Augmented higher order global–local theory and refined triangular element for laminated composite plates

The characteristics of higher order theories for laminated composite plate are that the number of unknowns are independent of the number of layers. However, they are unable to predict accurately the inter-element stresses and are also unsuitable for laminated plates with a large number of layers. Based on the third-order global – 1,2-3 order local higher order theory proposed by Li and Liu [Li XiaoYu and Liu D. Generalized laminate theories based on double superposition hypothesis. Int. J. Numer. Meth. Eng.,1997; 40: 1197–1212], which can predict accurately the interlaminar stresses, we propose an augmented higher order global–local theory for laminated composite plates and using it to estimate the applicability to the range of number of layers. The displacement field is composed of a mth-order (9 > m > 3) polynomial of global coordinate z in the thickness direction and 1,2-3 order power series of local coordinate ζk in the thickness direction of each layer. This theory can satisfy the free surface conditions and the geometric and stress continuity conditions at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this higher order theory, a refined three-node triangular element satisfying the requirement of C1 weak-continuity is presented. Numerical results show that the proposed higher order global–local theory can predict accurately in-plane stresses and transverse shear stresses from the constitutive equations, and it is still effective when the number of layers in laminated plates is more than five and up to 14. It is also shown that the present refined triangular element possesses higher accuracy compared with known elements.