (Novembre 2011) . - pp. 1373-1380 Mots-clés : Curved beams Dynamic analysis Inelastic behavior Geometric nonlinearity Résumé : This paper presents a finite-element formulation for the dynamic analysis of I-beams curved in-plan, in which geometric nonlinearities owing to large deflections and inelastic material behavior are taken into account. The developed finite element is based on the total Lagrangian formulation. Wagner and warping effects are considered in the analysis. The nonlinear dynamic equilibrium equations are solved by using Newmark’s step by step numerical integration procedure. The von Mises associative isotropic hardening model is used to formulate the metal plasticity. The elastic predictor-radial corrector algorithm is used to consider gradual yielding on the cross section and along the beam. Simpler finite-element formulations are also developed by excluding the effects of geometric and material nonlinearities. Numerical examples are provided to illustrate the significance of the effects of geometric and material nonlinearities on the dynamic behavior of I-beams that are curved in-plan. DEWEY : 624.17 ISSN : 0733-9445 En ligne : http://ascelibrary.org/sto/resource/1/jsendh/v137/i11/p1373_s1?isAuthorized=no

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