Finite element transient dynamic analysis of isotropic and fibre reinforced composite plates using a higher-order theory

A higher-order shear deformable C° continuous finite element is developed and employed to investigate the transient response of isotropic, orthotropic and layered anisotropic composite plates. The governing ordinary linear differential equations are integrated using the central difference explicit time integration scheme. A special mass matrix diagonalization scheme is adopted which conserves the total mass of the element and includes the effects due to rotary inertia terms. Numerical results for deflections and stresses are presented for rectangular plates under various boundary conditions and loadings. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the transient response are investigated. The numerical results are compared with those available in the literature, and with the results obtained by solving the same problems using the Mindlin plate element.

[1]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[2]  E. Hinton,et al.  Transient and pseudo‐transient analysis of Mindlin plates , 1980 .

[3]  E. Hinton,et al.  Free vibration and transient response of thick and thin plates using the finite element method , 1974 .

[4]  Tarun Kant,et al.  Numerical analysis of thick plates , 1982 .

[5]  J. N. Reddy,et al.  Analysis of laminated composite plates using a higher‐order shear deformation theory , 1985 .

[6]  R. Christensen,et al.  A High-Order Theory of Plate Deformation—Part 2: Laminated Plates , 1977 .

[7]  Herbert Reismann,et al.  Forced Motion of Elastic Plates , 1968 .

[8]  Lee R. Calcote,et al.  The analysis of laminated composite structures , 1969 .

[9]  E. Hinton,et al.  Further developments in transient and pseudo‐transient analysis of Mindlin plates , 1981 .

[10]  O. C. Zienkiewicz,et al.  A refined higher-order C° plate bending element , 1982 .

[11]  Pin Tong,et al.  Stability of transient solution of moderately thick plate by finite-difference method , 1971 .

[12]  Tarun Kant,et al.  A refined higher-order generally orthotropic C0 plate bending element , 1988 .

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

[14]  J. N. Reddy,et al.  Dynamic (transient) analysis of layered anisotropic composite‐material plates , 1983 .

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

[16]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[17]  E. Hinton,et al.  The dynamic transient analysis of axisymmetric circular plates by the finite element method , 1976 .

[18]  E. Reissner.  The effect of transverse shear deformation on the bending of elastic plates , 1945 .

[19]  H. Reismann,et al.  DYNAMICS OF RECTANGULAR PLATES , 1969 .

[20]  J. W. Leech,et al.  Stability of Finite-Difference Equation for the Transient Response of a Flat Plate , 1965 .

[21]  A. Gupta,et al.  A method of computing numerically integrated stiffness matrices , 1972 .