A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise theory based on the C0-HSDT for analyses of composite plates

Abstract A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) based on the first-order shear deformation theory (FSDT) using triangular element was recently proposed for static and dynamics analyses of Mindlin plates. In this paper, the CS-FEM-DSG3 is extended and incorporated with a layerwise theory for static and free vibration analyses of composite and sandwich plates. In the layerwise theory, the behavior of each layer follows the C 0 -type higher-order shear deformation theory (C 0 -HSDT) and the condition of displacement continuity is imposed at the interfaces of layers. The shear correction factor is hence no more necessary and the accuracy of transverse shear stresses is improved significantly. In the process of formulating the system stiffness matrix of the CS-FEM-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method (DSG3) is used to compute the strains. Then the strain smoothing technique on whole the triangular element is used to smooth the strains on these three sub-triangles. Some numerical studies have been conducted to demonstrate the efficient performance of the proposed formulation.

[1]  J. N. Reddy,et al.  On refined computational models of composite laminates , 1989 .

[2]  J. N. Reddy,et al.  A refined nonlinear theory of plates with transverse shear deformation , 1984 .

[3]  E. Carrera,et al.  Zig-Zag and interlaminar equilibria effects in large deflection and postbuckling analysis of multilayered plates , 1997 .

[4]  Hung Nguyen-Xuan,et al.  Static, free vibration and buckling analyses of stiffened plates by CS-FEM-DSG3 using triangular elements , 2013 .

[5]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

[6]  E. Reissner,et al.  On the Equations of Linear Shallow Shell Theory , 1969 .

[7]  K. Bhaskar,et al.  Untruncated infinite series superposition method for accurate flexural analysis of isotropic/orthotropic rectangular plates with arbitrary edge conditions , 2008 .

[8]  C.M.C. Roque,et al.  Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method , 2003 .

[9]  Hidenori Murakami,et al.  Laminated Composite Plate Theory With Improved In-Plane Responses , 1986 .

[10]  J. Ren,et al.  A new theory of laminated plate , 1986 .

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

[12]  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 .

[13]  Erasmo Carrera,et al.  A nonlinear finite element model using a unified formulation for dynamic analysis of multilayer composite plate embedded with SMA wires , 2013 .

[14]  T. Hughes,et al.  Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline , 2012 .

[15]  Siamak Noroozi,et al.  The development of laminated composite plate theories: a review , 2012, Journal of Materials Science.

[16]  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 .

[17]  N.G.R. Iyengar,et al.  A C0ELEMENT FOR THE FREE VIBRATION ANALYSIS OF LAMINATED COMPOSITE PLATES , 1996 .

[18]  J. Whitney,et al.  The Effect of Transverse Shear Deformation on the Bending of Laminated Plates , 1969 .

[19]  R. Christensen,et al.  A High-Order Theory of Plate Deformation—Part 2: Laminated Plates , 1977 .

[20]  Silvia Bertoluzza,et al.  A high order collocation method for the static and vibration analysis of composite plates using a first-order theory , 2009 .

[21]  Rakesh K. Kapania,et al.  Free vibration analysis of laminated plates using a layerwise theory , 1993 .

[22]  K. M. Liew,et al.  Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method , 2003 .

[23]  S. Srinivas,et al.  An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates , 1970 .

[24]  Hung Nguyen-Xuan,et al.  A cell-based smoothed discrete shear gap method (CS-DSG3) based on the C0-type higher-order shear deformation theory for static and free vibration analyses of functionally graded plates , 2013 .

[25]  Maenghyo Cho,et al.  Enhanced first-order theory based on mixed formulation and transverse normal effect , 2007 .

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

[27]  S. Srinivas,et al.  A refined analysis of composite laminates , 1973 .

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

[29]  C. Soares,et al.  Generalized layerwise HSDT and finite element formulation for symmetric laminated and sandwich composite plates , 2013 .

[30]  J. N. Reddy,et al.  A review of refined theories of laminated composite plates , 1990 .

[31]  Guirong Liu,et al.  A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems , 2009 .

[32]  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 .

[33]  António J.M. Ferreira,et al.  Analysis of Composite Plates Using a Layerwise Theory and Multiquadrics Discretization , 2005 .

[34]  C. S. Barcellos,et al.  Evaluation and verification of an HSDT-Layerwise generalized finite element formulation for adaptive piezoelectric laminated plates , 2011 .

[35]  G. R. Liu,et al.  A cell-based smoothed finite element method using three-node shear-locking free Mindlin plate element (CS-FEM-MIN3) for dynamic response of laminated composite plates on viscoelastic foundation , 2014 .

[36]  Erasmo Carrera,et al.  Variable kinematic models applied to free-vibration analysis of functionally graded material shells , 2010 .

[37]  Timon Rabczuk,et al.  Dynamic Responses of Composite Plates on the Pasternak Foundation Subjected to a Moving Mass by a Cell-based Smoothed Discrete Shear Gap (CS-FEM-DSG3) Method , 2013 .

[38]  Tarun Kant,et al.  Higher-order shear deformable theories for flexure of sandwich plates—Finite element evaluations , 1988 .

[39]  Chien H. Thai,et al.  Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method , 2012 .

[40]  C. Soares,et al.  A new trigonometric layerwise shear deformation theory for the finite element analysis of laminated composite and sandwich plates , 2012 .

[41]  Simon Wang,et al.  Vibration analysis of rectangular composite laminated plates using layerwise B-spline finite strip method , 2005 .

[42]  K. Y. Dai,et al.  A Smoothed Finite Element Method for Mechanics Problems , 2007 .

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

[44]  G. R. Liu,et al.  On Smoothed Finite Element Methods , 2010 .

[45]  R. Batra,et al.  Higher-Order Piezoelectric Plate Theory Derived from a Three-Dimensional Variational Principle , 2002 .

[46]  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 .

[47]  António J.M. Ferreira,et al.  Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter , 2008 .

[48]  Erasmo Carrera,et al.  Free vibration analysis of rotating composite blades via Carrera Unified Formulation , 2013 .

[49]  K. Y. Dai,et al.  Theoretical aspects of the smoothed finite element method (SFEM) , 2007 .

[50]  Hung Nguyen-Xuan,et al.  On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM) , 2009 .

[51]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[52]  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 .

[53]  C. Sun,et al.  A higher order theory for extensional motion of laminated composites , 1973 .

[54]  J. Reddy,et al.  Lévy Type Solutions for Symmetrically Laminated Rectangular Plates Using First-Order Shear Deformation Theory , 1987 .

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

[56]  E. Reissner,et al.  A Consistent Treatment of Transverse Shear Deformations in Laminated Anisotropic Plates , 1972 .

[57]  Hung Nguyen-Xuan,et al.  Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory , 2013 .

[58]  Mo Shing Cheung,et al.  Finite Strip Analysis of Anisotropic Laminated Composite Plates Using Higher-Order Shear Deformation Theory" , 1994 .

[59]  Erasmo Carrera,et al.  Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a Unified Formulation , 2014 .

[60]  Guirong Liu,et al.  A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements , 2009 .

[61]  J. Ashton,et al.  Anisotropic Plate Analysis-Boundary Conditions , 1970 .

[62]  J. Whitney,et al.  The Effect of Boundary Conditions on the Response of Laminated Composites , 1970 .

[63]  J. N. Reddy,et al.  Exact Solutions of Moderately Thick Laminated Shells , 1984 .

[64]  Chen Wanji,et al.  Free vibration of laminated composite and sandwich plates using global–local higher-order theory , 2006 .

[65]  Hung Nguyen-Xuan,et al.  Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3) , 2013 .

[66]  J. R. Banerjee,et al.  Refined dynamic stiffness elements applied to free vibration analysis of generally laminated composite beams with arbitrary boundary conditions , 2014 .

[67]  Paulo de Tarso R. Mendonça,et al.  HSDT-Layerwise analytical solution for rectangular piezoelectric laminated plates , 2010 .

[68]  S. Natarajan,et al.  Functionally graded material panel flutter by cell-based smoothed finite elements , 2013 .

[69]  Erasmo Carrera,et al.  Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis , 1998 .

[70]  Arthur W. Leissa,et al.  Analysis of a simply supported laminated anisotropic rectangular plate , 1970 .

[71]  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 .

[72]  Hung Nguyen-Xuan,et al.  A theoretical study on the smoothed FEM (S‐FEM) models: Properties, accuracy and convergence rates , 2010 .

[73]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[74]  Hung Nguyen-Xuan,et al.  An n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM) for solid mechanics , 2010 .

[75]  Adrian P. Mouritz,et al.  Review of advanced composite structures for naval ships and submarines , 2001 .

[76]  E. Reissner,et al.  On transverse bending of plates, including the effect of transverse shear deformation☆ , 1975 .