Nonlinear oscillations of laminated plates using an accurate four-node rectangular shear flexible material finite element

The objective of the present paper is to investigate the large amplitude vi bratory behaviour of unsymmetrically laminated plates. For this purpose, an efficient and accurate four-node shear flexible rectangular material finit e element (MFE) with six degrees of freedom per node (three displacements ( u, v, w) along the x, y and z axes, two rotations (theta (x) and theta (y)) about y and x axes and twist (theta (xy))) is developed. The element assum es bi-cubic polynomial distribution with sixteen generalized undetermined c oefficients for the transverse displacement. The fields for section rotatio ns theta (x) and theta (y), and in-plane displacements in and v are derived using moment-shear equilibrium and in-plane equilibrium equations of compo site strips along the x- and y-axes. The displacement field so derived not only depends on the element coordinates but is a function of extensional, b ending-extensional coupling, bending and transverse shear stiffness as well . The element stiffness and mass matrices are computed numerically by emplo ying 3 x 3 Gauss-Legendre product rules. The element is found to be free of shear locking and does not exhibit any spurious modes. In order to compute the nonlinear frequencies, linear mode shape corresponding to the fundamen tal frequency is assumed as the spatial distribution and nonlinear finite e lement equations are reduced to a single nonlinear second-order differentia l equation. This equation is solved by employing the direct numerical integ ration meshed. A series of numerical examples are solved to demonstrate the efficacy of the proposed element.