Analysis Of Crane Lattice Structure Of Bending And Torsion Coupling

When the existing finite element theory is extended from the plane problem to the space problem, the simple linear combination ignoring the interaction of the deformation leads to inaccurate calculation results. In this paper, some research results have been obtained through the study of the lattice structure and the real structure, based on the coupling of bending and torsion.On the basis of geometric nonlinear original plane beam element theory of large displacement, using the theory of the second-order stiffness matrix instead of the original linear stiffness matrix, a new complete balance equation is introduced, and due to considering the second order effect, this method is more accurate to solve the problem. Using the method of resonance coordinates, in the local coordinate system, the total amount and the incremental equilibrium equation of the space bar element are obtained by the Green strain combined with the virtual work, and the accuracy is verified by an example. Using of the space bar element increment and total equilibrium equation, according to the choice of the tower model structure type and parameter list, a series of MATLAB numerical calculation program is compiled. According to the results of numerical calculation, the condition of the coupling of bending and torsion is analyzed, and calculate the size of the additional torque. By using nonlinear iteration results, the axial force of the most bottom bar is calculated when the transverse load and bending moment are combined together. The displacement of each node was calculated under the action of the lateral load, moment and additional torque alone by using linear superposition method and calculated the axial force caused by the action of a single action. Through the comparison of the axial force size get the additional torsion of the tower by force effect sizes, and prove that the linear superposition may result in the formation of error.The equivalent method of lattice equivalent to the real abdominal model is studied, according to the equilibrium condition, the internal force of the rod is calculated, and combined with the structural mechanics related formula, in this paper, the tower model of equivalent bending moment of inertia of formula and the formula of torsion moment of inertia are got, and I calculates the structure of two kinds of six different cross section of equivalent bending moment of inertia and torsional moment of inertia and equivalent cross-sectional area. The interpolation theory of the spatial beam element at the centroid displacement field description, by considering the torsion effect caused by the cross section geometry deformation, the establishment of the any point of the space beam element deformation field function. According to the principle of virtual displacement, obtained spatial beam element stiffness matrix considering bending and torsion coupling [K] by integral solution.