An enriched 6-node MITC plate element for yield line analysis

A 6-node triangular Reissner-Mindlin plate element with eXtended Finite Element Method (XFEM) formulation for yield line analyses is presented. The XFEM formulation with regularized enrichment is employed to reproduce a displacement field with a locally high gradient in the vicinity of a yield line in plate structures. The MITC technique is employed to mitigate shear locking in both the smooth and the locally non-smooth displacement fields. Several numerical examples are presented to illustrate the effectiveness of the XFEM enrichment in yield line analysis as well as the necessity and the effectiveness of the MITC technique in shear locking alleviation in the XFEM formulation.

[1]  Kaspar Willam,et al.  Review of The Finite Element Method for Solid and Structural Mechanics, 6th Edition, by O. C. Zienkiewicz and R. L. Taylor , 2006 .

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

[3]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

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

[5]  T. Belytschko,et al.  Two‐scale shear band evolution by local partition of unity , 2006 .

[6]  T. Fries,et al.  The XFEM for high‐gradient solutions in convection‐dominated problems , 2009 .

[7]  Jin Xu,et al.  An XFEM frame for plate elements in yield line analyses , 2013 .

[8]  Ted Belytschko,et al.  On XFEM applications to dislocations and interfaces , 2007 .

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

[10]  Erasmo Carrera,et al.  MITC technique extended to variable kinematic multilayered plate elements , 2010 .

[11]  T. Fries.  A corrected XFEM approximation without problems in blending elements , 2008 .

[12]  Dominique Chapelle,et al.  Towards improving the MITC6 triangular shell element , 2007 .

[13]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[14]  Jin Xu,et al.  An XFEM plate element for high gradient zones resulted from yield lines , 2013 .

[15]  T. Belytschko,et al.  Analysis of three‐dimensional crack initiation and propagation using the extended finite element method , 2005 .

[16]  Ted Belytschko,et al.  An extended finite element method with higher-order elements for curved cracks , 2003 .

[17]  Chi King Lee,et al.  A two-dimensional co-rotational Timoshenko beam element with XFEM formulation , 2011, Computational Mechanics.

[18]  O. C. Zienkiewicz,et al.  The Finite Element Method for Solid and Structural Mechanics , 2013 .

[19]  H. Nguyen-Xuan,et al.  A smoothed finite element method for plate analysis , 2008 .

[20]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

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

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

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

[24]  M. Jirásek,et al.  Process zone resolution by extended finite elements , 2003 .

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

[26]  Jean-François Remacle,et al.  A computational approach to handle complex microstructure geometries , 2003 .

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

[28]  K. Bathe,et al.  The MITC7 and MITC9 Plate bending elements , 1989 .

[29]  Knud Winstrup Johansen,et al.  Yield-line Formulae for Slabs , 1972 .

[30]  T. Belytschko,et al.  Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods , 2008 .

[31]  G. Ventura,et al.  A regularized XFEM model for the transition from continuous to discontinuous displacements , 2008 .

[32]  Yeong-bin Yang,et al.  Solution method for nonlinear problems with multiple critical points , 1990 .

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

[34]  T. Belytschko,et al.  New crack‐tip elements for XFEM and applications to cohesive cracks , 2003 .

[35]  Elena Benvenuti,et al.  A regularized XFEM framework for embedded cohesive interfaces , 2008 .

[36]  Klaus-Jürgen Bathe,et al.  The MITC9 shell element in plate bending: mathematical analysis of a simplified case , 2011 .

[37]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

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

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

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

[41]  T. Belytschko,et al.  The extended/generalized finite element method: An overview of the method and its applications , 2010 .

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

[43]  T. Belytschko,et al.  Non‐linear analysis of shells with arbitrary evolving cracks using XFEM , 2005 .