Homogenization and a galerkin approximation in three–dimensional beam theory

References

• Geymonet , G. , Krasuki , F. and Marigo , J.J. 1987 . Stress Distribution in Anisotropic Elastic Composite Beams. Applications of Multiple Scaling in Mechanics , Paris : Marigo .
   Google Scholar
• Tutek , Z. 1987 . Applications of Multiple Scaling in Mechanics , Paris : Masson .
   Google Scholar
• Mascarenhas , M.L. and Trabucho , L. 1990 . Homogenized behaviour of a beam with a multicellular cross section . Appl. Analysis , 38 : 97 – 119 .
   Google Scholar
• Trabucho , L. and Viano , J.M. 1989 . Existence and Characterization of Higher Order Terms in an Asymptotic Expansion Method for Linearized Elastic Beams . J. Asymptotic Analysis , 2 : 223 – 255 .
   Google Scholar
• Trabucho , L. and Viano , J.M. 1990 . A new approach of Timoshenko's beam theory by the asymptotic expansion method . Mod. Math, et Anal. Num , 24 : 651 – 680 .
   Google Scholar
• Miara , B. and Trabucho , L. A Galerkin spectral approximation in linearized beam theory
   Google Scholar
• Bermudez , A. and Viano , J.M. 1984 . Une Justification des Equations de la Thermo - Elasticity des Poutres a Section Variable par des Methodes Asymptotiques . RAIRO , 18 : 347 – 376 .
   Google Scholar
• Cimetiere , A. , Geymonat , G. , LeDret , H. , Raoult , A. and Tutek , Z. 1988 . Asymptotic Theory and Analysis for Displacements and Stress Distributions in Nonlinear Elastic Straight Slender Rods . J. of Elasticity , 19 : 111 – 161 .
   Web of Science ®Google Scholar
• Mascarenhas , M.L. and Trabucho , L. 1987 . A Derivation of Generalized bending and torsion models for Multicellular Linearized Elastic Beams by Asymptotic Expansion Methods , Portugal : 4th National Congress on Theoretical and Applied Mechanics .
   Google Scholar
• Trabucho , L. and Viano , J.M. 1987 . Applications Qf Multiple Scaling in Mechanics , Paris : Masson .
   Google Scholar
• Trabucho , L. and Viano , J.M. 1988 . A derivation of generalized Saint Venant's torsion theory from three dimensional elasticity by asymptotic expansion methods . Applicable Analysis , 13 : 129 – 148 .
   Google Scholar
• Tutek , Z. and Aganovic , I. 1987 . A Justification of the One-Dimensional Linear Model of Elastic Beam . Math. Meth. Appl. Sci , 8 : 1 – 14 .
   Google Scholar
• Ciarlet , P.G. and Destuynder , P. 1979 . A justification of the two dimensional linear plate model . J. de Mecanique , 18 : 315 – 344 .
   Google Scholar
• Ciarlet , P.G. and Destuynder , P. 1979 . A justification of a nonlinear model in plate theory . Comp. Methods Appl. Mech. Engrg , 17-18 : 227 – 258 .
   Google Scholar
• Tartar , L. 1977 . Problemes d’Homogenisation dans les Equations aux Derivees Partielles , College de France : Cours Peccot .
   Google Scholar
• Murat , F. 1977-78 . H - Convergence . Seminaire d'Analyse Fonctionnelle et Numerique 1977/78 ,
   Google Scholar
• Cioranescu , D. and Saint Jean Paulin , J. 1979 . Homogenization in Open Sets with Holes . J. of Math. Anal. Appl , 71 : 590 – 607 .
   Web of Science ®Google Scholar
• Lene , F. 1984 . Contribution a 1’Etude des riateriaux Composites et de Leur Endommaqement , Paris : Univ. Pierre et Marie Curie .
   Google Scholar
• Benssoussan , A. , Lions , J.L. and Papanicolaou , G. 1978 . Asymptotic Analysis for Periodic Structures , Amsterdam : North Holland .
   Google Scholar
• Sanchez-Palencia , E. 1980 . Non Homogeneous Media and Vibration Theory . Lecture Notes in Physics , 127
   Google Scholar
• Ball , J. and Murat , F. 1984 . W1p - Quasiconvexity and Yariational Problems for Multiple Integrals . J. Funct. Anal , 58 : 225 – 253 .
   Web of Science ®Google Scholar