PROCEEDINGS OF THE RUSSIAN HIGHER SCHOOL
ACADEMY OF SCIENCES

Abstract
A spatial thin-walled beam end element is considered. When the center of gravity of the section does not coincide with its center of bending, there isn’t any uniform system of coordinates for the components of nodal forces and displacements. The axis passing through the center of the cross-section bend is taken as the axis of the beam. .A longitudinal force applied to the center of gravity of the cross section is taken to the center of the bend. The stiffness matrix of a spatial thin-walled beam end element with a longitudinal force in the center of the cross-section bend ob-tained by transferring nodal forces from the centre of gravity of the cross section to the center of the bend is given. The theory proposed by V.Z. Vlasov makes it possible to perform calculations of only plane frames with a particular design of joints. One of the main criteria of them is the equality of deplanations of section beams forming a node. A final element with nodes along the contours of the sections in the end sections of the beam is proposed to calculate spatial thin-walled beam systems. The stiffness matrix of the beam is obtained by transfer matrices of nodal forces and displacements. The deplanation in the end sections of the beam is transformed into the longitudinal movement of the nodes along the contours of the sections. An П-form beam finite element is proposed to be used in the numerical algorithm to form the stiffness matrix. The finite element representing the shape of the section that allows performing calculations of thin-walled beam systems in the nodes of connections in which there is no equality derived from the angle of torsion of the beam. The beams outside node connections are modeled be beam elements with nodes along the contours of the sections, while beam connection zones are modeled by finite shell elements. An example of the calculation of the console frame whose finite-element model is formed by a combination of finite elements is given. 

References

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