Geometrically nonlinear analysis of functionally graded shells using an edge-based smoothed MITC3 (ES-MITC3) finite elements

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of shells. In this study, the ES-MITC3 is extended to the geometrically nonlinear analysis of functionally graded shells. In the ES-MITC3, the stiffness matrices are obtained using the strain smoothing technique over the smoothing domains that formed by two adjacent MITC3 triangular shell elements sharing an edge. The material properties of functionally graded (FG) shells are assumed to vary through the thickness direction by a power rule distribution of volume fractions of the constituents. The nonlinear finite element formulation based on the first-order shear deformation theory with the von Kármán’s large deflection assumption is used to describe the large deformations of the FG shells. Several numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods.

[1]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

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

[3]  Hung Nguyen-Xuan,et al.  An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates , 2010 .

[4]  Timon Rabczuk,et al.  Phase-field analysis of finite-strain plates and shells including element subdivision , 2016 .

[5]  Trung Nguyen-Thoi,et al.  A stabilized smoothed finite element method for free vibration analysis of Mindlin–Reissner plates , 2009 .

[6]  Guangyao Li,et al.  Analysis of plates and shells using an edge-based smoothed finite element method , 2009 .

[7]  Hung Nguyen-Xuan,et al.  AN EDGE-BASED SMOOTHED FINITE ELEMENT METHOD FOR ANALYSIS OF LAMINATED COMPOSITE PLATES , 2013 .

[8]  H. Nguyen-Xuan,et al.  Improvement on MITC3 plate finite element using edge-based strain smoothing enhancement for plate analysis , 2017 .

[9]  Timon Rabczuk,et al.  Finite strain fracture of plates and shells with configurational forces and edge rotations , 2013 .

[10]  Q. Pham,et al.  An Edge-Based Smoothed MITC3 (ES-MITC3) Shell Finite Element in Laminated Composite Shell Structures Analysis , 2017, International Journal of Computational Methods.

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

[12]  Guirong Liu,et al.  ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS , 2009 .

[13]  K. M. Liew,et al.  GEOMETRICALLY NONLINEAR ANALYSIS OF FUNCTIONALLY GRADED SHELLS , 2009 .

[14]  Ted Belytschko,et al.  Immersed particle method for fluid–structure interaction , 2009 .

[15]  T. Hughes,et al.  A three-node mindlin plate element with improved transverse shear , 1985 .

[16]  J. L. Sanders,et al.  NONLINEAR THEORIES FOR THIN SHELLS , 1963 .

[17]  H. Nguyen-Xuan,et al.  A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates , 2010 .

[18]  T. Rabczuk,et al.  A meshfree thin shell method for non‐linear dynamic fracture , 2007 .

[19]  E. Ramm,et al.  A unified approach for shear-locking-free triangular and rectangular shell finite elements , 2000 .

[20]  J. N. Reddy,et al.  Large deformation analysis of functionally graded shells , 2007 .

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

[22]  Phill-Seung Lee,et al.  Phantom-node method for shell models with arbitrary cracks , 2012 .

[23]  Hung Nguyen-Xuan,et al.  Analysis of functionally graded plates using an edge-based smoothed finite element method , 2011 .

[24]  Loc V. Tran,et al.  Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates , 2016 .

[25]  Guirong Liu,et al.  An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures , 2009 .

[26]  P. Phung-Van,et al.  A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates , 2013 .

[27]  H. Nguyen-Xuan,et al.  Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling , 2017 .

[28]  J. N. Reddy,et al.  Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates , 1998 .

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

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

[31]  Sundararajan Natarajan,et al.  A combined scheme of edge-based and node-based smoothed finite element methods for Reissner–Mindlin flat shells , 2015, Engineering with Computers.

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

[33]  E. Hinton,et al.  Finite element analysis of geometrically nonlinear plate behaviour using a mindlin formulation , 1980 .

[34]  K. Bathe,et al.  The MITC3+ shell element enriched in membrane displacements by interpolation covers , 2018, Computer Methods in Applied Mechanics and Engineering.

[35]  Hung Nguyen-Xuan,et al.  An isogeometric finite element formulation for thermal buckling analysis of functionally graded plates , 2013 .

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

[37]  J. N. Bandyopadhyay,et al.  Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation , 2008 .

[38]  Christian Rey,et al.  The finite element method in solid mechanics , 2014 .

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

[40]  K. M. Liew,et al.  Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method , 2009 .

[41]  J. Reddy.  Analysis of functionally graded plates , 2000 .

[42]  H. Nguyen-Xuan,et al.  An edge-based smoothed three-node mindlin plate element (ES-MIN3) for static and free vibration analyses of plates , 2014 .

[43]  Hung Nguyen-Xuan,et al.  Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing , 2012 .

[44]  Hung Nguyen-Xuan,et al.  Static and free vibration analyses of composite and sandwich plates by an edge-based smoothed discrete shear gap method (ES-DSG3) using triangular elements based on layerwise theory , 2014 .

[45]  K. Bathe,et al.  The MITC4+ shell element and its performance , 2016 .

[46]  C.M.C. Roque,et al.  Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method , 2005 .

[47]  Trung Nguyen-Thoi,et al.  Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C0-HSDT , 2014 .

[48]  Erasmo Viola,et al.  Free vibration analysis of functionally graded panels and shells of revolution , 2009 .

[49]  Phill-Seung Lee,et al.  Performance of the MITC3+ and MITC4+ shell elements in widely-used benchmark problems , 2017 .

[50]  C. Soares,et al.  Bending response of functionally graded plates by using a new higher order shear deformation theory , 2012 .

[51]  H. Nguyen-Xuan,et al.  Static and vibration analysis of isotropic and functionally graded sandwich plates using an edge-based MITC3 finite elements , 2016 .

[52]  Roger A. Sauer,et al.  A NURBS-based Inverse Analysis for Reconstruction of Nonlinear Deformations of Thin Shell Structures , 2018, ArXiv.

[53]  Hui‐Shen Shen.  Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments , 2002 .

[54]  Guirong Liu,et al.  An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids , 2009 .

[55]  A Mixed Finite Element for the Nonlinear Bending Analysis of Laminated Composite Plates Based on FSDT , 2008 .

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

[57]  Hung Nguyen-Xuan,et al.  A cell‐based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner–Mindlin plates , 2012 .

[58]  Hung Nguyen-Xuan,et al.  A cell-based smoothed discrete shear gap method (CS-DSG3) using triangular elements for static and free vibration analyses of shell structures , 2013 .

[59]  Erasmo Viola,et al.  FREE VIBRATIONS OF FOUR-PARAMETER FUNCTIONALLY GRADED PARABOLIC PANELS AND SHELLS OF REVOLUTION , 2009 .

[60]  Hui-Shen Shen,et al.  POSTBUCKLING ANALYSIS OF PRESSURE-LOADED FUNCTIONALLY GRADED CYLINDRICAL SHELLS IN THERMAL ENVIRONMENTS , 2003 .

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

[62]  H. Pham-Quoc,et al.  Transient Analysis of Laminated Composite Shells Using an Edge-Based Smoothed Finite Element Method , 2017 .

[63]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .