A small strain, moderately large deflection finite element beam model with cross-sectional warping effect. (English) Zbl 0718.73087
Summary: A finite element model that can be applied to helicopter rotor blades has been developed with a particular emphasis on the proper representation of out-of-plane warping of arbitrary cross-sections. The model can describe accurately coupled bending, torsion and extensional behavior of beams undergoing small strain, moderately large deflection. The model can also handle beams with arbitrary cross-sections, taper, pretwist and planform. A main feature of the present approach is to introduce small warping displacement superimposed over flat cross-sections of a shear-flexible beam in the direction of the reference axis in deformed configuration. The nonlinear equilibrium equation resulting from finite element approximation is solved by the Newton-Raphson method. Numerical tests involving simple isotropic beams demonstrate the validity of the present approach.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74B20 | Nonlinear elasticity |
Keywords:
helicopter rotor blades; out-of-plane warping; arbitrary cross-sections; coupled bending; torsion; extensional behavior of beams; nonlinear equilibrium equation; Newton-Raphson methodReferences:
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