A layerwise theory for laminated composites in the framework of isogeometric analysis

Through-thickness modeling of laminated composites using a displacement-based isogeometric layerwise theory is presented. Layerwise theories provide accurate predictions of the three-dimensional stress states that are of prime importance in structural design. This is in sharp contrast to the class of equivalent-single-layer theories that yield no or limited information of three-dimensional stress states. The key idea of layerwise theories is to distinguish and separate the functions of approximation employed in the in-plane and out-of-plane directions. The rationale behind this choice emanates from the underlying physics, due to the balance of linear momentum and continuity of traction, the function describing the transverse displacement field should be C0-continuous at the interface between plies of different fiber angle orientation. The latter condition can be naturally facilitated through conscious use of isogeometric refinement schemes. Finally, a multiple model analysis is introduced. The aim is to demonstrate the use of the different models within predefined regions of a single laminate. The multiple model analysis concept is employed to simulate laminates with existing delaminations. The proposed models are verified considering laminated composite plates. The numerical results confirm the accuracy of the proposed models and shown that the isogeometric layerwise model outperforms its Lagrange polynomial-based counterpart.