Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory

Abstract

A multi-layered shell formulation is developed based on a layerwise deformation theory (Reddy, 2004) within the framework of isogeometric analysis (IGA). IGA utilizes Non-Uniform Rational B-splines (NURBS) to represent the geometry as well as to describe the field variables (Hughes et al., 2005). The high-order smoothness of NURBS offered the opportunity of capturing the structural deformation efficiently in a rotation-free manner. The derivation also follows a layerwise theory, which assumes a separate displacement field expansion within each layer, and considers transverse displacement component as C0-continuous at layer interfaces, thus resulting in a layerwise continuous transverse strain states. Since the in-plane and through-thickness integrations are carried out individually, this approach is capable of capturing the complete three-dimensional stress states in a two-dimensional setting, which improves the computational efficiency. A knot insertion technique is utilized for the discretization in the through-thickness direction, and C0-continuity is enforced by means of knot repetition at dissimilar material interfaces. The performance of the proposed model is demonstrated using multiple laminated composites and sandwich plates (including functionally graded material core) as examples. Numerical results prove the accuracy of the proposed formulation and show that the isogeometric layerwise shell is superior to its finite element counterpart.