A meshless element free Galerkin method (EFG) is presented to analyze the buckling of laminated composite plates using the classical (Kirchhoff's) plate theory (CPT) formulation. In the meshless EFG method, the moving least-squares (MLS) technique which does not satisfies the Kroneckar delta feature is used to set up the shape functions. The accuracy and the efficiency of the meshless EFG method are thus demonstrated by the numerical analysis of laminated composite plates with simply supported boundary conditions. Effects of the number of layers, ply orientations, the length-to-width ratio and modulus ratio on the dimensionless buckling loads are investigated. The results obtained by the EFG method are compared with those obtained by the CPT and the finite-element method (FEM). EFG results have good agreements with the analytical solutions. Comparison of results with the CPT as well as the FEM suggests that the meshless element free Galerkin method (EFG) yields an effective solution method for the analysis of laminated composite plates.

Simulation of fracture by using numerical methods is important to treat geometries that change in time. In this study, both numerical and experimental investigations are presented for the delamination under mode II loading, detailing the derivation of the formulations in numerical simulations of fracture. The simulation of the delamination under mode II loading based on the cohesive segments model was investigated by using a meshfree method. Then, an experimental investigation was used to verify the meshfree method's results. For tests under mode II loading, three-point end-notched flexure specimens, which are made of carbon/epoxy laminate (AS4/3501-6) which consists of 10 plies in [0] 10 and [0/90/0/90/0] s lay-up with delamination inserted in the middle of the laminate, were used for the interlaminar fracture toughness tests. The problem was solved for [0] 10 , [0/45/-45/90/0] s , [0/90/0/90/0] s , [0/90/0/90/30] s , [0/90/0/90/45] s and [0/90/0/90/60] s laminates with midplane delaminations, and the results were verified for different composite materials. The critical fracture force, which can be experimentally measured, was used to calculate the mode II delamination fracture toughness of the carbon/epoxy laminate. In addition, values of the integral for 209 (11 × 19) and 253 (11 × 23) background meshes with equivalent interval sizes were compared. For a relatively fine background mesh, the critical load was converged. Results obtained from the meshfree element-free Galerkin method showed very good agreement with experimental data for single-mode delamination under mode II loading. The results presented will help in the implementation of mesh design techniques that protect numerical accuracy while minimizing computational expense.

A numerical and experimental investigation for the analysis of delamination problem under mode I loading in composite material is presented. Firstly, the simulation of the delamination under mode I loading and failure of composite materials based on the cohesive segments model is investigated by using the meshfree method. With the partition of unity of moving least-squares shape functions, the discontinuities at the cohesive segments are approximated with additional degrees of freedom at the nodes. An iterative solution scheme between the continuous and discontinuous fields is presented to solve mode I delamination growth. Secondly, to verify the meshfree method’s results, an experimental investigation and the finite element method were used for the simulation of delamination. The experimental study used a double-cantilever beam made of carbon/epoxy laminate (AS4/3501-6) which consists of 10 plies in [0]10 and [0/90/0/90/0]s layup with delamination inserted in the middle of the laminate. The critical fracture force, which can be experimentally measured, was used to calculate the mode I delamination fracture toughness of the carbon/epoxy laminate. Results obtained from the meshfree method showed very good agreement with experimental data for single-mode delamination under mode I loading. The meshfree method could also be used effectively to produce delamination growth in composite laminates and is especially suitable for the simulation of complex delamination patterns that are difficult to model using traditional numerical methods.