Low-velocity impact responses of the stiffened composite laminated plates based on the progressive failure model and the layerwise/solid-elements method

Abstract Low-velocity impact responses and impact-induced damages evaluation problems are investigated for the stiffened composite laminated plates based on the progressive failure model and layerwise/solid-elements method (LW/SE). The LW/SE method, which was developed in our previous works (Li, Qing, et al., 2013; Li, Liu, et al., 2013) [1] , [2] for the composite laminated stiffened shells and sandwich plates, not only can obtain accurate displacements and stresses for composite laminates but also can consider complex stiffeners without any assumptions. In the present analysis method, impact responses are determined by the finite element code of LW/SE and the nonlinear Hertz’s contact law which enables consideration of local indentation produced by the indentor on the impacted surface. The 3D Hashin criteria in quadratic strain is employed to predict the initiation of the impact-induced damages. The effect of the accumulation of the damages on the stiffness of laminated plate and stiffeners is computed by using continuum damage mechanics. Several numerical examples are carried out to demonstrate the excellent predictive capability of current method and to study the influence of parameters on the impact responses and impact-induced damages. In addition, the present analysis method is used to study the multi-impacts problem of the stiffened composite laminated plate.

[1]  Fu-Kuo Chang,et al.  Impact identification of stiffened composite panels: I. System development , 2001 .

[2]  M. Mukhopadhyay,et al.  Finite element buckling analysis of stiffened plates , 1990 .

[3]  Z. Bažant,et al.  Crack band theory for fracture of concrete , 1983 .

[4]  Rakesh K. Kapania,et al.  A survey of recent shell finite elements , 2000 .

[5]  R. K. Mittal,et al.  A parametric study of the impact response and damage of laminated cylindrical composite shells , 2001 .

[6]  C. Sun,et al.  Indentation Law for Composite Laminates. , 1982 .

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

[8]  Donald F. Adams,et al.  Analysis of Composite Materials , 2002 .

[9]  K. Chandrashekhara,et al.  Nonlinear Impact Analysis of Laminated Cylindrical and Doubly Curved Shells , 1995 .

[10]  Nagesh R. Iyer,et al.  An efficient finite element model for static and vibration analysis of eccentrically stiffened plates/shells , 1992 .

[11]  Z. A. Siddiqi,et al.  Analysis of eccentrically stiffened plates with mixed boundary conditions using differential quadrature method , 1998 .

[12]  W Sleight David,et al.  Progressive Failure Analysis Methodology for Laminated Composite Structures , 1999 .

[13]  Erasmo Carrera,et al.  Analysis of Thin-Walled Structures With Longitudinal and Transversal Stiffeners , 2013 .

[14]  K. C. Biswal,et al.  Finite element analysis for stiffened laminated plates using higher order shear deformation theory , 1994 .

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

[16]  John T. Katsikadelis,et al.  Analysis of plates reinforced with beams , 2000 .

[17]  João Batista de Paiva,et al.  A special BEM for elastostatic analysis of building floor slabs on columns , 2003 .

[18]  E. Carrera Theories and Finite Elements for Multilayered Plates and Shells:A Unified compact formulation with numerical assessment and benchmarking , 2003 .

[19]  C. Sun,et al.  On the Impact of Initially Stressed Composite Laminates , 1985 .

[20]  Serge Abrate,et al.  Modeling of impacts on composite structures , 2001 .

[21]  George S. Springer,et al.  Impact damage of composites , 1986 .

[22]  Erasmo Carrera,et al.  Free Vibration Analysis of thin-walled cylinders reinforced with longitudinal and transversal stiffeners , 2013 .

[23]  Douglas S. Cairns,et al.  Transient response of graphite/epoxy and Kevlar/epoxy laminates subjected to impact , 1988 .

[24]  Brian Falzon,et al.  Predicting low-velocity impact damage on a stiffened composite panel , 2010 .

[25]  Nam Seo Goo,et al.  The effect of curvature on the dynamic response and impact-induced damage in composite laminates , 1997 .

[26]  S. W. Gong,et al.  Transient response of stiffened composite plates subjected to low velocity impact , 1999 .

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

[28]  Shen Pengcheng,et al.  Static, vibration and stability analysis of stiffened plates using B spline functions , 1987 .

[29]  M. H. Aliabadi,et al.  Boundary element analysis of shear deformable stiffened plates , 2002 .

[30]  K. M. Liew,et al.  Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method , 2006 .

[31]  Pedro P. Camanho,et al.  A continuum damage model for composite laminates: Part II – Computational implementation and validation , 2007 .

[32]  S. Abrate Impact on Laminated Composite Materials , 1991 .

[33]  J. N. Reddy,et al.  A GENERAL NON-LINEAR THIRD-ORDER THEORY OF PLATES WITH MODERATE THICKNESS , 1990 .

[34]  Toshiro Matsumoto,et al.  A boundary element method applied to the elastostatic bending problem of beam-stiffened plates , 2000 .

[35]  Siew Lok Toh,et al.  Impact response of laminated shells with orthogonal curvatures , 1995 .

[36]  Z. Hashin Analysis of Composite Materials—A Survey , 1983 .

[37]  Jostein Hellesland,et al.  Semi-analytical buckling strength analysis of plates with arbitrary stiffener arrangements , 2007 .

[38]  Yan Liu,et al.  A layerwise/solid-element method for the composite stiffened laminated cylindrical shell structures , 2013 .

[39]  Z. Hashin,et al.  A Fatigue Failure Criterion for Fiber Reinforced Materials , 1973 .

[40]  F. Chang,et al.  Impact identification of stiffened composite panels: II. Implementation studies , 2001 .

[41]  A. Deb,et al.  Finite element models for stiffened plates under transverse loading , 1988 .

[42]  Yan Liu,et al.  A layerwise/solid-element method of the linear static and free vibration analysis for the composite sandwich plates , 2013 .

[43]  Hyung Yun Choi,et al.  A New Approach toward Understanding Damage Mechanisms and Mechanics of Laminated Composites Due to Low-Velocity Impact: Part I—Experiments , 1991 .

[44]  Fu-Kuo Chang,et al.  Transient dynamic analysis of laminated composite plates subjected to transverse impact , 1989 .

[45]  Yan Liu,et al.  Three-dimensional semi-analytical model for the static response and sensitivity analysis of the composite stiffened laminated plate with interfacial imperfections , 2012 .

[46]  Rakesh K. Kapania,et al.  Low-velocity impact of laminated composites using a layerwise theory , 1994 .

[47]  M. Mukhopadhyay,et al.  Analysis of stiffened plate with arbitrary planform by the general spline finite strip method , 1992 .

[48]  E. Carrera Developments, ideas, and evaluations based upon Reissner’s Mixed Variational Theorem in the modeling of multilayered plates and shells , 2001 .

[49]  C. Sun,et al.  Dynamic response of anisotropic laminated plates under initial stress to the impact of a mass , 1975 .

[50]  Ik Hyeon Choi,et al.  Low-velocity impact analysis of composite laminates using linearized contact law , 2004 .

[51]  A. L. Dobyns,et al.  Analysis of Simply-Supported Orthotropic Plates Subject to Static and Dynamic Loads , 1981 .

[52]  Maria Augusta Neto,et al.  Influence of multi-impacts on GFRP composites laminates , 2013 .

[53]  R. K. Mittal,et al.  Impact response and damage in laminated composite cylindrical shells , 2003 .

[54]  Shuhua Zhu,et al.  Three-dimensional nonlinear progressive damage analysis on composite laminates based on continuum damage mechanics , 2009 .

[55]  Anant R. Kukreti,et al.  Analysis procedure for stiffened plate systems using an energy approach , 1993 .

[56]  Guanghui Qing,et al.  Free vibration analysis of stiffened laminated plates , 2006 .

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

[58]  Anant R. Kukreti,et al.  Analysis Procedure for Ribbed and Grid Plate Systems Used for Bridge Decks , 1990 .

[59]  Ireneusz Lapczyk,et al.  Progressive damage modeling in fiber-reinforced materials , 2007 .

[60]  Serge Abrate,et al.  Impact on Laminated Composites: Recent Advances , 1994 .

[61]  E. Reissner Note on the effect of transverse shear deformation in laminated anisotropic plates , 1979 .

[62]  K. M. Liew,et al.  Analysis of rectangular stiffened plates under uniform lateral load based on FSDT and element-free Galerkin method , 2005 .

[63]  Erasmo Carrera,et al.  Analysis of laminated doubly-curved shells by a layerwise theory and radial basis functions collocation, accounting for through-the-thickness deformations , 2011 .

[64]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[65]  Mark P. Rossow,et al.  Constraint method analysis of stiffened plates , 1978 .

[66]  Siew Lok Toh,et al.  The elastic response of orthotropic laminated cylindrical shells to low-velocity impact , 1994 .

[67]  Y Murray,et al.  IMPLEMENTATION AND VERIFICATION OF FIBER-COMPOSITE DAMAGE MODELS, FAILURE CRITERIA AND ANALYSIS IN DYNAMIC RESPONSE , 1990 .

[68]  M. Mukhopadhyay Stiffened plates in bending , 1994 .

[69]  Edward A. Sadek,et al.  A finite element model for the analysis of stiffened laminated plates , 2000 .

[70]  Yan-Lin Guo,et al.  Analysis of elastic-plastic interaction buckling of stiffened panels by spline finite strip method , 1993 .

[71]  Fu-Kuo Chang,et al.  A Model for Predicting Damage in Graphite/Epoxy Laminated Composites Resulting from Low-Velocity Point Impact , 1992 .