Incompatible extended layerwise method for laminated composite shells

The extended layerwise method (XLWM) was established in the previous studies [1,2] for the laminated composites with multiple delaminations and transverse crack based on the layerwise theory and extended finite element method (XFEM). In order to improve convergence rate, Wilson's incompatible freedom is introduced into the in-plane displacement discretization of the XLWM, and an incompatible extended layerwise method (IXLWM) is established for the laminated composite shells in this paper. The finite formulation of IXLWM is deduced from Hamilton's principle for composite shells with delamination and/or transverse crack. In the numerical examples, the composite beams, plates and spherical shells are used to validate the proposed IXLWM and investigate its convergence rate for the static responses and stress intensive factor (SIF). In addition, the influence of incompatible freedom in different directions on the convergence rate is studied.