Learned Gaussian quadrature for continuum-mechanics-based beam finite elements

초록

We propose a learned Gaussian quadrature (L-GQ) for continuum-mechanics-based beam elements that accurately accounts for cross-sectional warping while reducing integration cost. The method uses supervised pairs of system matrices—computed with reduced and sufficiently dense quadrature—to learn cross-section-dependent correction factors in a local coordinate frame. The learned factors are stored and reused for all elements sharing the same cross-section, and a coordinate transformation enables consistent global assembly. Across static and dynamic benchmarks involving straight and curved members and frame assemblies, L-GQ attains mass and stiffness matrices of comparable accuracy to standard Gaussian quadrature (S-GQ) while using markedly fewer points, yielding measurable wall-time savings. The approach enhances robustness and scalability for large structural models in which warping is essential. © 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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