Rotor blades as curved, twisted and tapered beam-like structures subjected to large deflections

Migliaccio, Giovanni; Ruta, Giuseppe

doi:10.1016/j.engstruct.2020.111089

Cited by 16 publications

(29 citation statements)

References 29 publications

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“…The results discussed right now are particularly interesting because the nature of our PDEs problem allows considering even separately the effects of the different 1D strain measures and geometric parameters (Λ α and k B1 ) in the determination of the scalar fields e 1 , e 2 , e 3 , which are necessary for calculating the strain fields (15), stress fields (8), and stress resultants (9).…”

Section: Analitycal Resultsmentioning

confidence: 95%

“…In general, all components of the strain measures are considered small in the sense their order of magnitude is at most ε. For the considered beam, the strain tensor E is written (as in [9]) in the form…”

Section: Geometry and Strain Measuresmentioning

confidence: 99%

“…isotropic or not). For completeness' sake, we also introduce the first Piola-Kirchhoff stress tensor P and Cauchy stress tensor C, which for our beam are P=TS and C=TST T (as in [9]). By using the stress tensor P, cross-sectional stress resultants are defined in terms of two vector fields, F (force) and M (moment), as follows…”

Section: Stress Measures and Balance Equationsmentioning

confidence: 99%

“…By using such ingredients, the resolution of the three-dimensional nonlinear elasticity problem is now reduced to the solution of two main problems: the first governs the cross-sectional warping motion and it's strong formulation can be given in terms of partial differential equations (PDEs) defined over a reference bi-dimensional domain (as is discussed in the next section). The second problem governs the centre-line motion and can be expressed in terms of a set of non-linear ordinary differential equations (ODEs) defined over a reference line (as in [9], for instance). It is worth noting that this approach reduces the computational effort and produces accurate results compared to nonlinear 3D-FEM approaches (as is shown also in the following).…”

Section: Stress Measures and Balance Equationsmentioning

confidence: 99%

“…Generally speaking, structural analyses show that the models and formulas commonly used for prismatic beams provide incorrect results in non-prismatic cases, as the variations in the dimensions and orientation of the transverse cross-sections produce non-trivial stress distributions absent in prismatic beams [9][10]. To date several models have been proposed for beamlike bodies, ranging from linear theories [11][12][13] to geometrically exact and asymptotic approaches [14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Efficient and Accurate Modeling of Non-Prismatic Beamlike Structures

Migliaccio¹

2021

14th International Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control

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Many complex engineering structures, e.g. components of helicopters, wind turbines, aircraft wings and propellers, are beamlike and non-prismatic. Structures of this kind may be tapered, pre-twisted, and even curved in their unstressed state, and undergo large displacements and 3D cross-sectional warping. Their mechanical modeling can be addressed via non-prismatic beam elements providing the appropriate compromise between computational efficiency and accuracy. Over the years many models have been proposed for beamlike structures, but general non-prismatic cases still require investigation. Formulas valid for prismatic beams, for example, generally provide incorrect results in non-prismatic cases, as the variation in the dimensions and orientation of the transverse cross-sections produce non-trivial stress distributions absent in prismatic beams. A model suitable for the aforementioned non-prismatic elements should properly describe their shape, explicitly consider the effects of their geometric design features on their stress and strain fields, account for large displacements, and provide the known results of prismatic cases. We propose a physical-mathematical model that accounts for all such requirements. The non-prismatic beam is seen as a collection of plane figures (the transverse cross-sections) attached at a 3D curve (the beam's centre-line). The centre-line's points may undergo large displacements. The transverse cross-sections are fully deformable and may undergo warpings in and out of plane. Assuming small warping and strain fields, a variational approach provides the field equations. The model obtained enables evaluating even analytically the effects of geometric parameters (such as taper) on the stress and strain fields. Numerical examples and comparisons with the results of nonlinear 3D-FEM analyses confirm the effectiveness of the proposed modeling approach.

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Section: Analitycal Resultsmentioning

confidence: 95%

Section: Geometry and Strain Measuresmentioning

confidence: 99%

Section: Stress Measures and Balance Equationsmentioning

confidence: 99%

Section: Stress Measures and Balance Equationsmentioning

confidence: 99%