Asymptotically exact theory of functionally graded elastic beams
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915109841928192 |
|---|---|
| author | Le, Khanh Chau Tran, Tuan Minh |
| author_facet | Le, Khanh Chau Tran, Tuan Minh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10772 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically exact theory of functionally graded elastic beams Le, Khanh Chau Tran, Tuan Minh Classical Physics Mathematical Physics 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. |
| title | Asymptotically exact theory of functionally graded elastic beams |
| topic | Classical Physics Mathematical Physics |
| url | https://arxiv.org/abs/2501.10772 |