Third order theory based quadrilateral element for delaminated composite plates with a hybrid method for satisfying continuity at delamination fronts

We present a four-node quadrilateral element based on the third order theory for analysis of composite plates with multiple delaminations, by employing a novel hybrid method for satisfying the continuity conditions at the delaminated fronts. In this method, the continuity of inplane displacement variables is satisfied by directly satisfying them at the midplanes of the sublaminates separated by delaminations, and employing the least squares method with respect to the shear rotation variables. The element is shown to yield very good accuracy in general, in comparison with experimental and three dimensional finite element (FE) solutions, and yield superior results to the other available analytical and FE solutions for static and free vibration responses of delaminated composite beams, and rectangular and skew composite plates under different boundary conditions. It is seen that the results from the existing continuity methods can have large error for thick beams/plates and for higher vibration modes, while the proposed hybrid method is generally very accurate and much superior to the existing methods.