Static and dynamic analysis of functionally graded sandwich plates using a finite volume method based on Mindlin theory

Purpose This study introduces an innovative approach that integrates the cell-vertex finite volume method (CV-FVM) with Mindlin plate theory (first-order shear deformation theory) for investigating the static bending, free vibration and dynamic behavior of functionally graded (FG) sandwich plates. Design/methodology/approach An innovative numerical approach is proposed by integrating the CV-FVM with Mindlin plate theory first-order shear deformation theory (FSDT). Based on Hamilton's principle, the general dynamic governing equations under external loading are derived and subsequently reduced to static and dynamic formulations. Spatial discretization of the governing equations is performed using the CV-FVM. To account for material non-uniformity, a coupled dynamic response solution system is constructed. For transient analyses, the Newmark time integration scheme is employed to establish a time-domain solution framework incorporating the spatio-temporal evolution of material properties. For harmonic response analyses, the Fourier transform is adopted to develop a frequency-domain solution model. Findings The numerical results obtained from the proposed method show excellent agreement with existing solutions reported in the literature under various material distributions, geometric configurations, boundary conditions and surface-to-core thickness ratios. In addition, the proposed approach effectively avoids shear locking in static analyses. Originality/value This study presents a unified CV-FVM-based numerical framework for both time-domain and frequency-domain analyses of FG sandwich plates. The method demonstrates high accuracy, robustness and flexibility in handling material non-uniformity, offering a valuable alternative to conventional finite element formulations.