Meshfree VDQ method for thermal-vibration coupling characteristic analysis of irregular thin plates

A meshless Variational Differential Quadrature (VDQ) method is proposed for thin plates with irregular geometric configurations. By integrating Differential Reproducing Kernel (DRK) interpolation technique and radial basis function approximation, a differential operator suitable for unstructured nodes is constructed. Meanwhile, an adaptive integral operator based on Voronoi diagram theory is developed to achieve numerical integration over irregular computational domains. The effectiveness of this method is validated through systematic investigations of thermally driven vibrations in both homogeneous single-layer plates and Functionally Graded Materials (FGM) with five typical boundary shapes, including square plates, round-corner-defective plates, square-corner-defective plates, circular-hole plates, and square-hole plates. Numerical results demonstrate that compared with traditional grid-based methods, the meshless VDQ method reduces the number of nodes while maintaining engineering accuracy requirements. In thermal-vibration analysis, the maximum deflection magnitudes for both types of plates exhibit a significant decrease trend: intact > round-corner-defective > square-corner-defective > circular-hole > square-hole, revealing the influence mechanism of irregular geometric boundaries on thermal-vibration responses of thin plate structures. This research provides an efficient and reliable numerical tool for thermal-vibration analysis of complex thin plate structures in aerospace, precision machinery, and other engineering fields.