Non-prismatic beams: A simple and effective Timoshenko-like model

Balduzzi, Giuseppe; Aminbaghai, Mehdi; Sacco, Elio; Füssl, Josef; Eberhardsteiner, Josef; Auricchio, Ferdinando

doi:10.1016/j.ijsolstr.2016.02.017

Cited by 74 publications

(70 citation statements)

References 37 publications

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“…With respect to planar non-prismatic beam modeling, several researchers (Bruhns 2003;Hodges et al 2010;Balduzzi et al 2016) have shown with different strategies that the main effect of the cross-section variation is a non-trivial stress distribution. Besides, the influence of cross-section variation on stress distributions can be predicted by exploiting several analytical solutions of the 2D elastic problem for an infinite long wedge known since the first half of the past century (Atkin 1938;Timoshenko and Goodier 1951).…”

Section: Literature Reviewmentioning

confidence: 99%

“…As a consequence of the non-trivial stress distribution, also the beams' shear strain depends on all the internal forces H, V, and M and, due to the symmetry of constitutive relations, both the curvature and the beams' axial strain depend on the vertical internal force V (Balduzzi et al 2016). The numerical examples discussed by Balduzzi et al (2016) demonstrate that the so far introduced relations deeply influence the whole beam behavior and can not be neglected.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The numerical examples discussed by Balduzzi et al (2016) demonstrate that the so far introduced relations deeply influence the whole beam behavior and can not be neglected. Furthermore, they confirm that non-prismatic beammodels differ from prismatic ones not only in terms of variable cross-section area and inertia, but they especially result in more complex relations between the independent variables.…”

Section: Literature Reviewmentioning

confidence: 99%

“…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%

“…According to the terminology introduced by Balduzzi et al (2016), the definition multilayer non-prismatic beam refers to a continuous body made of layers of different homogeneous materials, in which the geometry of each layer can vary arbitrarily along the prevailing dimension of the beam. Both researchers and practitioners are interested in non-prismatic beams since they allow to reach extremely important optimization goals such as the desired strength with the least material usage.…”

Section: Introductionmentioning

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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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Planar Timoshenko-like model for multilayer non-prismatic beams

Balduzzi

Aminbaghai

Auricchio

et al. 2017

Int J Mech Mater Des

Self Cite

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Exact Analytical Solution of the Pure Bending Problem of a Multilayer Wedge-Shaped Console

Ковальчук

Goryk

Antonets

2022

Lecture Notes in Mechanical Engineering

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Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

Vilar

Hadjiloizi

Masjedi

2022

Int J Mech Mater Des

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Emerging manufacturing technologies, including 3D printing and additive layer manufacturing, offer scope for making slender heterogeneous structures with complex geometry. Modern applications include tapered sandwich beams employed in the aeronautical industry, wind turbine blades and concrete beams used in construction. It is noteworthy that state-of-the-art closed form solutions for stresses are often excessively simple to be representative of real laminated tapered beams. For example, centroidal variation with respect to the neutral axis is neglected, and the transverse direct stress component is disregarded. Also, non-classical terms arise due to interactions between stiffness and external load distributions. Another drawback is that the external load is assumed to react uniformly through the cross-section in classical beam formulations, which is an inaccurate assumption for slender structures loaded on only a sub-section of the entire cross-section. To address these limitations, a simple and efficient yet accurate analytical stress recovery method is presented for laminated non-prismatic beams with arbitrary cross-sectional shapes under layerwise body forces and traction loads. Moreover, closed-form solutions are deduced for rectangular cross-sections. The proposed method invokes Cauchy stress equilibrium followed by implementing appropriate interfacial boundary conditions. The main novelties comprise the 2D transverse stress field recovery considering centroidal variation with respect to the neutral axis, application of layerwise external loads, and consideration of effects where stiffness and external load distributions differ. A state of plane stress under small linear-elastic strains is assumed, for cases where beam thickness taper is restricted to $$15^{\circ }$$ 15 ∘ . The model is validated by comparison with finite element analysis and relevant analytical formulations.

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Non-prismatic beams: A simple and effective Timoshenko-like model

Cited by 74 publications

References 37 publications

Planar Timoshenko-like model for multilayer non-prismatic beams

Planar Timoshenko-like model for multilayer non-prismatic beams

Exact Analytical Solution of the Pure Bending Problem of a Multilayer Wedge-Shaped Console

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

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