Geometrically non-linear analysis of laminated composite structures using a 4-node co-rotational shell element with enhanced strains

Abstract To demonstrate the solutions of linear and geometrically non-linear analysis of laminated composite plates and shells, the co-rotational non-linear formulation of the shell element is presented. The combinations of an enhanced assumed strain (EAS) in the membrane strains and assumed natural strains (ANS) in the shear strains improve the behavior of 4-node shell element. To secure computational efficiency in the incremental non-linear analysis, the present element uses the form of the resultant forces pre-integrated through the thickness. The transverse shear stiffness of the laminates is defined by an equilibrium approach instead of the shear correction factor. Numerical examples of this study show very good agreement with the references.

[1]  R. M. Natal Jorge,et al.  On the use of an enhanced transverse shear strain shell element for problems involving large rotations , 2003 .

[2]  George Z. Voyiadjis,et al.  A 4‐node assumed strain quasi‐conforming shell element with 6 degrees of freedom , 2003 .

[3]  T. Belytschko,et al.  Physical stabilization of the 4-node shell element with one point quadrature , 1994 .

[4]  Gilson R. Lomboy,et al.  A co-rotational 8-node assumed strain shell element for postbuckling analysis of laminated composite plates and shells , 2003 .

[5]  J. N. Reddy,et al.  A mixed shear flexible finite element for the analysis of laminated plates , 1984 .

[6]  B. J. Hsieh,et al.  Non-Linear Transient Finite Element Analysis with Convected Co--ordinates , 1973 .

[7]  J. M. A. César de Sá,et al.  Enhanced transverse shear strain shell formulation applied to large elasto‐plastic deformation problems , 2005 .

[8]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[9]  R. L. Harder,et al.  A proposed standard set of problems to test finite element accuracy , 1985 .

[10]  A. A. Fernandes,et al.  Analysis of 3D problems using a new enhanced strain hexahedral element , 2003 .

[11]  J. Whitney,et al.  Bending-Extensional Coupling in Laminated Plates Under Transverse Loading , 1969 .

[12]  K. Bathe,et al.  A continuum mechanics based four‐node shell element for general non‐linear analysis , 1984 .

[13]  Worsak Kanok-Nukulchai,et al.  An element-based 9-node resultant shell element for large deformation analysis of laminated composite plates and shells , 2004 .

[14]  Rakesh K. Kapania,et al.  Geometrically Nonlinear Finite Element Analysis of Imperfect Laminated Shells , 1986 .

[15]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[16]  Renato Natal Jorge,et al.  Development of shear locking‐free shell elements using an enhanced assumed strain formulation , 2002 .

[17]  Rüdiger Schmidt,et al.  Large rotations in first-order shear deformation FE analysis of laminated shells , 2006 .

[18]  H. Kebari,et al.  A stabilized 9‐node non‐linear shell element , 1992 .

[19]  S. J. Lee,et al.  A NINE-NODE ASSUMED STRAIN FINITE ELEMENT FOR LARGE-DEFORMATION ANALYSIS OF LAMINATED SHELLS , 1998 .

[20]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[21]  Eduardo N. Dvorkin,et al.  A formulation of general shell elements—the use of mixed interpolation of tensorial components† , 1986 .

[22]  Richard H. Macneal,et al.  Derivation of element stiffness matrices by assumed strain distributions , 1982 .

[23]  Ki-Du Kim,et al.  A co-rotational quasi-conforming 4-node resultant shell element for large deformation elasto-plastic analysis , 2006 .

[24]  Raimund Rolfes,et al.  Improved transverse shear stresses in composite finite elements based on first order shear deformation theory , 1997 .

[25]  Ki-Du Kim,et al.  Linear static and dynamic analysis of laminated composite plates and shells using a 4-node quasi-conforming shell element , 2005 .

[26]  Ekkehard Ramm,et al.  EAS‐elements for two‐dimensional, three‐dimensional, plate and shell structures and their equivalence to HR‐elements , 1993 .

[27]  Carlo Sansour,et al.  Families of 4-node and 9-node finite elements for a finite deformation shell theory. An assesment of hybrid stress, hybrid strain and enhanced strain elements , 2000 .

[28]  Ki-Du Kim,et al.  A 4-node co-rotational ANS shell element for laminated composite structures , 2007 .

[29]  Y. Stavsky,et al.  Elastic wave propagation in heterogeneous plates , 1966 .

[30]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory , 1990 .

[31]  Yavuz Başar,et al.  Refined shear-deformation models for composite laminates with finite rotations , 1993 .

[32]  Ahmed K. Noor,et al.  Anisotropy and shear deformation in laminated composite plates , 1976 .

[33]  O. C. Zienkiewicz,et al.  Analysis of thick and thin shell structures by curved finite elements , 1970 .

[34]  Taehyo Park,et al.  An 8-node assumed strain element with explicit integration for isotropic and laminated composite shells , 2002 .

[35]  F. L. Matthews,et al.  Large Deflection Behavior of Simply Supported Laminated Panels Under In-Plane Loading , 1985 .

[36]  F. Gruttmann,et al.  A linear quadrilateral shell element with fast stiffness computation , 2005 .

[37]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects , 1989 .

[38]  W. H. Wittrick.  Analytical, three-dimensional elasticity solutions to some plate problems, and some observations on Mindlin's plate theory , 1987 .