Free vibration of laminated composite plates subjected to in-plane stresses using trapezoidal p-element

A new trapezoidal p-element is applied to solve the free vibration problem of polygonal laminated composite plates subjected to in-plane stresses with various boundary conditions. Legendre orthogonal polynomials are employed as enriching shape functions. The element stiffness and mass matrices are analytically integrated in closed form. Since one can always break a triangle into three trapezoids by simply drawing three lines parallel to the three edges from any point in the triangle, the trapezoidal element is as good as the triangular element. Free vibration of rectangular, triangular and polygonal laminated plates with various boundary conditions and stacking sequences is analyzed. The present solutions are monotonically convergent, and they are in good agreement with the available published results.