A coupled FE-BIE model for the static analysis of Timoshenko beams bonded to an orthotropic elastic half-plane

Tezzon, Enrico; Tullini, Nerio; Lanzoni, Luca

doi:10.1016/j.enganabound.2016.07.009

Cited by 8 publications

(6 citation statements)

References 43 publications

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“…Mesh is refined several times at distances ( L , L / 8 , L / 16 , and L / 24 ) away from the edges of the thin film as shown in Figure 3 where the total length of the film is L = 2 a . In the previous studies about numerical simulation of thin-film/substrate systems, it has also been shown that algorithmically spaced mesh leads to more accurate results than a standard equally spaced partition [36, 37]. For example, Tezzon et al [37] studied a flexible beam bonded to an elastic orthotropic half-plane.…”

Section: Feamentioning

confidence: 99%

“…In the previous studies about numerical simulation of thin-film/substrate systems, it has also been shown that algorithmically spaced mesh leads to more accurate results than a standard equally spaced partition [36, 37]. For example, Tezzon et al [37] studied a flexible beam bonded to an elastic orthotropic half-plane. They modelled the substrate using three different square substrate meshes with a total width of 8 L , 16 L , and 32 L .…”

Section: Feamentioning

confidence: 99%

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The effect of material anisotropy on the mechanics of a thin-film/substrate system under mechanical and thermal loads

Nart

Alinia

Güler

2021

Mathematics and Mechanics of Solids

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In this study, the stress analysis for an orthotropic thin film bonded to an orthotropic elastic substrate is addressed using both the analytical and finite element methods. The analytical method employs the integrodifferential formulation with the aid of membrane assumption. Utilizing the finite element method, the effect of orientation of the material principal directions are studied. The loading scenarios include a temperature gradient imposed on the film and a far-field uniaxial tension on the substrate. The results of current study indicate that the ratio of the film to the substrate stiffness plays a leading role in the film stress distribution. For the mechanical loading applied to the substrate, a soft thin film attached to a relatively stiffer substrate is preferred. The film can tolerate the induced thermal stresses as it is bonded to a softer host structure. The rotation angle of material orthotropy directions significantly affects the stress singularity near the film edges up to a certain extent.

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Section: Feamentioning

confidence: 99%

Section: Feamentioning

confidence: 99%

The effect of material anisotropy on the mechanics of a thin-film/substrate system under mechanical and thermal loads

Nart

Alinia

Güler

2021

Mathematics and Mechanics of Solids

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“…Beams in perfect adhesion with an elastic half-plane are considered in (Tezzon et al, 2015;Tezzon et al, 2016). Differently with respect the proposed approach, traditional variational formulations are defined in terms of foundation displacements only (Selvadurai, 1979b;Selvadurai, 1980;Selvadurai, 1984).…”

Section: Variational Formulationmentioning

confidence: 99%

“…The FE-BIE coupling method has been originally introduced for the static analysis of both Euler-Bernoulli and Timoshenko beams in frictionless contact with a two-dimensional half-space (Tullini and Tralli, 2010) and it has been already extended to the corresponding buckling problem (Tullini et al, 2013a, Tullini et al, 2013b, Baraldi, 2019, and to the case of a fully adhesive contact (Tullini et al, 2012;Tezzon et al 2015;Tezzon et al 2016;Tezzon et al 2018). Effects of sharp and smooth beam edges in the buckling of a Timoshenko beam in frictionless and bilateral contact with an elastic half-plane was analysed in Falope et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Buckling of beams and coatings of finite width in bilateral frictionless contact with an elastic half-space

Baraldi

Tullini

2021

International Journal of Solids and Structures

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“…Moreover, in proximity of the inner section of a Timoshenko beam loaded by a concentrated transversal force the pressure distribution between the beam and the half-plane displays a logarithmic singularity and the shear stress is finite and discontinuous across the loaded section, whereas for the E-B beam model the pressure was found regular therein. Accurate numerical studies about the interfacial stresses between bars and beams and an elastic 2D halfplane can be found in Tezzon et al (2016) , recently extended to a 3D half-space ( Baraldi and Tullini, 2018 ).…”

mentioning

confidence: 99%

Buckling of a Timoshenko beam bonded to an elastic half-plane: Effects of sharp and smooth beam edges

Falope

Lanzoni

Radi

2020

International Journal of Solids and Structures

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The problem of a compressed Timoshenko beam of finite length in frictionless and bilateral contact with an elastic half-plane is investigated here. A Chebyshev series solution is found and, for some limiting cases, an analytic form solution is provided. The problem formulation leads to an integro-differential equation which can be transformed into an algebraic system by expanding the rotation of the beam cross sections in series of Chebyshev polynomials. An eigenvalue problem is then obtained, whose solution provides the buckling loads of the beam and, in turn, the corresponding buckling mode shapes. Beams with sharp or smooth edges are considered in detail, founding relevant differences. In particular, it is shown that beams with smooth edges cannot exhibit a rigid-body buckling mode. A limit value of the soil compliance is found for beam with sharp edges, below which an analytic buckling load formula is provided without loss of reliability. Finally, in agreement with the Galin solution for the rigid flat punch on a half-plane, a simple relation between the half-plane elastic modulus and the Winkler soil constant is found. Thus, a straightforward formula predicting the buckling loads of stiff beams resting on compliant substrates is proposed.

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A coupled FE-BIE model for the static analysis of Timoshenko beams bonded to an orthotropic elastic half-plane

Cited by 8 publications

References 43 publications

The effect of material anisotropy on the mechanics of a thin-film/substrate system under mechanical and thermal loads

The effect of material anisotropy on the mechanics of a thin-film/substrate system under mechanical and thermal loads

Buckling of beams and coatings of finite width in bilateral frictionless contact with an elastic half-space

Buckling of a Timoshenko beam bonded to an elastic half-plane: Effects of sharp and smooth beam edges

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