A novel 3D mixed finite‐element model for statics of angle‐ply laminates

Abstract

SUMMARYAnalysis of angle-ply laminates becomes critical and computationally involved because of the presence of extension-shear coupling. A reÿned three-dimensional, mixed, 18-node ÿnite-element (FE) model has been developed to analyse angle-ply laminates under static loading. The minimum potential energy principle has been used for the development of the mixed FE model, where the transverse stress components ( xz , yz and z , where z is the thickness direction) have been incorporated as the nodal degrees of freedom, in addition to the three displacement ÿelds. Further, continuity of transverse stress ÿelds through the thickness of the plate and layerwise continuity of displacement ÿelds have been enforced in the formulation. Because all the constitutive and the compatibility conditions have been ensured within the continuum, the present formulation is unique amongst the family of mixed FE models. Results have been obtained for various angle-ply laminates and compared with analytical and ÿnite-element solutions, which have been found to be in good agreement with them. Some new results on angle-ply with clamped-clamped support condition have also been presented to serve as benchmark results.

Hybrid-interface element for thick laminated composite plates

“…9. Results have been found to be in excellent agreement with the analytical solution by Pagano [18] and Mixed FE formulation of Desai et al [13]. Fig.…”

“…In mixed/hybrid finite element models developed using Reissner's variational principle, stress fields are assumed independent of the displacement fields and fundamental elasticity relation cannot be satisfied. On the other hand, 18-node, 3-dimensional (3-D) mixed FE model based on displacement theory satisfying fundamental elasticity relations has been presented by Ramtekkar et al [11,12] and Desai et al [13]. This model has been shown to provide reliable results for stress and displacement of laminated composites, satisfying continuity of displacements as well as the transverse stresses.…”

High‐order layerwise finite element for the damped free‐vibration response of thick composite and sandwich composite plates

“…Thick composite plates with few layers were studied in order to accentuate the capabilities of the method. The predictions of the current plate theory (HLPT) were compared with an exact solution [18], a mixed 3D finite element solution [40], a linear layerwise Ritz-type plate exact solution (LLPT) [20] and with damping predictions of a linear layerwise [21] and a first-order shear finite element solution (FSPT) [43]. Concerning the HLPT-finite element, reduced integration was used for the shear terms and full integration for the in-plane ones in all cases studied.…”

“…Di Sciuva and Gherlone [35] developed a high-order layerwise plate theory based on a third-order Hermitian distribution of the in-plane displacements and a linear Lagrangian approximation for the deflection through the thickness of each discrete layer to predict the static thermo-mechanical response of plate structures with damaged interfaces and developed a C 0 continuous 8-noded plate finite element [36]. As far as angle-ply thick composite or sandwich composite plates are concerned, most formulations published are based on modified Reissner-Mindlin theories [37][38][39], whereas Desai et al [40] developed a 3D finite element based on a mixed-field laminate theory to predict the static response of angle-ply composite plates. Yet, it seems that neither integrated high-order layerwise damping theories nor damped finite elements have been developed to account for the global and local damped dynamic response of thick composite and sandwich composite plates; moreover, the effect of local interlaminar shear response on modal damping has to be adequately quantified.…”

“…Each plate was modeled using a 10×10 element mesh in cantilever configuration on the left edge. The application of a 2 mm thick interlaminar damping layer at 1610 T. S. PLAGIANAKOS AND D. A. SARAVANOS (0.494a,0.494a)[40], point (0.5a,0.5a) (0.494a,0.049a)[40], point (0.5a,0)…”