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Steel and Composite Structures
  Volume 3, Number 3, June 2003 , pages 213-229

A high precision shear deformable element for free vibration of thick/thin composite trapezoidal plates
S. Haldar and M. C. Manna

     A high precision shear deformable triangular element has been proposed for free vibrationrnanalysis of composite trapezoidal plates. The element has twelve nodes at the three sides and four nodes inside the element. Initially the element has fifty-five degrees of freedom, which has been reduced to forty-eight by eliminating the degrees of freedom of the internal nodes through static condensation. Plates having different side ratios (b/a), boundary conditions, thickness ratios (h/a=0.01, 0.1 and 0.2), number of layers and fibre angle orientations have been analyzed by the proposed shear locking free element. Trapezoidal laminate with concentrated mass at the centre has also been analyzed. An efficient mass lumping scheme has been recommended, where the effect of rotary inertia has been included. For validation of the present element and formulation few results of isotropic trapezoidal plate and square composite laminate have been compared with those obtained from open literatures. The numerical results for composite trapezoidal laminate have been given as new results.
Key Words
    finite element; shear-locking free element; composite trapezoidal plate; rotary inertia; first order shear deformation theory; lump mass.
Department of Applied Mechanics, B. E. College (D. U.), Howrah-7111 03, lndia

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