An Improved Spectral Element Differential Method in Solving Nonlinear Thermoelastic Coupling Problems With Discontinuous Interfaces

Abstract

In this paper, the spectral element differential method (SEDM) is improved to solve the nonlinear thermoelastic coupling problems with interface thermal resistance and interface gap in composite structures. The utilization of both Lobatto and Chebyshev node sets in SEDM significantly enhances solution efficiency by replacing integration with direct differential. Moreover, for strongly nonlinear problems caused by thermal radiation, unknown terms are incorporated into the stiffness matrix, and the relaxation iteration technique is also employed, the convergence has been improved compared to traditional methods. Importantly, the element format of the SEDM for 3D problems with discontinuous interfaces is given specifically in this paper, and element-by-element loop assembly of stiffness matrices is realized. Numerical examples confirm the effectiveness of the present method in efficiently and accurately solving 2D and 3D problems with discontinuous interfaces. The present method not only achieves faster convergence than the traditional finite element method, but also attains higher accuracy with fewer degrees of freedom and shorter computational time. Compared to the spectral element method (SEM), the proposed method significantly reduces the computation time of the stiffness matrix. Furthermore, by employing the coupled SEM-SEDM approach, computational efficiency is enhanced while maintaining high precision in sensitive regions.