Nonlinear impact response of thin imperfect laminated plates using a reduction method

Abstract The nonlinear transient response of thin imperfect laminated plates subjected to impact loads is studied using a 48 DOF finite element based on the classical laminated plate theory. Comparison between the first-order shear deformation theory and the classical laminated plate theory is also made to study the effect of shear deformation. The modified Hertzian law by Tan and Sun is incorporated to evaluate the impact loads due to a projectile. The transient response of an example problem is obtained using both full and reduced equations of motion. A reduction method using Ritz vectors as the basis vectors is employed to reduce the size of the nonlinear problem and thus save computational effort. The resulting reduced (but still coupled) set of equations is integrated in a step-by-step fashion using the Newmark constant-average acceleration time integration scheme along with an iterative scheme for dynamic equilibrium. It is observed that geometric imperfections cause significant changes in the impact response of thin laminated plates. The reduction method used in this study was not found to be very efficient for obtaining the nonlinear impact responses. Further research is needed to develop reduction methods that are more suitable for studying nonlinear impact responses.

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

[2]  Rakesh K. Kapania,et al.  Buckling, postbuckling, and nonlinear vibrations of imperfect plates , 1987 .

[3]  A. N. Nahavandi,et al.  Modal Superposition Method for Computationally Economical Nonlinear Structural Analysis , 1979 .

[4]  Lakshman Watawala,et al.  Influence of initial geometric imperfections on vibrations of thin circular cylindrical shells , 1983 .

[5]  Klaus-Jürgen Bathe,et al.  On nonlinear dynamic analysis using substructuring and mode superposition , 1981 .

[6]  T. Y. Yang,et al.  Formulation of an imperfect quadrilateral doubly curved shell element for postbuckling analysis , 1986 .

[7]  Nicholas F. Morris,et al.  The use of modal superposition in nonlinear dynamics , 1977 .

[8]  R. L. Ramkumar,et al.  Low-velocity impact response of laminated plates , 1983 .

[9]  Rakesh K. Kapania,et al.  Geometrically Nonlinear Finite Element Analysis of Imperfect Laminated Shells , 1986 .

[10]  A. Noor.  Recent advances in reduction methods for nonlinear problems. [in structural mechanics , 1981 .

[11]  Rakesh K. Kapania,et al.  Reduction methods based on eigenvectors and Ritz vectors for nonlinear transient analysis , 1993 .

[12]  R. Clough,et al.  Dynamic analysis of large structural systems with local nonlinearities , 1979 .

[13]  J. N. Reddy,et al.  Geometrically nonlinear transient analysis of laminated composite plates , 1983 .

[14]  S. Remseth,et al.  Nonlinear static and dynamic analysis of framed structures , 1979 .

[15]  Use of reduced basis technique in the inverse dynamics of large space cranes , 1990 .

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

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

[18]  Rakesh K. Kapania,et al.  Dynamic buckling of imperfection-sensitive shell structures , 1987 .

[19]  T. M. Tan,et al.  Wave Propagation in Graphite/Epoxy Laminates Due to Impact. , 1982 .

[20]  C. Chang,et al.  Nonlinear Dynamical Response of Impulsively Loaded Structures: A Reduced Basis Approach , 1991 .

[21]  Alberto Cardona,et al.  A LOAD-DEPENDENT BASIS FOR REDUCED NONLINEAR STRUCTURAL DYNAMICS , 1985 .

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

[23]  C. Lanczos.  An iteration method for the solution of the eigenvalue problem of linear differential and integral operators , 1950 .

[24]  C. Sun,et al.  Dynamic large deflection response of composite laminates subjected to impact , 1985 .

[25]  Alberto Cardona,et al.  A reduction method for nonlinear structural dynamic analysis , 1985 .

[26]  LOW-VELOCITY IMPACT RESPONSE OF ORTHOTROPIC PLATES USING A HIGHER-ORDER THEORY , 1987 .

[27]  R. E. Nickell,et al.  Nonlinear dynamics by mode superposition , 1976 .

[28]  Tarun Kant,et al.  Non-linear dynamics of laminated plates with a higher-order theory and C0 finite elements , 1991 .

[29]  E. Wilson,et al.  Dynamic analysis by direct superposition of Ritz vectors , 1982 .

[30]  Fawzi E. Elghadamsi,et al.  An incremental mode-superposition for non-linear dynamic analysis , 1991 .

[31]  Ahmed K. Noor,et al.  Instability analysis of space trusses , 1983 .