A shear‐flexible triangular finite element model for laminated composite plates

Abstract

SUMMARYFormulation and numerical evaluation of a shear-flexible triangular laminated composite plate finite element is presented in this paper. The element has three nodes at its vertices, and displacements and rotations along with their first derivatives have been chosen as nodal degrees-of-freedom. Computation of element matrices is highly simplified by employing a shape function subroutine, and an optimal numerical integration scheme has been used to improve the performance. The element has satisfactory rate of convergence and acceptable accuracy with mesh refinement for thick as well as thin plates of both homogeneous isotropic and laminated anisotropic materials. The numerical studies also suggest that reliable prediction of the behaviour of laminated composite plates necessitates the use of higher order shear-flexible finite element models, and the proposed finite element appears to have some advantages over available elements.

Boundary element analysis of anisotropic Kirchhoff plates

“…** Centre of the edge of the plate parallel to y. 6.4% difference compared with the results of Lakshminarayana and Murthy (1984). However, as will be shown in another example below (a quasi-isotropic square plate with clamped edges), the results for moments obtained in this work are in good agreement with analytical solutions.…”

“…The total thickness of the laminate is h = 0.01 m. All layers have equal thickness. This problem was analysed by Rajamohan and Raamachandran (1999) using the charge simulation method and by Lakshminarayana and Murthy (1984) using the finite element method (FEM). A series solution for the transverse displacement in the centre of the plate was presented by Noor and Mathers (1975) by treating the plate as an equivalent single-layer orthotropic plate.…”

“…6), is compared in Table 2 with the finite element solution presented by Lakshminarayana and Murthy (1984) and the analytical solution presented by Noor and Mathers (1975). As can be seen, the same accuracy as the finite element results was obtained.…”

“…6). In Table 3, the results are compared with the results presented by Lakshminarayana and Murthy (1984) (FEM 1) and Noor and Mathers (1975) (FEM 2), both of whom used the finite element method.…”

Nonlinear oscillations of laminated plates using an accurate four-node rectangular shear flexible material finite element

“…In fact, in the case of thin plates with all edges clamped, the authors found that even a 32 x 32 mesh of QUAD4 elements over the whole plate does not yield converged frequencies. The slow convergence of QUAD4 elements in the case of thin plates is an established problem (see Lakshminarayana & Sridhara Murthy 1984), whose solution in the formal manner has been sought for long. The proposed element, being nonconforming, is found to converge from the top in the case of SSSS plates and from the bottom for CCCC plates.…”