Modelling of Composite Laminates Based on Isogeometric Layerwise Theory

摘要

The isogeometric paradigm is used to develop a displacement-based layerwise model for thick composite laminates. Layerwise theories provide accurate prediction of the three-dimensional stress state that is of prime importance in structural design. This is in sharp contrast to the class of equivalent single layer theories that yield no or inaccurate information about the transverse stress components. The key idea of layerwise methods is to impose different continuity requirements on the functions of approximation in the in-plane and out-of-plane directions. While maintaining higher-order continuity of the basis functions within a single layer is desirable, continuity of the transverse stresses, dictated by the equilibrium consideration, requires C~0-continuous basis at the interface of adjacent plies. Contrary to previously introduced approaches, the latter conditions can be naturally facilitated through conscious use of isogeometric refinement schemes. The details of the proposed approach are presented in a non-uniform rational B-spline based isogeometric framework. Combining the introduced layerwise and equivalent single layer theories, a multiple model analysis is presented. The aim is to demonstrate the use of the different models within predefined regions of a single laminate and to study the influence of the size of the layerwise region on the accuracy of transverse stresses. Finally, the multi model analysis concept is employed to simulate laminates with existing delaminations. The proposed models are verified considering laminated composite plate under cylindrical bending. The numerical results confirm the accuracy of the proposed models. The displacement and stresses are compared to the existing solutions and good agreement is found. It is also shown that the isogeometric layerwise approach outperforms its traditional Lagrange polynomial-based finite element counterpart on a per degree of freedom basis.