Three-dimensional nonlinear bending analysis of FG-CNTs reinforced composite plates using the element-free Galerkin method based on the S-R decomposition theorem

A three-dimensional element-free Galerkin method (EFG) based on the Strain-Rotation (S-R) decomposition theorem, named 3D-SR-EFG, is developed to investigate the nonlinear bending behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates. Due to its overcoming the deficiencies of classic finite deformation theories, S-R decomposition theorem can provide a reliable theoretical support for the geometrically nonlinear simulation. The incremental variational formulation based on the S-R decomposition theorem for three-dimensional static large deformation problems is derived from the updated co-moving coordinate formulation and principle of potential energy rate. Global weak-form EFG is adopted to obtain the discrete form of the formulation. Convergence and comparison studies are conducted to validate the numerical stability and accuracy of the proposed 3D-SR-EFG. The influences of volume fraction and distributions of CNTs, plate's aspect ratio and width-to-thickness ratio, boundary conditions on the nonlinear bending response of the CNTRC plates are numerically analyzed and discussed in parametric studies. Results demonstrate that the 3D-SR-EFG can effectively predict the nonlinear bending behavior of the CNTRC plates. This work also further extends the applications of the S-R decomposition theorem.