A domain decomposition method for elastodynamic problems of functionally graded elliptic shells and panels with elastic constraints

Abstract

A highly efficient and accurate semi-analytical domain decomposition method for elastodynamic problems of functionally graded elliptic shells and panels with elastic constraints on the basis of the first-order shear deformation theory is presented. Firstly, according to the first-order shear deformation theory, the dynamic energy functional of elastic shell structure is established. Then, the multi-segment partitioning technique is used to segment the shell along the circumference and axis direction. Thirdly, the modified variational principle and least-squares weighted residual method are adopted to ensure the inherent continuity between segments. On this basis, the virtual springs are evenly arranged on each boundary to simulate the boundary forces, and then the desired boundary conditions can be simulated. The displacements of each shell domain are expanded as double Jacobi orthogonal polynomials in the circumferential and axial variable. Lastly, the piecewise matrices for a segment are assembled directly in a similar way to that of the finite element method, and the elastodynamic problems of functionally graded elliptic shells and panels are obtained by the variational operation with respect to generalized coordinate vectors. The numerical comparison shows high computational efficiency and accuracy of the present method. All the calculation results in this paper can be used as benchmark data for future scholars to study this structure.