A superconvergent meshfree collocation formulation for laminated composite plates with particular focus on convergence analysis

A superconvergent meshfree collocation formulation is presented for the accurate analysis of laminated composite plates, where the convergence characteristic is particularly investigated. The shear locking is resolved through the employment of a mixed formulation that takes the in-plane displacements, deflection, rotations and shear forces as primary variables. The resulting meshfree collocation equations are attained by introducing the recursive gradients constructed from the first order gradients of meshfree shape functions. Subsequently, the convergence of both the standard meshfree collocation approach and the proposed recursive gradient meshfree collocation formulation is theoretically analyzed for the system of mixed discrete equations corresponding to laminated composite plates. These theoretical results clearly identify the basis degree discrepancy issue for meshfree collocation analysis of laminated composite plates. More importantly, this accuracy deficiency is successfully removed by the recursive gradient meshfree collocation formulation, which essentially achieves a desirable superconvergence for the meshfree laminated plate solutions. The superior accuracy and locking free performance of the present meshfree collocation formulation is thoroughly demonstrated by numerical results.