The modal behavior of the MITC3+ triangular shell element

The static modal behavior of the MITC3+ shell element is investigated in detail.We provide insight into how shear locking occurs on the mode level.The performance of the MITC3+ shell element is presented in dynamic mode solutions. In this paper, we investigate the static and dynamic modal behavior of the MITC3+ triangular shell element (Lee and Bathe, 2004; Lee et al., 2014). We focus on bending-dominated situations because such shell problems are particularly difficult to solve when using low-order elements. For comparison, the pure displacement-based (DISP3), MITC3 and MITC4 shell elements are also studied. First, static mode solutions are performed for a single right-angled shell element and an assemblage of two right-angled shell elements. The detailed strain fields are established in the bending modes. This study provides insight into how shear locking occurs on the mode level. We then analytically show how the MITC3+ shell element properly represents the pure bending conditions in a two-sided clamped plate problem. Considering free plate and free hyperboloid shell problems, we finally present the excellent performance of the MITC3+ shell element in dynamic mode solutions.

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

[2]  Sinniah Ilanko,et al.  Bounded natural frequencies of completely free rectangular plates , 2008 .

[3]  K. Bathe,et al.  Measuring convergence of mixed finite element discretizations: an application to shell structures , 2003 .

[4]  Dominique Chapelle,et al.  A shell problem ‘highly sensitive’ to thickness changes , 2003 .

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

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

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

[8]  Dominique Chapelle,et al.  The Finite Element Analysis of Shells - Fundamentals - Second Edition , 2011 .

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

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

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

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

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

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

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

[16]  Lourenço Beirão da Veiga,et al.  Asymptotic energy behavior of two classical intermediate benchmark shell problems , 2002 .

[17]  J. Argyris,et al.  The TRIC shell element: theoretical and numerical investigation , 2000 .

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

[19]  Phill-Seung Lee,et al.  The MITC3+ shell element in geometric nonlinear analysis , 2015 .

[20]  Phill-Seung Lee,et al.  Insight into 3-node triangular shell finite elements: the effects of element isotropy and mesh patterns , 2007 .

[21]  Carlo Lovadina,et al.  A SHELL CLASSIFICATION BY INTERPOLATION , 2002 .

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

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

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

[25]  Arthur W. Leissa,et al.  The free vibration of rectangular plates , 1973 .

[26]  Rodolfo Rodríguez,et al.  Computation of the vibration modes of plates and shells by low-order MITC quadrilateral finite elements , 2003 .

[27]  Klaus-Jürgen Bathe,et al.  A triangular six-node shell element , 2009 .

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