A local gradient smoothing method for solving the free vibration model of functionally graded coupled structures

Abstract

In this paper, a meshless method for analyzing the free vibration of four-parameter functionally graded composite shells is presented, which is based on moving least square (MLS) approximation and local gradient smoothing method (LGSM). Firstly, the displacement field model of the substructure is established by using the first order shear deformation theory (FSDT), and the governing equation of the substructure is obtained by using Hamilton principle. Starting from the MLS approximation the displacement field of substructure, the derivative of the shape function is approximated by the LGSM, and the vibration analysis models of each substructure are established respectively. Then, the vibration model of the whole coupling structure is established by coupling each substructure with the displacement coordination relation of the substructure, and the vibration model of the whole coupling structure is established. For the vibration problems considering different boundary conditions, the results obtained from the meshless vibration model are compared with the FEM results to verify the accuracy and applicability of the established analysis model. At the same time, in order to improve the accuracy of the solution, the convergence analysis is also carried out. Finally, in order to enrich the research content, the influence of geometric parameters and material parameters of the structure on the vibration characteristics of the whole structure is studied. The results show that this method can effectively analyze the free vibration of the coupled structure.