Abstract
We explicitly characterize boundary conditions that are compatible with low order variational principles. The freedom afforded by adding in a null Lagrangian without altering the Euler–Lagrange equation significantly expands the range of variationally admissible boundary conditions, although not all possibilities are permitted. Applications to several fundamental problems arising in elastostatics, including bars, beams, and plates, are presented.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 75-108 |
| Number of pages | 34 |
| Journal | Journal of Elasticity |
| Volume | 155 |
| Issue number | 1-5 |
| DOIs | |
| State | Published - Jul 2024 |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Nature B.V.
Keywords
- 49K15
- 49K20
- 49S05
- 58E12
- 74B05
- 74B20
- 74K10
- 74K20
- Beam
- Boundary condition
- Calculus of variations
- Elastica
- Elasticity
- Euler–Lagrange equations
- Minimal surface
- Null Lagrangian
- Piola–Kirchhoff stress
- Plate
- Traction
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