Static and dynamic response of moderately thick laminated beams with damage

Abstract

The bending and vibration response of thin and moderately thick laminated beams with ply damage or delaminations is studied using a new discrete-layer laminated beam finite element. The two-noded C° element is based on a new generalized form of the first-order zig-zag laminate theory, and has only four degrees of freedom per node, regardless of the number of layers in the laminate. The element formulation employs the penalty-function concept in conjunction with an interdependent element interpolation scheme, making the element very accurate and robust for application to thick and thin laminated beams. The element stiffness coefficients are exactly integrated without giving rise to shear locking, and a consistent force and mass matrix is derived. The compliant layer concept is employed to simulate delaminations. Comparison of numerical results using the current model with predictions of exact elasticity solutions demonstrates that the current model is capable of accurately simulating the response of thin and moderately thick laminates that contain damage. Additional comparisons with equivalent single-layer theories indicate that the layerwise construction and kinematics must be explicitly taken into account when modelling laminates whose layers have drastically different stiffness properties, as is the case when damage is present.