The use of numerical layerwise theory in the analysis of composite plates

In this thesis layerwise B-spline finite strip method approaches have been developed for free vibration and geometrically nonlinear static analyses of laminated composite plates. In order to account for delamination kinematics, the layerwise computational model has been extended with step function supplements to allow the possible displacement jumps across delamination interfaces. On the basis of such a model, layerwise Bkk and Bkk-i spline finite strip methods have been developed for buckling and postbuckling analysis of delaminated composite laminates. In conjunction with the contact laws the computational model has been used in the development of both Bkk and Bkk-i spline finite strip method capabilities for geometrically nonlinear transient analysis of composite laminates subjected to low-velocity impact. The geometrical non-linearity has been taken into consideration by use of von Karman’s non-linear strain-displacement relationship and a total Lagrangian formulation.

The failure analysis of composite laminates has been incorporated into the layerwise Bkk and Bkk-i spline finite strip method capabilities for static, postbuckling and impact analyses. In order to account for the nature of the progressive failure, stress-based failure criteria and material degradation rules have been accommodated into each loading/time increment according to failure mechanisms. The presence of delamination in the laminates will cause stress singularity at the delamination tip and therefore make a stress-based failure criterion inappropriate for predicting delamination propagation. The fracture mechanics-based criterion by means of energy release rate has been employed for the prediction of delamination propagation. For the purpose of efficiently and effectively modelling an arbitrary delamination, point and distributed interface spring models have been developed by the introduction of inplane and out-of-the-plane imaginary springs.

A wide range of numerical applications has been conducted and comparison has been made with available analytical and experimental results. The accuracy, efficiency, convergence and versatility of the layerwise Bkk and Bkk-i spline finite strip methods have been demonstrated.