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

PY - 2024/12/9

Y1 - 2024/12/9

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.

M3 - Article

VL - 65

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 3

ER -