On the Elastoplastic Stress Concentration at Reentrant Corners of Thin-Walled Cross Sections Subjected to Pure Torsion

The phenomena that occur during compression of hybrid thin-walled columns with open cross-sections in the elastic range are discussed. Nonlinear buckling problems were solved within Koiter’s approximation theory. A multimodal approach was assumed to investigate an effect of symmetrical and anti-symmetrical buckling modes on the ultimate load-carrying capacity. Detailed simulations were carried out for freely supported columns with a C-section and a top-hat type section of medium lengths. The columns under analysis were made of two layers of isotropic materials characterized by various mechanical properties. The results attained were verified with the finite element method (FEM). The boundary conditions applied in the FEM allowed us to confirm the eigensolutions obtained within Koiter’s theory with very high accuracy. Nonlinear solutions comply within these two approaches for low and medium overloads. To trace the correctness of the solutions, the Riks algorithm, which allows for investigating unsteady paths, was used in the FEM. The results for the ultimate load-carrying capacity obtained within the FEM are higher than those attained with Koiter’s approximation method, but the leap takes place on the identical equilibrium path as the one determined from Koiter’s theory.

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A torsion bending element for thin-walled beams with open and closed cross sections

Computers & Structures ◽

10.1016/0045-7949(94)00509-2 ◽

1995 ◽

Vol 55 (6) ◽

pp. 1045-1054 ◽

Cited By ~ 42

Author(s):

H. Shakourzadeh ◽

Y.Q. Guo ◽

J.-L. Batoz

Keyword(s):

Cross Sections ◽

Thin Walled

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Stress concentration factors for the torsion of curved beams of arbitrary cross-section

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406jmes303 ◽

2006 ◽

Vol 220 (12) ◽

pp. 1709-1726 ◽

Cited By ~ 1

Author(s):

R E Cornwell

Keyword(s):

Finite Element ◽

Stress Concentration ◽

Cross Section ◽

Cross Sections ◽

Shear Stresses ◽

Curved Beams ◽

Finite Element Implementation ◽

Out Of Plane ◽

Concentration Factors ◽

Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

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Interactive buckling of thin-walled beam-columns with open and closed cross-sections

Thin-Walled Structures ◽

10.1016/0263-8231(93)90025-6 ◽

1993 ◽

Vol 15 (3) ◽

pp. 159-183 ◽

Cited By ~ 28

Author(s):

Zbigniew Kołakowski

Keyword(s):

Cross Sections ◽

Beam Columns ◽

Thin Walled ◽

Interactive Buckling

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Numerical Investigation of Cross-Section on Aluminum A6063 Thin-Walled Structures under Low-Velocity Impact Loading

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1019.96 ◽

2014 ◽

Vol 1019 ◽

pp. 96-102

Author(s):

Ali Taherkhani ◽

Ali Alavi Nia

Keyword(s):

Energy Absorption ◽

Cross Section ◽

Cross Sections ◽

Peak Load ◽

Circular Cross Section ◽

Absorption Capacity ◽

Energy Absorption Capacity ◽

Thin Walled Structures ◽

Thin Walled ◽

Crush Strength

In this study, the energy absorption capacity and crush strength of cylindrical thin-walled structures is investigated using nonlinear Finite Elements code LS-DYNA. For the thin-walled structure, Aluminum A6063 is used and its behaviour is modeled using power-law equation. In order to better investigate the performance of tubes, the simulation was also carried out on structures with other types of cross-sections such as triangle, square, rectangle, and hexagonal, and their results, namely, energy absorption, crush strength, peak load, and the displacement at the end of tubes was compared to each other. It was seen that the circular cross-section has the highest energy absorption capacity and crush strength, while they are the lowest for the triangular cross-section. It was concluded that increasing the number of sides increases the energy absorption capacity and the crush strength. On the other hand, by comparing the results between the square and rectangular cross-sections, it can be found out that eliminating the symmetry of the cross-section decreases the energy absorption capacity and the crush strength. The crush behaviour of the structure was also studied by changing the mass and the velocity of the striker, simultaneously while its total kinetic energy is kept constant. It was seen that the energy absorption of the structure is more sensitive to the striker velocity than its mass.

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