The nonlinear bending-torsion theory for curved rods as \(\Gamma\)-limit of three-dimensional elasticity. (English) Zbl 1133.74027
Summary: The problem of rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in variational setting. Considering different scalings of three-dimensional energy and passing to the limit as the diameter of the beam goes to zero, we derive a nonlinear model for strings and a bending-torsion theory for rods.
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74K05 | Strings |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
| 35Q72 | Other PDE from mechanics (MSC2000) |
