Boundary conditions for elastic beam bending

Yang Gao; Si-Peng Xu; Bao-Sheng Zhao

doi:10.1016/j.crme.2006.11.001

Boundary conditions for elastic beam bending

Presented by: Évariste Sanchez-Palencia

Yang Gao ¹ ; Si-Peng Xu ²; Bao-Sheng Zhao ³

¹ College of Science, China Agricultural University, Beijing 100083, China
² College of Engineering, Ocean University of China, Qingdao 266071, China
³ School of Mechanical Engineering, University of Science and Technology, Liaoning, Anshan 114044, China

Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 1-6.

Abstract
Résumé

For beam bending problem, the reciprocal theorem and P–N solution are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. Through generalizing the method proposed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. When stress and mixed conditions are imposed on the beam edge, these decaying state conditions are derived explicitly, and they are used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of beam theories. More importantly, the appropriate boundary conditions with two different sets of mixed edge-data are obtained for the first time.

Dans le problème de la flexion des poutres nous utilisons le théorème de réciprocité et la solution de Papkovich–Neuber pour trouver, de manière inédite, les conditions mixtes de tension aux limites avec une exactitude appropriée à tous les ordres d'approximation. En généralisant la méthode proposée par Gregory et Win, on établit l'ensemble des conditions nécessaires pour les données sur les cotés assurant l'existence des solutions évanescentes. Dans le cas où les conditions sur les tensions mixtes sont imposées sur le coté d'une poutre, les conditions assurant l'apparition d'états évanescents sont dérivées explicitement. Nous les utilisons par la suite dans une formulation correcte des conditions aux limites pour la solution intérieure. Nos conditions sur les tensions coïncident avec celles obtenues par la théorie de la flexion des poutres usuelle. Le résultat le plus important est l'obtention, pour la première fois, des conditions aux limites appropriées avec deux ensembles différents des données mixtes sur le bord de la poutre.

Received: 2006-07-27
Accepted: 2006-10-10
Published online: 2006-12-04

DOI: 10.1016/j.crme.2006.11.001

Keywords: Computational solid mechanics, Boundary conditions, Beam bending, Decaying states, Regular states
Mot clés : Mécanique des solides numérique, Conditions aux limites, Fléxion des poutres, États évanescents, États réguliers

Author's affiliations:

Yang Gao ¹; Si-Peng Xu ²; Bao-Sheng Zhao ³

¹ College of Science, China Agricultural University, Beijing 100083, China
² College of Engineering, Ocean University of China, Qingdao 266071, China
³ School of Mechanical Engineering, University of Science and Technology, Liaoning, Anshan 114044, China

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     title = {Boundary conditions for elastic beam bending},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {1--6},
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     language = {en},
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Yang Gao; Si-Peng Xu; Bao-Sheng Zhao. Boundary conditions for elastic beam bending. Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 1-6. doi : 10.1016/j.crme.2006.11.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.11.001/

References
Cited by

[1] R.D. Gregory; F.Y.M. Wan Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory, J. Elast., Volume 14 (1984), pp. 27-64

[2] R.D. Gregory; F.Y.M. Wan On plate theories and Saint-Venant's principle, Int. J. Solids Struct., Volume 21 (1985), pp. 1005-1024

[3] R.D. Gregory; F.Y.M. Wan Edge effect in the stretching of plates (P. Ladeveze, ed.), Local Effects in the Analysis of Structures, Elsevier Science Publishers, Amsterdam, 1985, pp. 35-54

[4] R.D. Gregory; F.Y.M. Wan On the interior solution for linearly elastic plate, ASME J. Appl. Mech., Volume 55 (1988), pp. 551-559

[5] Y.H. Lin; F.Y.M. Wan First integrals and the interior solution for orthotropic plates in plane strain or axisymmetric deformations, Stud. Appl. Math., Volume 79 (1988), pp. 93-125

[6] F.Y.M. Wan Stress boundary conditions for plate bending, Int. J. Solids Struct., Volume 40 (2003), pp. 4107-4123

[7] Y. Gao; M.Z. Wang Comment on “Stress boundary conditions for plate bending” by F.Y.M. Wan [Int. J. Solids Struct. 40 (2003) 4107–4123], Int. J. Solids Struct., Volume 46 (2006), pp. 1854-1855

[8] F.Y.M. Wan Author's response to Comment by Yang Gao and Min-Zhong Wang on “Stress boundary conditions for plate bending” by F.Y.M. Wan [Int. J. Solids Struct. 40 (2003) 4107–4123], Int. J. Solids Struct., Volume 46 (2006), p. 1856

[9] S.P. Timoshenko; J.C. Goodier Theory of Elasticity, McGraw–Hill, New York, 1970

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