Partial-mixed special finite element for the analysis of multilayer composites and FGM

References

• Andrianarison , O. and Benjeddou , A. 2012 . Hamiltonian partial mixed finite element – state space symplectic semi-analytical approach for the piezoelectric composites and FGM analysis . Acta Mechanica , doi:10.1007/s00707-012-0646-8
   Web of Science ®Google Scholar
• Auricchio , F. and Sacco , E. 1999 . A mixed-enhanced finite element for the analysis of laminated composite plates . International Journal for Numerical Methods in Engineering , 44 : 1481 – 1504 .
   Web of Science ®Google Scholar
• Bahar , L.Y. 1977 . A mixed method in elasticity . Journal of Applied Mechanics , 44 : 790 – 791 .
   Google Scholar
• Benjeddou , A. and Andrianarison , O. 2006 . A heat mixed variational theorem for thermoelastic multilayered composites . Computers and Structures , 84 ( 19–20 ) : 1247 – 1255 .
   Google Scholar
• Benner , P. , Mehrmann , V. and Xu , H. 1998 . A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils . Numerische Matematik , 78 : 3229 – 3258 .
   Web of Science ®Google Scholar
• Birman , V. and Byrd , L.W. 2007 . Modeling and analysis of functionally graded materials and structures . Applied Mechanics Reviews , 60 ( 5 ) : 195 – 216 .
   Web of Science ®Google Scholar
• Brezzi , F. and Fortin , M. 1991 . Mixed and hybrid finite element method , Springer-Verlag .
   Google Scholar
• Courant , R. and Hilbert , D. 1989 . Methods of mathematical physics I, II , USA : John Wiley .
   Google Scholar
• Desai , Y.M. , Ramtekkar , G.S. and Shah , A.H. 2003 . A novel 3D mixed finite element model for statics of angle-ply laminates . International Journal for Numerical Methods in Engineering , 57 : 1695 – 1716 .
   Web of Science ®Google Scholar
• Goldstein , H. , Poole , C. and Safko , J. 2002 . Classical mechanics , London : Addison Wesley .
   Google Scholar
• Kreja , I. 2011 . A literature review on computational models for laminated composite and sandwich panels . Central European Journal of Engineering , 1 ( 1 ) : 59 – 80 .
   Google Scholar
• Li , R. , Zhong , Y. and Tian , B. 2011 . On new symplectic superposition method for exact solutions of rectangular cantilever thin plates . Mechanics Research Communications , 38 : 111 – 116 .
   Web of Science ®Google Scholar
• Pagano , N.J. 1970 . Exact solutions for rectangular bidirectional composites and sandwich plates . Journal of Composite Materials , 4 : 20 – 34 .
   Web of Science ®Google Scholar
• Reissner , E. 1984 . On a certain mixed variational theory and proposed applications . International Journal of Numerical Methods in Engineering , 20 : 1366 – 1368 .
   Web of Science ®Google Scholar
• Robaldo , A. , Benjeddou , A. and Carrera , E. 2005 . Unified formulation for FE thermoelastic analysis of multilayered anisotropic composite plates . Journal of Thermal Stresses , 28 ( 10 ) : 1031 – 1065 .
   Web of Science ®Google Scholar
• Sheng , H.Y. and Ye , J.Q. 2002 . A state space finite element for laminated composite plates . Computer Methods in Applied Mechanics and Engineering , 191 : 4259 – 4276 .
   Web of Science ®Google Scholar
• Sheng , H.Y. and Ye , J.Q. 2005 . A state space finite element for axisymmetric bending of angle-ply laminated cylinder with clamped edges . Composite Structures , 68 : 119 – 128 .
   Web of Science ®Google Scholar
• Souriau J.M. (1997). Structures of dynamical systems: A symplectic view of physics. Progress in Mathematics 149. Paris: Lavoisier.
   Google Scholar
• Steele , C.R. and Kim , Y.Y. 1992 . Modified mixed variational principle and the state-vector equation for elastic bodies and shells of revolution . Journal of Applied Mechanics , 59 : 587 – 595 .
   Web of Science ®Google Scholar
• Van Loan , C. 1984 . A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix . Linear Algebra Application , 61 : 233 – 251 .
   Web of Science ®Google Scholar
• Washizu , K. 1968 . Variational method in elasticity and plasticity , New York , NY : Pergamon Press .
   Google Scholar
• Wu , C.P. and Li , H.Y. 2010a . The RMVT and PVD based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates . Composite Structures , 92 : 2476 – 2496 .
   Web of Science ®Google Scholar
• Wu , C.P. and Li , H.Y. 2010b . An RMVT-based third order shear deformation theory for multilayered functionally graded material plate . Composite Structures , 92 : 2591 – 2595 .
   Web of Science ®Google Scholar
• Zhang , Y.X. and Yang , C.H. 2009 . Recent developments in finite element analysis for laminated composite plates . Composite Structures , 88 : 147 – 157 .
   Web of Science ®Google Scholar
• Zou , G. and Tang , L. 1995 . A semi-analytical solution for laminated composite plates in Hamilltonian system . Computer Methods in Applied Mechanics and Engineering , 128 : 395 – 404 .
   Web of Science ®Google Scholar