The MITC3+ shell element in geometric nonlinear analysis

We present the MITC3+ shell finite element for geometric nonlinear analysis.The Lagrangian formulation is employed allowing for large displacement kinematics.An excellent performance of the element is demonstrated in nonlinear example solutions. In this paper, we present the MITC3+ shell finite element for geometric nonlinear analysis and demonstrate its performance. The MITC3+ shell element, recently proposed for linear analysis 1, represents a further development of the MITC3 shell element. The total Lagrangian formulation is employed allowing for large displacements and large rotations. Considering several analysis problems, the nonlinear solutions using the MITC3+ shell element are compared with those obtained using the MITC3 and MITC4 shell elements. We conclude that the MITC3+ shell element shows, in the problems considered, the same excellent performance in geometric nonlinear analysis as already observed in linear analysis.

[1]  K. Y. Sze,et al.  Popular benchmark problems for geometric nonlinear analysis of shells , 2004 .

[2]  B. Brank,et al.  On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells , 1995 .

[3]  LeePhill-Seung,et al.  The MITC3+ shell element in geometric nonlinear analysis , 2015 .

[4]  C. Choi,et al.  An Efficient Four Node Degenerated Shell Element Based on the Assumed Covariant Strain , 1994 .

[5]  Carlo Sansour,et al.  On hybrid stress, hybrid strain and enhanced strain finite element formulations for a geometrically exact shell theory with drilling degrees of freedom , 1998 .

[6]  N. F. Knight,et al.  Raasch Challenge for Shell Elements , 1997 .

[7]  K. Bathe,et al.  Development of MITC isotropic triangular shell finite elements , 2004 .

[8]  Phill-Seung Lee,et al.  The quadratic MITC plate and MITC shell elements in plate bending , 2010, Adv. Eng. Softw..

[9]  Gennady M. Kulikov,et al.  A family of ANS four‐node exact geometry shell elements in general convected curvilinear coordinates , 2010 .

[10]  Miguel Luiz Bucalem,et al.  A mixed formulation for general triangular isoparametric shell elements based on the degenerated solid approach , 2000 .

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

[12]  D. Chapelle,et al.  The Finite Element Analysis of Shells - Fundamentals , 2003 .

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

[14]  Klaus-Jürgen Bathe,et al.  The inf–sup condition and its evaluation for mixed finite element methods , 2001 .

[15]  K. Bathe.  Finite Element Procedures , 1995 .

[16]  Sven Klinkel,et al.  A robust non-linear solid shell element based on a mixed variational formulation , 2006 .

[17]  Ted Belytschko,et al.  Assumed strain stabilization procedure for the 9-node Lagrange shell element , 1989 .

[18]  J. N. Reddy,et al.  Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures , 2007 .

[19]  Sung-Cheon Han,et al.  An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions , 2013 .

[20]  K. Bathe,et al.  The MITC3 shell finite element enriched by interpolation covers , 2014 .

[21]  Alexander G Iosilevich,et al.  An inf-sup test for shell finite elements , 2000 .

[22]  Hsiao Kuo-Mo,et al.  Nonlinear analysis of shell structures by degenerated isoparametric shell element , 1989 .

[23]  Demetres Briassoulis,et al.  Non-linear behaviour of the RFNS element??large displacements and rotations , 2002 .

[24]  Phill-Seung Lee,et al.  A new MITC4+ shell element , 2017 .

[25]  Jong Hoon Kim,et al.  A three-node C0 ANS element for geometrically non-linear structural analysis , 2002 .

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

[27]  Phill-Seung Lee,et al.  Towards improving the MITC9 shell element , 2003 .

[28]  Phill-Seung Lee,et al.  On the asymptotic behavior of shell structures and the evaluation in finite element solutions , 2002 .

[29]  Dominique Chapelle,et al.  The mathematical shell model underlying general shell elements , 2000 .

[30]  Kyungho Yoon,et al.  Improving the MITC3 shell finite element by using the Hellinger-Reissner principle , 2012 .

[31]  Phill-Seung Lee,et al.  A 6‐node triangular solid‐shell element for linear and nonlinear analysis , 2017 .

[32]  Ekkehard Ramm,et al.  A deformation dependent stabilization technique, exemplified by EAS elements at large strains , 2000 .

[33]  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 .

[34]  Klaus-Jürgen Bathe,et al.  Spurious modes in geometrically nonlinear small displacement finite elements with incompatible modes , 2014 .

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

[36]  Phill-Seung Lee,et al.  Measuring the convergence behavior of shell analysis schemes , 2011 .

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

[38]  K. Y. Sze,et al.  Curved quadratic triangular degenerated‐ and solid‐shell elements for geometric non‐linear analysis , 2003 .

[39]  Eduardo N. Dvorkin,et al.  Our discrete-Kirchhoff and isoparametric shell elements for nonlinear analysis—An assessment , 1983 .

[40]  C.W.S. To,et al.  Hybrid strain based three node flat triangular shell elements—II. Numerical investigation of nonlinear problems , 1995 .

[41]  E. Providas,et al.  A simple finite element model for the geometrically nonlinear analysis of thin shells , 1999 .

[42]  Phill-Seung Lee,et al.  Insight into finite element shell discretizations by use of the basic shell mathematical model , 2005 .

[43]  Yavuz Başar,et al.  Finite-rotation shell elements for the analysis of finite-rotation shell problems , 1992 .

[44]  J. Argyris.  An excursion into large rotations , 1982 .

[45]  M. W. Chernuka,et al.  A simple four-noded corotational shell element for arbitrarily large rotations , 1994 .

[46]  K. Bathe,et al.  Fundamental considerations for the finite element analysis of shell structures , 1998 .

[47]  T. Belytschko,et al.  Projection schemes for one-point quadrature shell elements , 1994 .

[48]  Klaus-Jürgen Bathe,et al.  3D-shell elements for structures in large strains , 2013 .

[49]  Kyungho Yoon,et al.  Nonlinear performance of continuum mechanics based beam elements focusing on large twisting behaviors , 2014 .

[50]  Phill-Seung Lee,et al.  The MITC3+shell element and its performance , 2014 .

[51]  Klaus-Jürgen Bathe,et al.  Finite Element Method , 2008, Wiley Encyclopedia of Computer Science and Engineering.

[52]  Victoria Vampa,et al.  ANALYSIS OF IN-LAYER STRAINS IN THE LOW ORDER MITC SHELL ELEMENT , 2007 .

[53]  Sung W. Lee,et al.  An assumed strain triangular curved solid shell element formulation for analysis of plates and shells undergoing finite rotations , 2001 .

[54]  M. L. Bucalem,et al.  Finite element analysis of shell structures , 1997 .