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

Migliaccio, Giovanni

doi:10.1007/s00707-022-03247-x

Cited by 8 publications

(6 citation statements)

References 31 publications

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“…tensor product, and prime denotes s-derivative. Specifically, for small strain and warping fields, E is written as in [16], i.e., 2E = T T H+H T T˗2I, where H is the derivative of RA with respect to RB (deformation gradient) and I is the identity tensor.…”

Section: Mechanical Modelmentioning

confidence: 99%

“…a a , which is related to S via the deformation gradient H and is associated with the stress in the body actual state [3,16].…”

Section: Mechanical Modelmentioning

confidence: 99%

“…Following [16], and studying inhomogeneous beams with tapered, pre-twisted cross-sections and external actions (as in a Saint-Venant's beam) applied only at the end cross-sections, we write the cross-sectional strains, E11, Eα1, in the form…”

Section: Mechanical Modelmentioning

confidence: 99%

“…This result is interesting as it allows us to consider the individual effect of each 1D strain by solving PDEs whose solution only depends on the shape of the cross-sectional domain Σ. Such PDEs admit closed-form solutions only in a few cases (e.g., [3,16]), but can always be solved numerically. However, apart from directly determining the scalar fields ei and the relevant strains and stresses, we can obtain analytical information on these latter without explicitly solving the PDEs ( 5)-( 6), as is discussed in the following section.…”

Section: Mechanical Modelmentioning

confidence: 99%

“…Literature works usually address tapered beams undergoing small displacements, assume Navier's formula for the cross-sectional normal stresses, and derive formulas for the corresponding shear stresses by the static equilibrium of a beam slice in its reference (undeformed) state. Migliaccio's works [5,15,16] do not rely on such assumptions, account for the effects of large displacements, and is the basis of the present study.…”

Section: Introductionmentioning

confidence: 99%

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Stress and strain fields in non-prismatic inhomogeneous beams

Migliaccio

2023

Theoretical and Applied Mechanics - AIMETA 2022

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Abstract. Beamlike structures are commonly studied via 1D beam models, which are more efficient than 3D finite element methods, but do not permit accurate predictions of 3D stresses in non-prismatic cases. Despite the progress made in their modeling, either via direct 1D approaches or dimensional reductions from 3D formulations, the accurate analytical prediction of stresses and strains in beamlike yet 3D elements, with non-uniform properties both in terms of materials and cross-section shape, subject to large displacements, is an open problem. This work presents a model for such elements that is particularly suitable for efficient numerical implementations and that allows accurate analytical predictions of stresses and strains. A paradigmatic example shows the importance of non-trivial stress terms that are absent in prismatic homogeneous elements and the inadequacy of usual beam models and stepped-beam approaches when dealing with predictions of stresses and strains in non-prismatic inhomogeneous cases.

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Section: Mechanical Modelmentioning

confidence: 99%

“…a a , which is related to S via the deformation gradient H and is associated with the stress in the body actual state [3,16].…”

Section: Mechanical Modelmentioning

confidence: 99%

Section: Mechanical Modelmentioning

confidence: 99%

Section: Mechanical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stress and strain fields in non-prismatic inhomogeneous beams

Migliaccio

2023

Theoretical and Applied Mechanics - AIMETA 2022

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Axial–torsional coupled static behavior of inhomogeneous pretwisted cantilever beams

Genel

Tüfekçi

2023

Acta Mech

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On the role of different nonlinear damping forms in the dynamic behavior of the generalized Beck’s column

Migliaccio,

D’Annibale

2024

Nonlinear Dyn

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The influence of internal and external nonlinear damping forms on the dynamics of a generalized Beck’s column, namely a visco-elastic cantilever beam, subjected to conservative and non-conservative loads at its free end, is investigated. A variational principle provides the equations of motion of the system, which are properly recast into an integro-differential form. The linear stability analysis of the system is then carried out and bifurcation points are detected in the space of parameters associated with the conservative and non-conservative loads. Starting from Hopf’s bifurcation points, a post-critical analysis, based on the Method of Multiple Scales is directly performed on the continuous system, avoiding any a-priori discretization. This method provides the bifurcation equations whose analysis reveals the double nature of nonlinear damping, which can be beneficial or detrimental in terms of stable or unstable bifurcated equilibria. It is found that both the internal and external forms of nonlinear damping can turn a supercritical instability of the system into a subcritical one, thus revealing another destabilizing effect of damping, beyond the very well-known one occurring in the linear field. Numerical simulations, grounded on a Galerkin discretization of the original system, confirm the analytical findings.

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

Cited by 8 publications

References 31 publications

Stress and strain fields in non-prismatic inhomogeneous beams

Stress and strain fields in non-prismatic inhomogeneous beams

Axial–torsional coupled static behavior of inhomogeneous pretwisted cantilever beams

On the role of different nonlinear damping forms in the dynamic behavior of the generalized Beck’s column

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