A lock-free material finite element for non-linear oscillations of laminated plates

The objective of the present paper is to propose an efficient, accurate and robust four-node shear flexible composite plate element with six degrees o f freedom per node to investigate the non-linear oscillatory behavior of un symmetrical laminated plates. The degrees of freedom considered are three d isplacement (u, v, w) along x-, y- and z-axis, two rotations (theta(x), the ta(y)) about y- and x-axis and twist theta(xy). The element employs coupled displacement field, which is derived using moment-shear equilibrium and in -plane equilibrium of composite strips along the x- and L.-axis. The displa cement field so derived not only depend on the element co-ordinates but are a function of extensional, bending-extensional, bending and transverse she ar stiffness coefficients as well. A bi-cubic polynomial distribution with 16 generalized undetermined coefficients for the transverse displacement is assumed. The element stiffness and mass matrices are computed numerically by employing 3 x 3 Gauss Legendre product rules. The element is found to be free of shear locking and does not exhibit any spurious modes. The element is found to be free of shear locking and does not exhibit any spurious mod es. In order to compute the non-linear frequencies, linear mode shape corre sponding to fundamental frequency is assumed as the spatial distribution an d non-linear finite element:equations are reduced to a single non-linear se cond order ordinary differential equation. This equation is solved by emplo ying direct numerical integration method. A series of numerical examples is solved to demonstrate the efficacy of the proposed material finite element . (C) 2000 Academic Press.