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High-order time-spectral BEM for efficient elastodynamic analysis
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DOI：10.1016/j.compstruc.2025.108076.png)
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Abstract
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This study presents a novel boundary element method (BEM) framework for the accurate and efficient numerical solution of elastodynamic problems. By reformulating the time-derivative terms as equivalent body forces, the method enables the use of static fundamental solutions for dynamic analysis, thereby eliminating the need for frequency-domain transformations or the construction of complex time-dependent Green’s functions. In the temporal domain, instead of directly approximating the time-differentiation operators, a more stable time-spectral integration technique based on orthogonal polynomial expansions is introduced. This scheme can, in principle, achieve arbitrary-order of accuracy in the temporal space and eliminate the strict time-step limitations inherent in conventional finite-difference-based schemes. Moreover, the resulting coefficient matrix is time-independent and therefore needs to be computed only once for the entire time-marching process. To evaluate domain integrals, discontinuous triangular elements are employed for spatial discretization, and a scaled coordinate transformation (SCT) technique is employed to address singularities arising from source-field point coincidences. Preliminary numerical experiments in elastodynamic analysis demonstrate that the proposed framework is robust and flexible for long-time dynamic simulations, particularly in problems involving rapid transients or complex geometries.
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