Analytical derivation of a general 2D non-prismatic beam model based on the Hellinger–Reissner principle

Beltempo, Angela; Balduzzi, Giuseppe; Alfano, Giulio; Auricchio, Ferdinando

doi:10.1016/j.engstruct.2015.06.020

Cited by 32 publications

(39 citation statements)

References 16 publications

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“…The present method results are in excellent agreement with reference values and are further enhanced with refined discretization. Another example concerns the static behavior of cantilever beams of length L = 10 m of variable thickness under tip load forcing F = −100 kN; see [51]. In Figure 4, we present a comparison between the FEM and data obtained from [51] regarding the transverse displacement.…”

Section: Resultsmentioning

confidence: 99%

A Non-Linear BEM–FEM Coupled Scheme for the Performance of Flexible Flapping-Foil Thrusters

Anevlavi

Filippas

Karperaki

et al. 2020

JMSE

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Recent studies indicate that nature-inspired thrusters based on flexible oscillating foils show enhanced propulsive performance. However, understanding the underlying physics of the fluid–structure interaction (FSI) is essential to improve the efficiency of existing devices and pave the way for novel energy-efficient marine thrusters. In the present work, we investigate the effect of chord-wise flexibility on the propulsive performance of flapping-foil thrusters. For this purpose, a numerical method has been developed to simulate the time-dependent structural response of the flexible foil that undergoes prescribed large general motions. The fluid flow model is based on potential theory, whereas the elastic response of the foil is approximated by means of the classical Kirchhoff–Love theory for thin plates under cylindrical bending. The fully coupled FSI problem is treated numerically with a non-linear BEM–FEM scheme. The validity of the proposed scheme is established through comparisons against existing works. The performance of the flapping-foil thrusters over a range of design parameters, including flexural rigidity, Strouhal number, heaving and pitching amplitudes is also studied. The results show a propulsive efficiency enhancement of up to 6% for such systems with moderate loss in thrust, compared to rigid foils. Finally, the present model after enhancement could serve as a useful tool in the design, assessment and control of flexible biomimetic flapping-foil thrusters.

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Section: Resultsmentioning

confidence: 99%

A Non-Linear BEM–FEM Coupled Scheme for the Performance of Flexible Flapping-Foil Thrusters

Anevlavi

Filippas

Karperaki

et al. 2020

JMSE

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“…To the author's knowledge, the most enhanced modeling approaches that seem capable to overcome all the so far discussed limitations have been presented by Rubin (1999), Hodges et al (2008Hodges et al ( , 2010, Auricchio et al (2015), Beltempo et al (2015a), and Balduzzi et al (2016). In greater detail, Rubin (1999), Hodges et al (2008Hodges et al ( , 2010 limit their investigations to planar tapered beams whereas Auricchio et al (2015), Beltempo et al (2015a), and Balduzzi et al (2016) consider more complex geometries.…”

Section: Literature Reviewmentioning

confidence: 99%

“…On the one hand, the beam model proposed by Rubin (1999) seems to achieve the best compromise between simplicity and effectiveness. On the other hand, both the derivation procedure and the resulting models proposed by Auricchio et al (2015) and Beltempo et al (2015a) seem sometimes scarcely manageable and computationally expensive. Finally, Balduzzi et al (2016) propose a simple and effective modeling approach capable to describe the behavior of a large class of nonprismatic homogeneous beam bodies using the independent variables usually adopted in prismatic Timoshenko beam models.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In greater detail, Rubin (1999), Hodges et al (2008Hodges et al ( , 2010 limit their investigations to planar tapered beams whereas Auricchio et al (2015), Beltempo et al (2015a), and Balduzzi et al (2016) consider more complex geometries. On the one hand, the beam model proposed by Rubin (1999) seems to achieve the best compromise between simplicity and effectiveness.…”

Section: Literature Reviewmentioning

confidence: 99%

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Planar Timoshenko-like model for multilayer non-prismatic beams

Balduzzi

Aminbaghai

Auricchio

et al. 2017

Int J Mech Mater Des

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This paper aims at proposing a Timoshenkolike model for planar multilayer (i.e., non-homogeneous) non-prismatic beams. The main peculiarity of multilayer non-prismatic beams is a non-trivial stress distribution within the cross-section that, therefore, needs a more careful treatment. In greater detail, the axial stress distribution is similar to the one of prismatic beams and can be determined through homogenization whereas the shear distribution is completely different from prismatic beams and depends on all the internal forces. The problem of the representation of the shear stress distribution is overcame by an accurate procedure that is devised on the basis of the Jourawsky theory. The paper demonstrates that the proposed representation of cross-section stress distribution and the rigorous procedure adopted for the derivation of constitutive, equilibrium, and compatibility equations lead to Ordinary Differential Equations that couple the axial and the shear bending problems, but allow practitioners to calculate both analytical and numerical solutions for almost arbitrary beam geometries. Specifically, the numerical examples demonstrate that the proposed beam model is able to predict displacements, internal forces, and stresses very accurately and with moderate computational costs. This is also valid for highly heterogeneous beams characterized by thin and extremely stiff layers.

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“…In recent years, several non-prismatic beam models have been proposed in an attempt to overcome the so far discussed problematic [21] [22] [23] [24]. Unfortunately, the most of them suffer from severe limitations e.g., they can tackle only symmetric and linearly tapered beams, present energy inconsistency, or lead to extremely complicated equations.…”

Section: Introductionmentioning

confidence: 99%

Serviceability Analysis of Non-Prismatic Timber Beams: Derivation and Validation of New and Effective Straightforward Formulas

Balduzzi¹,

Hochreiner²,

Füssl³

et al. 2017

OJCE

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This paper provides innovative and effective instruments for the simplified analysis of serviceability limit states for pitched, kinked, and tapered GLT beams. Specifically, formulas for the evaluation of maximal horizontal and vertical displacements are derived from a recently-proposed Timoshenko-like nonprismatic beam model. Thereafter, the paper compares the proposed serviceability analysis formulas with other ones available in literature and with highlyrefined 2D FE simulations in order to demonstrate the effectiveness of the proposed instruments. The proposed formulas lead to estimations that lie mainly on the conservative side and the errors are smaller than 10% (exceptionally up to 15%) in almost all of the cases of interest for practitioners. Conversely, the accuracy of the proposed formulas decreases for thick and highly-tapered beams since the beam model behind the proposed formulas cannot tackle local effects (like stress concentrations occurring at bearing and beam apex) that significantly influence the beam behavior for such geometries. Finally, the proposed formulas are more accurate than the ones available in literature since the latter ones often provide non-conservative estimations and errors greater than 20% (up to 120%).

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Analytical derivation of a general 2D non-prismatic beam model based on the Hellinger–Reissner principle

Cited by 32 publications

References 16 publications

A Non-Linear BEM–FEM Coupled Scheme for the Performance of Flexible Flapping-Foil Thrusters

A Non-Linear BEM–FEM Coupled Scheme for the Performance of Flexible Flapping-Foil Thrusters

Planar Timoshenko-like model for multilayer non-prismatic beams

Serviceability Analysis of Non-Prismatic Timber Beams: Derivation and Validation of New and Effective Straightforward Formulas

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