Stiffness Matrix of Thin-Walled Open Bar Subject to Bending, Bending Torsion and Shift of Cross Section Middle Surface

One of the main stages in the analysis of complex 3D structures and engineering constructions made of thin-walled open bars using FEM is a stiffness matrix developing. Taking into account middle surface shear deformation caused by the work of tangential stresses in the formula to calculate a potential energy of thin-walled open bars, the authors obtain an important correction at calculation of the bar deformation and fundamental frequencies. The results of the analysis of the free end buckling of a cantilever H-bar under plane bending differ from exact solution by 0.53%. In the course of comparison of the obtained results with the cantilever bar buckling regardless the middle surface shear deformation, an increase made 16.6%. The stiffness matrix of a thin-walled open bar developed in the present work can be integrated into any software suite using FEM for the analysis of complex 3-D structures and engineering constructions with n-freedoms.