A fast polynomial-FE method for the vibration of the composite laminate quadrilateral plates and shells based on the segmentation strategy

The finite element method is widely applicable to various kinds of models. Nonetheless, as the size and frequency domain of the solving model increase, it encounters challenges related to high memory consumption and slow solution speed. To enhance the computational efficiency while preserving its existing advantages, this study incorporates the Jacobi polynomial with a segmentation strategy into the finite element method for addressing the vibration analysis of composite laminate quadrilateral flat and curved plates. In this method, the dynamic stiffness matrix of a finite element is multiplied on both sides by a matrix composed of Jacobi polynomial basis functions, thereby transforming the expression form of the dynamic stiffness matrix from FE form to meshless form and reducing its size. Additionally, the segmentation strategy is introduced to divide the model into multiple blocks, enhancing convergence and calculation efficiency by altering the sparsity pattern of the dynamic stiffness matrix. Convergence research, validation studies, limitations studies, and parametric studies are conducted. The method demonstrates evident advantages in computational efficiency for random surface quadrilateral models requiring dense mesh description while maintaining a certain level of accuracy.