NURBS-based isogeometric formulation for linear and nonlinear buckling analysis of laminated composite plates using constrained and unconstrained TSDTs

Two isogeometric plate models employing Reddy's third-order shear deformation theory (TSDT) and unconstrained third-order shear deformation theory (UTSDT) are presented and compared for linear and nonlinear buckling analysis of laminated composite plates with and without imperfection and subjected to different inplane loads. Cubic non-uniform rational B-spline (NURBS) basis functions that easily satisfy $C^{\text{1}}$ continuity of the IGA-TSDT model are employed. The total Lagrangian approach in conjunction with the principle of virtual work is used to derive the governing equations. The primary and secondary solutions are traced using a tangent based arc-length method with a simple branch switching technique. The performance of the models is evaluated by validation and comparison with solutions obtained using ANSYS, Navier method (for linear analysis only), and those in the literature. The buckling response is significantly affected by pre-buckling boundary conditions and strain-displacement relations. The nonlinear buckling approach, among other approaches, is observed to be the most accurate methodology for an arbitrarily laminated composite plate. Further, IGA-UTSDT with nine DOF gives marginal improvement over IGA-TSDT with five DOF at the cost of computation. The IGA-TSDT is observed to be superior to FEM-TSDT in terms of computation demand and performance.