2025/01/18 by Khanh Chau Le, Le, Khanh Chau, Tuan Minh Tran +1 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Composite Structure Analysis and Optimization #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2501.10772
We construct a one-dimensional first-order theory for functionally graded elastic beams using the variational-asymptotic method. This approach ensures an asymptotically exact one-dimensional equations, allowing for the precise determination of effective stiffnesses in extension, bending, and torsion via numerical solutions of the dual variational problems on the cross-section. Our theory distinguishes itself by offering a rigorous error estimation based on the Prager-Synge identity, which highlights the limits of accuracy and applicability of the derived one-dimensional model for beams with continuously varying elastic moduli across the cross section.