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Validation of Bredt's formulas by the method of asymptotic splitting

Schmidrathner, Christian

Wiley ; 2018

In: PAMM Vol. 18, No. 1 ( 2018-12)

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In: PAMM, Wiley, Vol. 18, No. 1 ( 2018-12)

Abstract: The equations describing torsion of prismatic bars with thin‐walled closed cross sections, known as Bredt's formulas, are verified using the method of asymptotic splitting. In particular, the strong formulation of the Saint Venant problem of a straight beam is expanded asymptotically. At first, well‐known technical assumptions of the shear stress distribution are validated. Further, the influence of a transverse force acting on the beam is considered. This shear force causes a deformation of the cross section and therefore an adaption of Bredt's formulas. Two distinct formulations of the shear center, called the kinematic and the energetic shear center, are obtained. The latter are verified in numerical experiments.

Type of Medium: Online Resource

ISSN: 1617-7061 , 1617-7061

URL: Issue

URL: Article

DOI: 10.1002/pamm.v18.1

DOI: 10.1002/pamm.201800050

Language: English

Publisher: Wiley

Publication Date: 2018

detail.hit.zdb_id: 2078931-2

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Flexible belt hanging on two pulleys: Contact problem at non-material kinematic description

Vetyukov, Yury ; Oborin, Evgenii ; Scheidl, Jakob ; [et al.]

Elsevier BV ; 2019

In: International Journal of Solids and Structures Vol. 168 ( 2019-08), p. 183-193

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In: International Journal of Solids and Structures, Elsevier BV, Vol. 168 ( 2019-08), p. 183-193

Type of Medium: Online Resource

ISSN: 0020-7683

URL: Article

DOI: 10.1016/j.ijsolstr.2019.03.034

Language: English

Publisher: Elsevier BV

Publication Date: 2019

detail.hit.zdb_id: 218287-7

detail.hit.zdb_id: 2012750-9

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Non‐material finite element rod model for out‐of‐plane bending of an elastic strip with natural curvature

Schmidrathner, Christian ; Vetyukov, Yury

Wiley ; 2019

In: PAMM Vol. 19, No. 1 ( 2019-11)

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In: PAMM, Wiley, Vol. 19, No. 1 ( 2019-11)

Abstract: A novel finite element formulation for elastic unshearable rods in three‐dimensional space is presented. Looking forward to future implementations of axially moving belts, we use a mixed Eulerian‐Lagrangian kinematic formulation, which has the advantage that the element nodes are fixed in one spatial coordinate and the material points are flowing through the mesh, hence it is possible to discretize the elements in the free spans coarser than the ones in contact with the pulleys. Here, we present the solution of hanging rods with a flat cross‐section including a natural curvature, which causes an out‐of‐plane bending as well as torsion of the rod. For validation purposes we limit ourselves to equilibrium solutions (for which purely Lagrangian elements would be also applicable) with clamped boundary conditions. The results are compared with a shell model of the hanging strip. Preliminary results concerning the frictionless contact problem for a steel belt hanging on two pulleys are discussed.

Type of Medium: Online Resource

ISSN: 1617-7061 , 1617-7061

URL: Issue

URL: Article

DOI: 10.1002/pamm.v19.1

DOI: 10.1002/pamm.201900235

Language: English

Publisher: Wiley

Publication Date: 2019

detail.hit.zdb_id: 2078931-2

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Non‐material finite element rod model for the lateral run‐off in a two‐pulley belt drive

Schmidrathner, Christian ; Vetyukov, Yury ; Scheidl, Jakob

Wiley ; 2022

In: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Vol. 102, No. 1 ( 2022-01)

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In: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley, Vol. 102, No. 1 ( 2022-01)

Abstract: A novel mixed Eulerian‐Lagrangian rod finite element formulation based on the theory of unshearable, extensible rods is presented. Geometric imperfections (natural curvature) are introduced to investigate and predict the phenomenon of lateral run‐off in the benchmark problem of a two‐pulley belt drive. The concise description of normal and tangential contact between pulleys and belt contributes to the efficient computation of transient solutions. In resemblance of belt shear theory, it relies on the notion of a thin intermediate layer that connects the belt and the pulleys elastically. Various practically relevant transient solutions are validated against corresponding shell finite element computations available in the literature.

Type of Medium: Online Resource

ISSN: 0044-2267 , 1521-4001

URL: Issue

URL: Article

DOI: 10.1002/zamm.v102.1

DOI: 10.1002/zamm.202100135

RVK:

ZG 1100

Language: English

Publisher: Wiley

Publication Date: 2022

detail.hit.zdb_id: 203011-1

detail.hit.zdb_id: 1474638-4

SSG: 17,1

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Mixed Eulerian–Lagrangian description in the statics of a flexible belt with tension and bending hanging on two pulleys

Scheidl, Jakob ; Vetyukov, Yury ; Oborin, Evgenii ; [et al.]

Wiley ; 2018

In: PAMM Vol. 18, No. 1 ( 2018-12)

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In: PAMM, Wiley, Vol. 18, No. 1 ( 2018-12)

Abstract: Studying the mechanics of thin, axially moving strings, beams or plates (e.g.: belt drives, cable cars, …) at mixed Eulerian–Lagrangian description, which features the transformation of material coordinates to spatial ones, is more appropriate than the classical material (Lagrangian) one, see [1, 2]. Aiming at testing a newly proposed non‐material finite element formulation we study the statics of a looped belt as a rod hanging in contact with two pulleys. Numerical experiments demonstrate rapid mesh convergence as well as correspondence to semi‐analytical results and conventional Lagrangian finite element solutions.

Type of Medium: Online Resource

ISSN: 1617-7061 , 1617-7061

URL: Issue

URL: Article

DOI: 10.1002/pamm.v18.1

DOI: 10.1002/pamm.201800060

Language: English

Publisher: Wiley

Publication Date: 2018

detail.hit.zdb_id: 2078931-2

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Buckling of a clamped strip‐like beam with a linear pre‐stress distribution

Schmidrathner, Christian

Wiley ; 2020

In: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Vol. 100, No. 7 ( 2020-07)

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In: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley, Vol. 100, No. 7 ( 2020-07)

Abstract: A thin linear elastic strip is clamped at both ends and subjected to a linear stress distribution across its width. We use Kirchhoff beam theory to study this problem. If displacements out of the strips own plane are prohibited, the straight configuration remains stable as long as the compression is not too high. With the three‐dimensional spatial description of the rod theory, we find possible buckling modes even in the case of average tensile stresses in the beam. Comparison with shell and beam finite elements shows excellent agreement with the analytical investigation, also with respect to the supercritical behavior.

Type of Medium: Online Resource

ISSN: 0044-2267 , 1521-4001

URL: Issue

URL: Article

DOI: 10.1002/zamm.v100.7

DOI: 10.1002/zamm.201900336

RVK:

ZG 1100

Language: English

Publisher: Wiley

Publication Date: 2020

detail.hit.zdb_id: 203011-1

detail.hit.zdb_id: 1474638-4

SSG: 17,1

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Mixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validation

Scheidl, Jakob ; Vetyukov, Yury ; Schmidrathner, Christian ; [et al.]

Elsevier BV ; 2021

In: International Journal of Mechanical Sciences Vol. 204 ( 2021-08), p. 106572-

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In: International Journal of Mechanical Sciences, Elsevier BV, Vol. 204 ( 2021-08), p. 106572-

Type of Medium: Online Resource

ISSN: 0020-7403

URL: Article

DOI: 10.1016/j.ijmecsci.2021.106572

Language: English

Publisher: Elsevier BV

Publication Date: 2021

detail.hit.zdb_id: 1498168-3

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