TY - JOUR

T1 - STUDY OF RESTRAINED TORSION OF THIN-WALLED OPEN-SECTION BEAMS USING THE ASYMPTOTIC SPLITTING METHOD

AU - Горынин, Арсений Глебович

AU - Горынин, Глеб Леонидович

AU - Голушко, Сергей Кузьмич

N1 - The work was carried out within the framework of the program of the Center for the National Technological Initiative of the Novosibirsk State University \u201CModeling and Development of New Functional Materials With Specified Properties\".

PY - 2024/6

Y1 - 2024/6

N2 - A problem of restrained torsion of thin-walled beams under the action of an end torque is considered. The asymptotic splitting method is applied to obtain a system of resolving equations that describes combined torsion, tension-compression, and bending of the beam. The example of typical cross sections is used to compare the resulting model with a stress-strain state in the beam, determined in the calculation using the developed model and three-dimensional numerical calculation by the finite element method. The resulting mathematical model is analyzed and its advantages are revealed and compared to the widely used Vlasov theory. It is shown that the developed model does not contain the restrictions imposed by the Vlasov theory hypotheses, such as the nondeformability of the cross-sectional contour and the absence of shear strains on the middle surface. The resulting model makes it possible in many cases to more accurately determine the emerging stress-strain state. In particular, it is shown that the developed model accounts for the presence of a boundary layer near the clamped end, which arises during torsion of angle sections and makes a significant contribution to longitudinal stresses, while the Vlasov theory does not allow for the recovery of the arising longitudinal stresses.

AB - A problem of restrained torsion of thin-walled beams under the action of an end torque is considered. The asymptotic splitting method is applied to obtain a system of resolving equations that describes combined torsion, tension-compression, and bending of the beam. The example of typical cross sections is used to compare the resulting model with a stress-strain state in the beam, determined in the calculation using the developed model and three-dimensional numerical calculation by the finite element method. The resulting mathematical model is analyzed and its advantages are revealed and compared to the widely used Vlasov theory. It is shown that the developed model does not contain the restrictions imposed by the Vlasov theory hypotheses, such as the nondeformability of the cross-sectional contour and the absence of shear strains on the middle surface. The resulting model makes it possible in many cases to more accurately determine the emerging stress-strain state. In particular, it is shown that the developed model accounts for the presence of a boundary layer near the clamped end, which arises during torsion of angle sections and makes a significant contribution to longitudinal stresses, while the Vlasov theory does not allow for the recovery of the arising longitudinal stresses.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85211387148&origin=inward&txGid=4dd744c965b32d46cb19015a1d49c28f

U2 - 10.1134/S002189442403012X

DO - 10.1134/S002189442403012X

M3 - Article

VL - 65

SP - 502

EP - 518

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 3

ER -