Poisson's Contraction Effects in a Deep Laminated Composite Beam

Abstract

Poisson's contraction effects in a deep, asymmetrically stacked composite beam is studied in detail through a new finite element formulation. The exact solution of static part of the governing equation is used as interpolating function for displacements. As a result, the element is locking free, giving exact stiffness matrix and a consistent mass matrix, which is derived using exact material-dependent shape functions. The main features that differentiate the elementary and a deep member subjected to axial loading are the dispersiveness of axial response and creation of an additional contractional mode. These features are effectively captured by the present element. The contractional wave appears after a certain frequency (called the cut-off frequency) along with the axial, bending, and shear wave. The studies show that Poisson's contraction has negligible effect on the static response, whereas the high-frequency modes of vibration show significant deviation from elementary member response for low slenderness ratio, where it is found that coupling reduces effect of Poisson's contraction. Wave solutions are compared with 2-D plane stress finite element (FE) solutions.