Non-Prismatic Beam-Like Structures with 3D Cross-Sectional Warping

Migliaccio, Giovanni

doi:10.23967/wccm-eccomas.2020.222

Cited by 5 publications

(30 citation statements)

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“…It is worth noting that similar but generally more complex expressions for E 11 , E 21 , E 31 can be obtained for other non-prismatic beams as well (see, e.g., [6,21]). However, we do not discuss here all cases in which we can obtain closed-form solutions to problem ( 16)-( 17), but we present another interesting example (in section 3.2) and then proceed to compare the results of our model with those of nonlinear 3D-FEM simulations to verify its effectiveness in terms of computational efficiency and accuracy (section 4).…”

Section: Tapered Beam With Circular Solid Cross-sectionsmentioning

confidence: 66%

“…Proceeding as in [21], the components E 11 , E 21 , and E 31 of E, related to the out-of-plane deformation of the transverse cross-sections, can be written in the form…”

Section: Analitycal Resultsmentioning

confidence: 99%

“…In this section we introduce the main ingredients of our model, further details of which can be found in [21]. Then, we present tapered beams for which we can provide analytical formulas for evaluating their stress and strain fields (section 3) and, subsequently, provide comparisons with the results of nonlinear 3D-FEM simulations (section 4).…”

Section: Mechanical Modelmentioning

confidence: 99%

“…where the proper orthogonal tensor field i i T a b ≅ ∅ describes the relative orientation between triads a i and b i , ∅ being the usual tensor (or dyadic) product, while the vector fields k A and k B are such that i A i a k a ⁄ ≅ ⇔ and i B i b k b ⁄ ≅ ⇔ , ˄ being the usual cross-product and apex-prime denoting the derivative with respect to s (further details are in [21]).…”

Section: Geometry and Strain Measuresmentioning

confidence: 99%

“…Π e =Π i ). The exploitation of such principle is a usual technique in continuum mechanics to obtain balance equations in terms of the problem's unknowns (see, e.g., [20][21][22]). In our case, it enables writing balance equations for the stress resultants, F and M, in the form 0 0…”

Section: Stress Measures and Balance Equationsmentioning

confidence: 99%

See 4 more Smart Citations

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: Tapered Beam With Circular Solid Cross-sectionsmentioning

confidence: 66%

“…Proceeding as in [21], the components E 11 , E 21 , and E 31 of E, related to the out-of-plane deformation of the transverse cross-sections, can be written in the form…”

Section: Analitycal Resultsmentioning

confidence: 99%

Section: Mechanical Modelmentioning

confidence: 99%

Section: Geometry and Strain Measuresmentioning

confidence: 99%

Section: Stress Measures and Balance Equationsmentioning

confidence: 99%

See 3 more Smart Citations

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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Analytical evaluation of stresses and strains in inhomogeneous non-prismatic beams undergoing large deflections

Migliaccio

2022

Acta Mech

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A new shear formula for tapered beamlike solids undergoing large displacements

Migliaccio

Ruta²,

Barsotti

et al. 2022

Meccanica

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In many engineering applications it is often necessary to determine the flow of shear stresses in the cross-sections of beam-like bodies. Taking a cue from Jourawski's well-known formula, several scholars have proposed expressions for evaluating the shear stresses in non-prismatic linear elastic beams, where longitudinal variations in the size and shape of the cross-sections produces complex stress fields. In the present paper, a new shear formula, derived using a mechanical model developed in a previous work, is presented for tapered beams subject to even large displacements and small strains. Numerical examples and comparisons with results obtained using other formulas in the literature and non-linear 3D-FEM simulations show how the new formula constitutes an important generalization of the previous ones and is able to provide particularly accurate results.

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Non-Prismatic Beam-Like Structures with 3D Cross-Sectional Warping

Cited by 5 publications

References 0 publications

Efficient and Accurate Modeling of Non-Prismatic Beamlike Structures

Efficient and Accurate Modeling of Non-Prismatic Beamlike Structures

Analytical evaluation of stresses and strains in inhomogeneous non-prismatic beams undergoing large deflections

A new shear formula for tapered beamlike solids undergoing large displacements

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