Fourier cosine series method for solving the generalized thin-walled column buckling problem for Dirichlet boundary conditions / Charles C. Ike in REVUE DES COMPOSITES ET DES MATERIAUX AVANCES, Vol. 29, N° 3 (06/2019)  

[article]  inREVUE DES COMPOSITES ET DES MATERIAUX AVANCES > Vol. 29, N° 3 (06/2019) . - p. 131-137 Titre : Fourier cosine series method for solving the generalized thin-walled column buckling problem for Dirichlet boundary conditions Type de document : texte imprimé Auteurs : Charles C. Ike, Auteur ; Hyginus N. Omah, Auteur ; Benjamin O. Mama, Auteur ; Clifford U. Nwoji, Auteur ; Edwin U. Ikwueze, Auteur Année de publication : 2019 Article en page(s) : p. 131-137 Note générale : Bibliogr. Langues : Anglais (eng) Tags : 'Méthode  des  séries  en  cosinus  de  Fourier'  'Problème  flambement  généralisé  poteaux  élastiques  à  parois  minces'  'Equation  caractéristique'  valeurs  propres  algébriques'  'Valeur  propre'  'Fonctions  déplacement  modal'  'Charge  critique' Index. décimale : 620.11 Matériaux (propriétés, résistance) Résumé : The Fourier cosine series method was used to obtain solutions to the generalized elastic thin-walled column buckling problem for the case of Dirichlet end boundary conditions. The problem is a boundary value problem given by a set of three coupled ordinary differential equations with three unknown displacement functions, and subject to the Dirichlet end boundary conditions. By choosing the origin of the longitudinal coordinate at the middle of the column, the Fourier cosine series was found to be a suitable shape function for the problem and hence the three displacement modal functions were represented using Fourier cosine series, with unknown modal amplitudes. The Fourier cosine series representation of the unknown displacement modal functions simplified the problem to an algebraic eigenvalue problem given by a set of homogenous algebraic equations whose nontrivial solution yielded the characteristic buckling equation. The stability equation was obtained as a third-degree polynomial for the asymmetric cross-sectioned column. For asymmetric cross-sections, the buckling modes were obtained as coupled flexural-torsional modes. For bisymmetric cross-sections, the buckling modes were uncoupled and failure could be flexural or flexural-torsional. For monosymmetric cross-sections, one of the buckling modes is uncoupled while the others are coupled ; and failure could be by either Euler bending or bending-torsional buckling. The solutions obtained in this work agree with results obtained by previous researchers. Note de contenu : - THEORETICAL FRAMEWORK - METHOD : Dirichlet boundary conditions and Fourier cosine series for the buckling mode functions - Application of the Fourier cosine series method - RESULTS : Reduction to algebraic eigenvalue problem - Special cases of the generalised elastic thin-walled column buckling problem DOI : https://doi.org/10.18280/rcma.290301 En ligne : https://www.iieta.org/download/file/fid/17476 Format de la ressource électronique : Pdf Permalink : https://e-campus.itech.fr/pmb/opac_css/index.php?lvl=notice_display&id=34858 [article]

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Modified single finite Fourier cosine integral transform method for finding the critical elastic buckling loads of first order shear deformable beams with fixed ends / Charles C. Ike in REVUE DES COMPOSITES ET DES MATERIAUX AVANCES, Vol. 29, N° 6 (12/2019)  

[article]  inREVUE DES COMPOSITES ET DES MATERIAUX AVANCES > Vol. 29, N° 6 (12/2019) . - p. 357-362 Titre : Modified single finite Fourier cosine integral transform method for finding the critical elastic buckling loads of first order shear deformable beams with fixed ends Type de document : texte imprimé Auteurs : Charles C. Ike, Auteur ; Clifford U. Nwoji, Auteur ; Hyginus N. Onah, Auteur ; Benjamin O. Mama, Auteur ; Michael E. Onya, Auteur Année de publication : 2019 Article en page(s) : p. 357-362 Note générale : Bibliogr. Langues : Français (fre) Tags : 'Equation  de  flambement  caractéristique'  'Charge  critique  élastique'  'Problème  valeur  propre'  'Théorie  des  poutres  déformation  par  cisaillement  du  premier  ordre'  'méthode  transformation  intégrale  en  cosinus  Fourier  finie  simple  modifiée' Index. décimale : 620.11 Matériaux (propriétés, résistance) Résumé : This paper proposes a novel modified single finite Fourier cosine integral transform, which determines the elastic buckling loads of moderately-thick, fixed-end beams made of homogeneous, isotropic, linear elastic materials. First, such a beam was modelled with a fourth-order ordinary differential equation, according to the first-order shear deformation theory. Then, the single finite Fourier cosine integral transform was modified to satisfy all the boundary conditions at the fixed ends,using the apriori knowledge, and provide an exact buckling mode (shape) function for the beam. Through the modified transform, the boundary value problem was converted to an algebraic eigenvalue problem, which canbe described by a set of homogeneous algebraic equations. For nontrivial solutions, the characteristic buckling equation was drived from the vanishing of the determinant of the coefficient matrix. Solving the characteristic buckling equation, the authors obtained the eigenvalues and thus derived the buckling loads. The critical buckling load was found to correspond to the first buckling mode. The proposed modified transform gave exact expressions for the buckling loads and the critical buckling load of the fixed ends, because the integral kernel function satisfies all the boundary conditions, and the transform on the domain governing equation satisfies all the domain equations. The solutions of our method agree well with the previous studies. Note de contenu : - THEORY : Assumptions - Displacement components - Strain field components - Stress fields - Total potential energy functional, π - METHOD DOI : https://doi.org/10.18280/rcma.290603 En ligne : https://www.iieta.org/download/file/fid/21501 Format de la ressource électronique : Pdf Permalink : https://e-campus.itech.fr/pmb/opac_css/index.php?lvl=notice_display&id=34947 [article]

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