Global-local analysis of laminated plates by node-dependent kinematic finite elements with variable ESL/LW capabilities

Abstract This work presents a class of plate finite elements (FEs) formulated with node-dependent kinematics, which can be used to construct global-local models with high numerical efficiency. Taking advantage of Carrera Unified Formulation (CUF), plate theory kinematics can be individually defined on each FE node, realizing a variation of refinement levels within the in-plane domain of one element. When used in the bridging zone between a global model and a locally refined one, an efficient global-local model can be constructed. Elements with variable ESL/LW kinematics from node to node are developed and applied in the global-local analysis of laminated structures. This work includes numerical examples in which LW models with refined kinematics are employed in local regions while ESL models are adopted in the less critical area, and modeling domains are connected by transition zone composed of elements with node-dependent kinematics. The obtained results are compared with solutions from literature and 3D FE modeling. For laminated plates with local effects to be considered, the proposed plate models can reduce the computational costs significantly while guaranteeing numerical accuracy without using special global-local coupling methods.

[1]  Erasmo Carrera,et al.  Analysis of reinforced and thin-walled structures by multi-line refined 1D/beam models , 2013 .

[2]  Jin-U Park,et al.  Efficient finite element analysis using mesh superposition technique , 2003 .

[3]  Hans Petter Langtangen,et al.  A unified mesh refinement method with applications to porous media flow , 1998 .

[4]  Franco Brezzi,et al.  The three‐field formulation for elasticity problems , 2005 .

[5]  R. J. Callinan,et al.  Analysis of multi-layer laminates using three-dimensional super-elements , 1984 .

[6]  J. N. Reddy,et al.  Variable Kinematic Modelling of Laminated Composite Plates , 1996 .

[7]  N. J. Pagano,et al.  Global-local laminate variational model , 1983 .

[8]  E. Carrera.  Theories and finite elements for multilayered, anisotropic, composite plates and shells , 2002 .

[9]  Erasmo Carrera,et al.  Multi-scale modelling of sandwich structures using hierarchical kinematics , 2011 .

[10]  Pablo J. Blanco,et al.  A variational approach for coupling kinematically incompatible structural models , 2008 .

[11]  John D. Whitcomb,et al.  Application of iterative global/local finite-element analysis. Part 1: Linear analysis , 1993 .

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

[13]  E. Carrera,et al.  MITC9 shell finite elements with miscellaneous through-the-thickness functions for the analysis of laminated structures , 2016 .

[14]  D. Thompson,et al.  2-D to 3-D global/local finite element analysis of cross-ply composite laminates , 1990 .

[15]  J. Reddy,et al.  THEORIES AND COMPUTATIONAL MODELS FOR COMPOSITE LAMINATES , 1994 .

[16]  Erasmo Carrera,et al.  Coupling of hierarchical piezoelectric plate finite elements via Arlequin method , 2012 .

[17]  Xiaoshan Lin,et al.  A novel one-dimensional two-node shear-flexible layered composite beam element , 2011 .

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

[19]  J. Fish.  The s-version of the finite element method , 1992 .

[20]  Ernst Rank,et al.  COMPUTATIONAL CONTACT MECHANICS BASED ON THE rp-VERSION OF THE FINITE ELEMENT METHOD , 2011 .

[21]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[22]  Erasmo Carrera,et al.  Refined finite element solutions for anisotropic laminated plates , 2018 .

[23]  Guillaume Rateau,et al.  The Arlequin method as a flexible engineering design tool , 2005 .

[24]  Gaetano Giunta,et al.  Variable kinematic beam elements coupled via Arlequin method , 2011 .

[25]  Erasmo Carrera,et al.  Use of Lagrange multipliers to combine 1D variable kinematic finite elements , 2013 .

[26]  Erasmo Carrera,et al.  Multi-line enhanced beam model for the analysis of laminated composite structures , 2014 .

[27]  Jonathan B. Ransom,et al.  On Multifunctional Collaborative Methods in Engineering Science , 2001 .

[28]  Maria Cinefra,et al.  A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites , 2016 .

[29]  Huu-Tai Thai,et al.  Static behavior of composite beams using various refined shear deformation theories , 2012 .

[30]  Erasmo Carrera,et al.  Node-dependent kinematics, refined zig-zag and multi-line beam theories for the analysis of composite structures , 2017 .

[31]  Julio F. Davalos,et al.  Analysis of laminated beams with a layer-wise constant shear theory , 1994 .

[32]  E. Carrera,et al.  Heat conduction and Thermal Stress Analysis of laminated composites by a variable kinematic MITC9 shell element , 2015 .

[33]  Gaetano Giunta,et al.  Variable kinematic plate elements coupled via Arlequin method , 2012 .

[34]  Philippe Vidal,et al.  Coupling of heterogeneous kinematics and Finite Element approximations applied to composite beam structures , 2014 .

[35]  Erasmo Carrera,et al.  Analysis of Complex Structures Coupling Variable Kinematics One-Dimensional Models , 2014 .

[36]  J. Reddy.  An introduction to the finite element method , 1989 .

[37]  H. Dhia.  Problèmes mécaniques multi-échelles: la méthode Arlequin , 1998 .

[38]  E. Carrera,et al.  Multilayered plate elements accounting for refined theories and node-dependent kinematics , 2017 .

[39]  Alfio Quarteroni,et al.  Extended Variational Formulation for Heterogeneous Partial Differential Equations , 2011, Comput. Methods Appl. Math..

[40]  Lorenzo Dozio,et al.  Bending analysis of composite laminated and sandwich structures using sublaminate variable-kinematic Ritz models , 2016 .

[41]  Erasmo Carrera,et al.  Finite Element Analysis of Structures through Unified Formulation , 2014 .

[42]  Mohammad A. Aminpour,et al.  A coupled analysis method for structures with independently modelled finite element subdomains , 1995 .

[43]  C. Chinosi,et al.  MITC9 Shell Elements Based on Refined Theories for the Analysis of Isotropic Cylindrical Structures , 2013 .

[44]  Hachmi Ben Dhia,et al.  Multiscale mechanical problems: the Arlequin method , 1998 .

[45]  Karan S. Surana,et al.  Two-dimensional curved beam element with higher-order hierarchical transverse approximation for laminated composites , 1990 .

[46]  Jacob Fish,et al.  UNSTRUCTURED MULTIGRID METHOD FOR SHELLS , 1996 .