Static and dynamic analysis of high-order defective sandwich beams by a novel weak-form quadrature element method

Abstract

This paper proposes a novel weak-form quadrature element method for analyzing defective sandwich beams with various boundary conditions. Discrete governing equation can be derived using Gauss-Lobatto points through the extended high-order sandwich panel theory and the energy variational principle. Based on the static equivalence principle, the unknown quantities at internal quadrature points can be determined using the physical quantities at endpoints while maintaining accuracy. This method significantly reduces the size of the modified element matrix, leading to a smaller global matrix. The proposed method is validated through dynamic and static numerical examples involving defective sandwich beams with different boundary conditions and geometric parameters. The results are compared with existing methods, demonstrating the rapid convergence and high accuracy of the proposed method in predicting displacements and stresses. The influence of defects on the mechanical behavior of sandwich beams is analyzed.