A rod model for large bending and torsion of an elastic strip with a geometrical imperfection

Vetyukov, Yury; Schmidrathner, Christian

doi:10.1007/s00707-019-02378-y

Cited by 9 publications

(5 citation statements)

References 25 publications

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“…This example has been studied in detail in [5]. We consider a beam with constant initial curvature Ω 0 1 and length L, which is longer than the distance H between its clamped ends and subjected to gravity.…”

Section: Resultsmentioning

confidence: 99%

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

Schmidrathner

Vetyukov

2019

Proc Appl Math and Mech

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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.

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Section: Resultsmentioning

confidence: 99%

“…We consider a beam with constant initial curvature Ω 0 1 and length L, which is longer than the distance H between its clamped ends and subjected to gravity. This example has been studied in detail in [5]. We compare three kinematic quantities: the displacements u x and u y and the torsional rotation ψ at the center of the strip.…”

Section: Resultsmentioning

confidence: 99%

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

Schmidrathner

Vetyukov

2019

Proc Appl Math and Mech

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“…Both strings are simply supported at 𝑥 = ±𝐻∕2 and their sags can be computed easily [28]. Sag differences as well as lateral displacements of clamped rods with natural curvature are studied semi-analytically in [29].…”

Section: Benchmark Problemsmentioning

confidence: 99%

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

2021

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Funding informationÖsterreichische Forschungsförderungsgesellschaft, Grant/Award Number: 861493 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.

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“…Given the boundary condition, the bending moment of end O is zero. Substitute x = 0, M u0 = 0 into the above formula, ζ u = 0 can be obtained [21]. Therefore, the deflection curve equation, rotating equation, and bending moment equation of the upper column can be written as follows:…”

Section: Analysis Of Bending Deformationmentioning

confidence: 99%

Nonlinear Analysis of Steel Structure Bent Frame Column Bearing Transverse Concentrated Force at the Top in Factory Buildings

Wang

Weng

et al. 2020

Metals

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The steel bent frame structure of single-story factory buildings is actually a spatial structure system. Different bent frame columns are connected with the roof of bent frame structure, making the columns work and bearing the load together. In the steel frame of the factory building with bridge cranes below 20 t, variable-section columns with corbels are used to bear the crane load. In this article, the steel bent frame column of single-story factory buildings was taken as the research object. The bent frame column was simplified as a cantilever variable stepped column bearing a transverse concentrated force at the top. After simplifying the model, the theoretical formula of deflection, rotating angle, and bending moment of the compression rod was put forward. Moreover, bending deformation and stability of variable stepped columns were analyzed in order to obtain the theoretical and practical formula, then the ANSYS software was used to simulate the bent column.

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A rod model for large bending and torsion of an elastic strip with a geometrical imperfection

Cited by 9 publications

References 25 publications

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

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

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

Nonlinear Analysis of Steel Structure Bent Frame Column Bearing Transverse Concentrated Force at the Top in Factory Buildings

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