Assumed-strain solid–shell formulation for the six-node finite element SHB6: evaluation on non-linear benchmark problems

References

• Abed-Meraim , F. and Combescure , A. 2002 . SHB8PS – a new adaptive, assumed-strain continuum mechanics shell element for impact analysis . Computers & Structures , 80 : 791 – 803 .
   Web of Science ®Google Scholar
• Abed-Meraim , F. and Combescure , A. 2009 . An improved assumed strain solid–shell element formulation with physical stabilization for geometric nonlinear applications and elastic-plastic stability analysis . International Journal for Numerical Methods in Engineering , 80 : 1640 – 1686 .
   Web of Science ®Google Scholar
• Belytschko , T. and Bindeman , L.P. 1993 . Assumed strain stabilization of the eight node hexahedral element . Computer Methods in Applied Mechanics and Engineering , 105 : 225 – 260 .
   Web of Science ®Google Scholar
• Brush , D.O. and Almroth , B.O. 1975 . Buckling of bars, plates and shells , New York , NY : McGraw-Hill .
   Google Scholar
• Dvorkin , E.N. and Bathe , K.-J. 1984 . Continuum mechanics based four-node shell element for general non-linear analysis . Engineering Computations , 1 : 77 – 88 .
   Google Scholar
• Fish , J. and Belytschko , T. 1988 . Elements with embedded localization zones for large deformation problems . Computers & Structures , 30 : 247 – 256 .
   Web of Science ®Google Scholar
• Hauptmann , R. and Schweizerhof , K. 1998 . A systematic development of solid-shell element formulations for linear and non-linear analyses employing only displacement degrees of freedom . International Journal for Numerical Methods in Engineering , 42 : 49 – 69 .
   Web of Science ®Google Scholar
• Killpack , M. and Abed-Meraim , F. 2011 . Limit-point buckling analyses using solid, shell and solid–shell elements . Journal of Mechanical Science and Technology , 25 : 1105 – 1117 .
   Web of Science ®Google Scholar
• Klinkel , S. and Wagner , W. 1997 . A geometrical non-linear brick element based on the EAS-method . International Journal for Numerical Methods in Engineering , 40 : 4529 – 4545 .
   Web of Science ®Google Scholar
• Klinkel , S. , Gruttmann , F. and Wagner , W. 1999 . A continuum based three-dimensional shell element for laminated structures . Computers & Structures , 71 : 43 – 62 .
   Web of Science ®Google Scholar
• Leahu-Aluas , I. and Abed-Meraim , F. 2011 . A proposed set of popular limit-point buckling benchmark problems . Structural Engineering and Mechanics , 38 : 767 – 802 .
   Web of Science ®Google Scholar
• Legay , A. and Combescure , A. 2003 . Elastoplastic stability analysis of shells using the physically stabilized finite element SHB8PS . International Journal for Numerical Methods in Engineering , 57 : 1299 – 1322 .
   Web of Science ®Google Scholar
• MacNeal , R.H. and Harder , R.L. 1985 . A proposed standard set of problems to test finite element accuracy . Finite Elements in Analysis and Design , 1 : 3 – 20 .
   Google Scholar
• Puso , M.A. 2000 . A highly efficient enhanced assumed strain physically stabilized hexahedral element . International Journal for Numerical Methods in Engineering , 49 : 1029 – 1064 .
   Web of Science ®Google Scholar
• Reese , S. , Wriggers , P. and Reddy , B.D. 2000 . A new locking-free brick element technique for large deformation problems in elasticity . Computers & Structures , 75 : 291 – 304 .
   Web of Science ®Google Scholar
• Riks , E. 1979 . An incremental approach to the solution of snapping and buckling problems . International Journal for Numerical Methods in Engineering , 15 : 524 – 551 .
   Google Scholar
• Simo , J.C. and Armero , F. 1992 . Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes . International Journal for Numerical Methods in Engineering , 33 : 1413 – 1449 .
   Web of Science ®Google Scholar
• Simo , J.C. and Hughes , T.J.R. 1986 . On the variational foundations of assumed strain methods . Journal of Applied Mechanics, ASME , 53 : 51 – 54 .
   Web of Science ®Google Scholar
• Simo , J.C. and Rifai , M.S. 1990 . A class of mixed assumed strain methods and the method of incompatible modes . International Journal for Numerical Methods in Engineering , 29 : 1595 – 1638 .
   Web of Science ®Google Scholar
• Simo , J.C. , Armero , F. and Taylor , R.L. 1993 . Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems . Computer Methods in Applied Mechanics and Engineering , 110 : 359 – 386 .
   Web of Science ®Google Scholar
• Sze , K.Y. , Liu , X.H. and Lo , S.H. 2004 . Popular benchmark problems for geometric nonlinear analysis of shells . Finite Elements in Analysis and Design , 40 : 1551 – 1569 .
   Web of Science ®Google Scholar
• Timoshenko S.P., & Gere J.M. (1966). Théorie de la stabilité élastique, 2nd ed., Dunod. (Theory of elastic stability). New York: McGraw-Hill.
   Google Scholar
• Trinh , V.D. , Abed-Meraim , F. and Combescure , A. 2011 . A new assumed strain solid–shell formulation “SHB6” for the six-node prismatic finite element . Journal of Mechanical Science and Technology , 25 : 2345 – 2364 .
   Web of Science ®Google Scholar
• Wall , W.A. , Bischoff , M. and Ramm , E. 2000 . A deformation dependent stabilization technique, exemplified by EAS elements at large strains . Computer Methods in Applied Mechanics and Engineering , 188 : 859 – 871 .
   Web of Science ®Google Scholar
• Wriggers , P. and Reese , S. 1996 . A note on enhanced strain methods for large deformations . Computer Methods in Applied Mechanics and Engineering , 135 : 201 – 209 .
   Web of Science ®Google Scholar
• Zhu , Y.Y. and Cescotto , S. 1996 . Unified and mixed formulation of the 8-node hexahedral elements by assumed strain method . Computer Methods in Applied Mechanics and Engineering , 129 : 177 – 209 .
   Web of Science ®Google Scholar