Free vibration of functionally graded sandwich shallow shells in thermal environments by a differential quadrature hierarchical finite element method

摘要

This paper presents a differential quadrature hierarchical finite element method (DQHFEM) for dynamic analyses of functionally graded material (FGM) sandwich shallow shells in thermal and non-thermal environments. A layer-wise theory based on the first-order shear deformation theory (FSDT) for each layer was adopted. Effective material properties of the FGM are estimated according to Voigt's rule of mixture (ROM) and/or Mori-Tanaka (MT) scheme. For the shells in thermal environment, a nonlinear temperature distribution in thickness direction is considered and the elastic properties are assumed to be temperature dependent. The results obtained from the proposed formulation are validated with those available in literatures. Natural frequencies obtained from Sander's, Love's and Donnell's shell theories for different geometric and boundary conditions are compared with each other first to assess the performance of different shell theories for FGM sandwich shells under non-thermal environment. Then the effects of volume fraction index, core thickness and temperature gradient on natural frequencies of FGM sandwich shells are investigated. The presented DQHFEM is much like the fixed interface mode synthesis method but does not need modal analysis and is of high accuracy. This work is the first application of the method to functionally graded sandwich shells in thermal environments.