High-order time-spectral BEM for efficient dynamic analysis of 2D thin-walled structures

Accurate and stable solutions for transient dynamic problems have long been a critical challenge in computational mechanics due to the complex nature of time-dependent behaviors and the numerical stiffness that often arises in such simulations. Among the numerical methods developed for solving dynamic problems, the boundary element method (BEM) has attracted significant attention due to its ability to reduce the problem dimensionality and provide high accuracy on unbounded domains. However, conventional BEM formulations for dynamic analysis often depend on complex time-dependent fundamental solutions, utilize finite-difference-based time-stepping schemes, or rely on frequency-domain transformations. These approaches typically involve high computational cost and considerable implementation complexity. Moreover, they usually suffer from strict stability constraints that impose severe limitations on the time-step size. To address this issue, this study proposes a novel time-spectral boundary element method (BEM) framework tailored for the efficient and accurate dynamic analysis of thin-walled structural components, which are common in aerospace, mechanical, and civil engineering applications. The core innovation lies in the temporal discretization strategy, where a time-spectral integration technique based on Gaussian orthogonal polynomial expansions is employed. This approach captures the temporal variation of the solution with high fidelity and significantly reduces the number of required time steps, thereby lowering the computational burden without compromising accuracy. Compared with conventional time-marching BEM schemes, which often suffer from stability limitations and accumulated errors over long simulation periods, the proposed framework demonstrates superior numerical stability and faster convergence. These advantages are particularly pronounced in long-duration dynamic simulations, where the method maintains high accuracy while significantly decreasing total computation time. For the spatial discretization, the method integrates the scaled coordinate transformation BEM (SCT-BEM), which transforms domain integrals into equivalent boundary integrals. This allows the method to retain the classical BEM advantage of boundary-only discretization, eliminating the need for domain meshing and reducing preprocessing complexity. To further enhance numerical robustness, especially for problems involving thin geometries where near-singular integrals frequently occur, a nonlinear coordinate transformation technique is incorporated. This effectively regularizes the near-singular behavior of the integrals, improving solution accuracy and algorithmic stability. The validity and efficiency of the proposed method are demonstrated through numerical experiments involving transient heat conduction and wave propagation problems. The results show excellent agreement with analytical solutions and reference numerical results, highlighting the method’s capability to resolve complex dynamic behavior with high precision. The proposed framework holds significant potential for extension to more complex problems, including multi-dimensional, nonlinear, and coupled multi-physics problems. Such developments would greatly enhance its applicability to real-world engineering challenges, such as fluid–structure interaction, thermo-mechanical coupling, and damage propagation in advanced materials. Moreover, the integration of adaptive computational strategies, such as adaptive time-stepping, error estimation, and local mesh refinement, is expected to further improve the computational efficiency and accuracy of the method, particularly in large-scale simulations where resource constraints remain a critical concern.