Transient dynamics of laminated beams: an evaluation with a higher-order refined theory

A higher-order refined model with seven degrees of freedom per node and cubic axial, quadratic transverse shear and linear transverse normal strain components is presented for the transient dynamic analysis of composite and sandwich beams. This shear correction coefficient free theory considers each layer of the beam to be in a state of plane stress. A special lumping scheme is employed for the evaluation of the diagonal mass matrix and a central difference predictor scheme is used to solve the dynamic equilibrium equation. The excellent performance of the higher-order model in comparison with the first-order theory is clearly brought out through numerical experiments.

[1]  Thomas J. R. Hughes,et al.  A simple and efficient finite element for plate bending , 1977 .

[2]  Mario Paz,et al.  Structural Dynamics: Theory and Computation , 1981 .

[3]  M. Levinson,et al.  A new rectangular beam theory , 1981 .

[4]  R. Christensen,et al.  A HIGH-ORDER THEORY OF PLATE DEFORMATION, PART 1: HOMOGENEOUS PLATES , 1977 .

[5]  R. Nickel,et al.  Convergence of consistently derived Timoshenko beam finite elements , 1972 .

[6]  Tarun Kant,et al.  On the performance of higher order theories for transient dynamic analysis of sandwich and composite beams , 1997 .

[7]  A modified form of the central difference predictor scheme for damped nonlinear systems , 1994 .

[8]  Tarun Kant,et al.  FREE VIBRATION ANALYSIS OF FIBER REINFORCED COMPOSITE BEAMS USING HIGHER ORDER THEORIES AND FINITE ELEMENT MODELLING , 1996 .

[9]  J. Reddy,et al.  A higher order beam finite element for bending and vibration problems , 1988 .

[10]  J. Archer.  Consistent matrix formulations for structural analysis using finite-element techniques. , 1965 .

[11]  N. G. Stephen,et al.  A second order beam theory , 1979 .

[12]  S. Timoshenko,et al.  LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars , 1921 .

[13]  Tarun Kant,et al.  A finite element model for a higher-order shear-deformable beam theory , 1988 .

[14]  E. Hinton,et al.  Geomechanics abstract Presentation and interpretation of dataA note on mass lumping and related processes in the finite element method : 3F, 1T, 13R. EARTHQ. ENGNG STRUCT. DYN., V4, N3, JAN–MAR. 1976, P245–249 , 1976 .

[15]  H. G. Allen.  Analysis and design of structural sandwich panels , 1969 .

[16]  K. K. Kapur.  Vibrations of a Timoshenko Beam, Using Finite‐Element Approach , 1966 .

[17]  J. N. Reddy,et al.  On the Solutions to Forced Motions of Rectangular Composite Plates , 1982 .

[18]  R. D. Henshell,et al.  A Timoshenko beam element , 1972 .

[19]  Sudhakar Ramamoorthy Marur,et al.  A comparative study of C0 and C1 elements for linear and nonlinear transient dynamics of building frames , 1991 .

[20]  Gangan Prathap,et al.  Beam elements based on a higher order theory—I. Formulation and analysis of performance , 1996 .

[21]  E. A. Witmer,et al.  Finite-element analysis of large elastic- plastic transient deformations of simple structures , 1971 .

[22]  E. P. Popov,et al.  Introduction to Mechanics of Solids , 1968 .

[23]  Khalilollah Khozeimeh,et al.  Inelastic Response of Frames to Dynamic Loads , 1971 .

[24]  O. Zienkiewicz,et al.  A note on mass lumping and related processes in the finite element method , 1976 .

[25]  J. K. Chen,et al.  Nonlinear transient responses of initially stressed composite plates , 1985 .