An improved enhanced solid shell element for static and buckling analysis of shell structures

This paper presents an improved higher order solid shell element for static and buckling analysis of laminated composite structures based on the enhanced assumed strain (EAS). The transverse shear strain is divided into two parts: the first one is independent of the thickness coordinate and formulated by the assumed natural strain (ANS) method; the second part is an enhancing part, which ensures a quadratic distribution through the thickness. This allows removing the shear correction factors and improves the accuracy of transverse shear stresses. In addition, volumetric locking is completely avoided by using the optimal parameters in the EAS method. The formulated finite element is implemented to study the static and buckling behavior of shell structures and to investigate the influence of some parameters on the buckling load. Comparisons of numerical results with those extracted from literature show the acceptable performance of the developed element.

[1]  K. Bathe,et al.  A four‐node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation , 1985 .

[2]  R. M. Natal Jorge,et al.  A new volumetric and shear locking‐free 3D enhanced strain element , 2003 .

[3]  G. Dhatt,et al.  A formulation of the non linear discrete Kirchhoff quadrilateral shell element with finite rotations and enhanced strains , 2005 .

[4]  Sven Klinkel,et al.  A continuum based three-dimensional shell element for laminated structures , 1999 .

[5]  M. L. Bucalém,et al.  Higher‐order MITC general shell elements , 1993 .

[6]  G. N. Jazar,et al.  Linear static analysis and finite element modeling for laminated composite plates using third order shear deformation theory , 2003 .

[7]  R. Hauptmann,et al.  On volumetric locking of low‐order solid and solid‐shell elements for finite elastoviscoplastic deformations and selective reduced integration , 2000 .

[8]  K. Y. Sze,et al.  A hybrid stress ANS solid‐shell element and its generalization for smart structure modelling. Part I—solid‐shell element formulation , 2000 .

[9]  J. Degrieck,et al.  An optimal versatile partial hybrid stress solid‐shell element for the analysis of multilayer composites , 2013 .

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

[11]  Anton Matzenmiller,et al.  A Solid-Shell Element with Enhanced Assumed Strains for Higher Order Shear Deformations in Laminates , 2008 .

[12]  A. Hajlaoui,et al.  Buckling analysis of a laminated composite plate with delaminations using the enhanced assumed strain solid shell element , 2012 .

[13]  J. N. Reddy,et al.  Vibration suppression of laminated shell structures investigated using higher order shear deformation theory , 2004 .

[14]  Fakhreddine Dammak,et al.  Discrete double directors shell element for the functionally graded material shell structures analysis , 2014 .

[15]  X. G. Tan,et al.  Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics , 2003 .

[16]  E. Ramm,et al.  Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept , 1994 .

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

[18]  J. N. Reddy,et al.  A higher-order shear deformation theory of laminated elastic shells , 1985 .

[19]  Ahmed K. Noor,et al.  Stability of multilayered composite plates , 1975 .

[20]  E. Ramm,et al.  Shear deformable shell elements for large strains and rotations , 1997 .

[21]  R. Hauptmann,et al.  Extension of the ‘solid‐shell’ concept for application to large elastic and large elastoplastic deformations , 2000 .

[22]  J. Degrieck,et al.  A novel versatile multilayer hybrid stress solid-shell element , 2013 .

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