GENERALIZED FINITE DIFFERENCE METHOD FOR BENDING AND MODAL ANALYSIS OF FUNCTIONALLY GRADED CARBON NANOTUBE-REINFORCED COMPOSITE PLATES

Composite plates have always received much attention. In view of excellent mechanical properties of functionally graded carbon nanotube-reinforced composite (FG-CNTRC), it is particularly important to study the mechanical behavior of FG-CNTRC plates by scholars. Based on the first order shear deformation theory, a novel meshless collocation method, generalized finite difference method (GFDM), is applied to the bending and modal analysis of FG-CNTRC plates. Based on the multivariate Taylor series expansion and the moving least-squares theory, the partial derivatives of the underdetermined displacements at a certain node can be represented by a linear combination of the displacements of its neighboring nodes in the GFDM implementation. The proposed GFDM not only has the advantages of avoiding meshing generation and numerical integration, but also provides the sparse system, which overcomes the highly ill-conditioned assembled matrix issue existed in most of meshless collocation methods. Hence the method has advantages of simple-form, easy-to-use and -implement, which is generally used in a variety of scientific and engineering problems. The numerical model for the bending and modal analysis of FG-CNTRC plates in the GFDM implementation is firstly proposed. Then the computational validity and convergence of the GFDM are analysed by some benchmark cases. Finally, the influences of different distributional types, volume fraction, rotational angle of CNTs, inclination angle of plate, thickness to span ratio, length-width ratio and boundary conditions on the structural bending and modal are investigated in details.