The Theory Of Open Thin-Walled Beam Considering The Shear Deformation And Numerical Analysis

In the traditional mechanical calculations of open thin-walled beam often ignored transverse shear deformation and torsion shear deformation. To taken into account the shear deformation, Euler-Bernoulli beam and Vlasov thin-walled beam were improved.3D element stiffness matrix of thin-walled beam considering shear deformation is derived from stiffness method and finite element method, and then compare the expression torsional stiffness coefficient of these two matrices and verify the correctness of these two improved stiffness matrix.Studies have shown that the shear deformation greater impact on the higher order vibration of open thin-walled beam, in order to get accurate dynamic stiffness matrix which considering shear deformation, governing differential equation of coupled bending and torsional vibration of the improved Euler-Bernoulli beam and Vlasov thin-walled beam is formed by D'Alembert principle, finally using the dynamic stiffness matrix method, the the expression of dynamic stiffness matrix is presented, the frequency of example is calculated using Wittrick-Williams (W-W) algorithm, and with the results of other were compared. It's found that the relative error is less than 3%, when the numerical solutions are compared with the first three results of natural frequency of considering rotary inertia and shear deformation effects.In the calculation of the truss structure, the connection model directly affect the mechanical properties of the whole structure. In order to consider the characteristics of the connection model, using connect element method, to form new connect elements which not only able to consider the behaviour of semi-rigid connections, and can consider the warp displacement of transmission by the numerical method, and put these elements into the program of space frame. With this program, the calculations of the static response of the structures with different member connections, as well as the natural frequency of the portal frame with semi-rigid connection were done, finally use software to verify the correctness of the outcome of the program.