An overview of layerwise theories for composite laminates and structures: Development, numerical implementation and application

Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizations

“…Moreover, our approach makes the use of 3D models viable: as pointed out in [46], the assembly burden is one the main obstacles that prevents their use in the analysis of laminated composites with a large number of laminae. However, it is worth reminding that other operations, such as the solution of the linear system of equations, are still dominated by the number of degrees of freedom and function's continuity (see, e.g., the discussion in [20,21] for isogeometric discretizations).…”

“…From that vast literature it is easy to realize that a high percentage of the published finite element models correspond to 2D plate and shell models [44,46,67]. The two-dimensional FEM models are primarily founded on two main composite theories: the equivalent single-layer [44,45] and layerwise [15,29,54] approaches.…”

“…The two-dimensional FEM models are primarily founded on two main composite theories: the equivalent single-layer [44,45] and layerwise [15,29,54] approaches. As discussed in the review [46], layerwise based FEM models, that present good compromise between accuracy and computational cost, combine an in-plane 2D FEM discretization with additional degrees of freedom for describing the displacements and/or transverse stresses of all the material layers. In these approaches the number of required degrees of freedom scales linearly with the number of plies.…”

“…Similarly, 3D elasticity models are able to accurately reproduce the laminate's strain and stress profiles by representing each ply with one or more elements along its thickness. As in the case of layerwise approaches, the number of degrees of freedom scales linearly with the number of layers, but, additionally, the computational cost of the matrix assembly is very high compared to 2D models [46]. In this paper we propose a new methodology that significantly reduces this assembly cost, becoming analogous to the complex-ity of a 2D problem and independent of the total number of material layers.…”

Free vibration analysis of Timoshenko beams reinforced by BNNTs and a comparison with CNT-reinforced composite

“…Yan et al [19] investigated dynamic behavior of edge-cracked exponentially distributed FG beams on an elastic foundation under the action of a moving load using Timoshenko beam theory. Liew et al [20] conducted a review on layerwise theories for composite laminates and structures, representing the recent development of layerwise theories, their numerical implementation, and application in the analysis of composite laminated structures. Utilizing Reddy's higher-order shear deformation theory and taking advantage of IMLS-R method, Zhang and Selim [21] studied free vibration behavior of CNTRC functionally graded thick laminated composite plates, considering 4 different distributions for CNTs and analyzing the impact of different parameters on the vibration behavior.…”