A generalized adaptive finite element analysis of laminated plates

A generalized approach for adaptive finite element analysis of laminated composite structures is presented in this study. The approach quantifies and controls discretization and modeling error. The goal of this paper is to present an economical, easily computable and relatively robust error estimator. A patch recovery based discretization error estimator is used and a goal based one shot adaptive procedure is implemented to control the discretization error. An explicit indicator, for estimation of modeling error, has been proposed for the laminated composites. The quality of the discretization and modeling error estimators is studied through numerical examples. The effectiveness of the proposed approach is also demonstrated through the analysis of damaged laminates. The key advantage of the proposed approach is that the desired mesh and models in the laminate are adapted automatically to achieve the user specified error tolerances in discretization and modeling errors.

[1]  I. Babuska,et al.  The problem of plate modeling: theoretical and computational results , 1992 .

[2]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[3]  Ratan Jha,et al.  47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference , 2006 .

[4]  Rüdiger Verfürth,et al.  A posteriori error estimation and adaptive mesh-refinement techniques , 1994 .

[5]  Pierre Ladevèze,et al.  A damage computational method for composite structures , 1992 .

[6]  Preetam Mohite,et al.  Reliable Computation of Local Quantities of Interest in Composite Laminated Plates , 2005 .

[7]  J. N. Reddy,et al.  Linear and non-linear failure analysis of composite laminates with transverse shear , 1992 .

[8]  Local quality of smoothening based a-posteriori error estimators for laminated plates under transverse loading , 2002 .

[9]  Olivier Allix,et al.  Identification and forecast of delamination in composite laminates by an interlaminar interface model , 1998 .

[10]  Ivo Babuška,et al.  Validation of A-Posteriori Error Estimators by Numerical Approach , 1994 .

[11]  R. Verfürth.  A review of a posteriori error estimation techniques for elasticity problems , 1999 .

[12]  Ivo Babuška,et al.  On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach , 1981 .

[13]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[14]  I. Babuska,et al.  The plate paradox for hard and soft support , 1990 .

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

[16]  Kumar Vemaganti,et al.  Hierarchical modeling of heterogeneous solids , 2006 .

[17]  J. Tinsley Oden,et al.  Adaptive hpq-finite element methods of hierarchical models for plate- and shell-like structures , 1996 .

[18]  E. Stein,et al.  h - and d -adaptive FE methods for two-dimensional structural problems including post-buckling of shells , 1992 .

[19]  Ivo Babuška,et al.  A posteriori error estimation for hierarchic models of elliptic boundary value problems on thin domains , 1996 .

[20]  K. Bathe,et al.  Review: A posteriori error estimation techniques in practical finite element analysis , 2005 .

[21]  Pierre Ladevèze,et al.  Modelling and identification of the mechanical behaviour of composite laminates in compression , 1994 .

[22]  Ivo Babuška,et al.  Pollution-error in the h -version of the finite-element method and the local quality of a-posteriori error estimators , 1994 .

[23]  Pierre Ladevèze,et al.  Damage modelling of the elementary ply for laminated composites , 1992 .

[24]  Thomas Grätsch,et al.  Review: A posteriori error estimation techniques in practical finite element analysis , 2005 .

[25]  S. Ohnimus,et al.  Coupled model- and solution-adaptivity in the finite-element method , 1997 .

[26]  I. Babuska,et al.  The finite element method and its reliability , 2001 .

[27]  Barna A. Szabó,et al.  Hierarchic models for laminated plates and shells , 1999 .

[28]  A Review of A Posteriori Error Estimation , 1996 .

[29]  P. M. Mohite,et al.  Accurate computation of critical local quantities in composite laminated plates under transverse loading , 2006 .

[30]  J. Tinsley Oden,et al.  Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials: I. Error estimates and adaptive algorithms , 2000 .

[31]  Christoph Schwab,et al.  On the posteriori estimation of the modeling error for the heat conduction in a plate and its use for adaptive hierarchical modeling , 1994 .

[32]  O. Allix,et al.  Interlaminar interface modelling for the prediction of delamination , 1992 .

[33]  L. Wahlbin,et al.  Local behavior in finite element methods , 1991 .

[34]  Christoph Schwab,et al.  A-posteriori modeling error estimation for hierarchic plate models , 1996 .

[35]  C. Upadhyay,et al.  Region-by-region modeling of laminated composite plates , 2007 .

[36]  I. Babuska,et al.  Benchmark computation and performance evaluation for a rhombic plate bending problem , 1989 .

[37]  I. Babuska,et al.  A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles , 1994 .

[38]  E. Carrera.  Historical review of Zig-Zag theories for multilayered plates and shells , 2003 .

[39]  Alberto Corigliano,et al.  Damage analysis of interlaminar fracture specimens , 1995 .

[40]  Ivo Babuška,et al.  A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method , 1995 .

[41]  N. J. Pagano,et al.  Elastic Behavior of Multilayered Bidirectional Composites , 1972 .

[42]  J. Tinsley Oden,et al.  Hierarchical modeling of heterogeneous solids , 1996 .

[43]  J. Tinsley Oden,et al.  Estimation of modeling error in computational mechanics , 2002 .

[44]  J. Oden,et al.  Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials: Part II: a computational environment for adaptive modeling of heterogeneous elastic solids , 2001 .

[45]  Pierre Ladevèze,et al.  ERROR ESTIMATION AND MESH OPTIMIZATION FOR CLASSICAL FINITE ELEMENTS , 1991 .

[46]  S. Ohnimus,et al.  Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems , 1999 .

[47]  Ivo Babuška,et al.  Hierarchic modeling of plates , 1991 .

[48]  C. Upadhyay,et al.  Focussed adaptivity for laminated plates , 2003 .