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#6799. A two-dimensional formulation for the homogenization of helical beam-like structures under bending loads
| December 2026 | publication date |
| Proposal available till | 26-05-2025 |
| 4 total number of authors per manuscript | 0 $ |
| The title of the journal is available only for the authors who have already paid for |
| Journal’s subject area: |
| Applied Mathematics; Modeling and Simulation; Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics; Materials Science (all); |
| place 1 | place 2 | place 3 | place 4 |
| Free | Free | Free | Free |
| 2350 $ | 1200 $ | 1050 $ | 900 $ |
Contract №6799.1   | Contract №6799.2 | Contract №6799.3 | Contract №6799.4 |
1 place - free (for sale)
2 place - free (for sale)
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4 place - free (for sale)
Abstract:
In this paper, a two-dimensional formulation is proposed for modeling the mechanical behavior of helical beam-like structures subjected to bending loads. Helical structures include multi-wire cables, which are widely used in engineering applications. An accurate representation of their mechanical behavior typically requires large-size three-dimensional finite element models. The proposed formulation, written on the cross-section only, offers a tremendous reduction of computational cost. Based on the asymptotic expansion method, the formulation is derived within the framework of homogenization theory. The first-order approximation of the three-dimensional problem is obtained from the solution of two successive problems: a microscopic three-dimensional problem and a macroscopic one-dimensional problem. The latter corresponds to the equilibrium equations of a straight Navier–Bernoulli–Saint Venant beam, which effective elastic properties can be post-processed from the solution of the microscopic problem, rewritten in a helical curvilinear coordinate system (twisting system). Thanks to this coordinate system, we demonstrate that the microscopic problem can be reduced to the cross-section and solved by a two-dimensional finite element analysis. In the twisting system, it is shown that bending loads yet depend on the axial coordinate and require a specific treatment leading to separate variable solutions in the axial variable of complex type. Therefore, this paper advances one step further than previous papers in which the microscopic problem was reduced to a two-dimensional formulation with the drawback that only axial loads (extensional or torsional) could be considered. Numerical results are presented for cylinders, springs, and seven-wire strands. Good agreement with analytical solutions is achieved. Interestingly, the formulation allows an accurate analysis of mechanical contact effects on the homogenized properties.
Keywords:
Beam; Bending; Cable; Finite element; Helical; Homogenization; Spring; Strand
Contacts :
2 place - free (for sale)
3 place - free (for sale)
4 place - free (for sale)
Abstract:
In this paper, a two-dimensional formulation is proposed for modeling the mechanical behavior of helical beam-like structures subjected to bending loads. Helical structures include multi-wire cables, which are widely used in engineering applications. An accurate representation of their mechanical behavior typically requires large-size three-dimensional finite element models. The proposed formulation, written on the cross-section only, offers a tremendous reduction of computational cost. Based on the asymptotic expansion method, the formulation is derived within the framework of homogenization theory. The first-order approximation of the three-dimensional problem is obtained from the solution of two successive problems: a microscopic three-dimensional problem and a macroscopic one-dimensional problem. The latter corresponds to the equilibrium equations of a straight Navier–Bernoulli–Saint Venant beam, which effective elastic properties can be post-processed from the solution of the microscopic problem, rewritten in a helical curvilinear coordinate system (twisting system). Thanks to this coordinate system, we demonstrate that the microscopic problem can be reduced to the cross-section and solved by a two-dimensional finite element analysis. In the twisting system, it is shown that bending loads yet depend on the axial coordinate and require a specific treatment leading to separate variable solutions in the axial variable of complex type. Therefore, this paper advances one step further than previous papers in which the microscopic problem was reduced to a two-dimensional formulation with the drawback that only axial loads (extensional or torsional) could be considered. Numerical results are presented for cylinders, springs, and seven-wire strands. Good agreement with analytical solutions is achieved. Interestingly, the formulation allows an accurate analysis of mechanical contact effects on the homogenized properties.
Keywords:
Beam; Bending; Cable; Finite element; Helical; Homogenization; Spring; Strand
Contacts :
