A high precision coupled bending-extension triangular finite element for laminated plates

It is well recognized that the estimation of interlaminar stresses and strain energy release rates is important in designing laminated composite panels. Generally coupled bending-extension finite elements are necessary to study laminates to include the effects of coupling and/or combined transverse and extensional loads. Such elements are normally formulated adapting the classical theory of bending and extension. While the classical laminated plate theory of bending has provision to obtain interlaminar stresses due to transverse loading, it is necessary to include certain higher order terms in the extensional theory in order to obtain the interlaminar stresses due to inplane loads. A high precision triangular element based on a theory which includes both the bending and extension with necessary higher order terms is presented in this paper. The performance of this element is validated with the aid of examples. Numerical results for displacements in symmetric and unsymmetric laminates under bending loads have been given. Numerical results for interlaminar stresses in symmetric and unsymmetric laminates have been given for the well-known benchmark problem of a coupon with free edges. Strain energy release rate components at the delamination tip in coupons with unsymmetric sublaminates have been given. The effects of delamination length and location on the components of the strain energy release rate have been studied. Results indicated that with the use of this element, the interlaminar stresses can be estimated reasonably accurately, over a major part of the laminate except in a small local region close to the free edge. Global-local analysis with three-dimensional elements in the local region, is suggested to obtain local stresses more accurately. Interlaminar stresses at the boundary of a hole in a perforated plate under extension have been obtained to illustrate the use of the present element in a global-local analysis strategy