Finite element formulation including interlaminar stress calculations

Predictor–corrector procedures for analysis of laminated plates using standard Mindlin finite element models

“…The method of integrating the equilibrium condition to obtain the transverse shear stress from the in-plane stress had been commonly adopted and also applied to many of the ad hoc finite element models for laminate analysis [4][5][6]9,10]. However, most of these models suffer from an increasing number of nodal parameters with the number of plies and/or non-conventional nodal kinetic d.o.f.s [5,7,[9][10][11]14,16]. On the other hand, there are seldom any works that apply and detail how to apply the method to conventional finite element models such as the nine-node first order Mindlin (also known as C 0 ) plate element which are available in most commercial codes.…”

“…A large volume of works in the laminate analysis using higher order Mindlin theories or their variants in which the displacement assumption is independent of the lamination have been reported, see [3][4][5][6] for examples. It is clear that the accuracy of the theories increase with their orders.…”

“…Its obvious drawback is that a problem can quickly become intractable when the number of plies increases [7][8][9][10][11]. While the in-plane stress prediction is far more accurate than that transverse shear stress prediction in both approaches, a common practice for obtaining a more accurate transverse shear stress is to integrate the derivative of the in-plane stress with respect to the thickness coordinate according to the stress equilibrium condition [4][5][6]9,10]. It is also possible to start the displacement interpolation with the layerwise approach and condense some of the displacement parameters by enforcing the zero shear traction and traction reciprocity conditions.…”

“…Owing to its versatility, finite element method has been the dominating engineering tool for structural/stress analysis. Among the ad hoc formulated finite element models for laminate analysis, most of them suffer from an increasing number of nodal parameters with the number of plies and/or non-conventional nodal kinetic d.o.f.s which render them obscure to ordinary finite element practitioners [5,7,[9][10][11]14,16].…”

Geometrically Nonlinear Stress Recovery in Composite Laminates

“…For such plates, the distortion of the deformed normal due to transverse shear is dependent, not only on the laminate thickness, but also on the orientation and degree of orthotropy of the individual layers [29]." Engblom and Ochoa [30] integrate the equation of equilibrium in the transverse direction to find the transverse normal stress. [32].…”