The Calculation And Analysis Method Of Spatial Beam Structure Considering Bending And Torsion Coupling Effect

When the existing analysis theory of beam structure is extended from plane problem to space problem,in most cases,it is just a simple linear combination and superposition of the results of the plane theory,and neglecting the coupling between deformation,therefore,under the condition of geometric nonlinear analysis in the case of large flexural space flexural torsion beam structures with flexural rigidity and torsion stiffness,the calculation results are not accurate.However,the static analysis of the coupling effect of bending and torsion is very few,so we can not see a general and complete finite element model of the coupling effect of bending and torsion.Therefore,the two-way curved space beam element whose centroid of the cross section and the shear center are not coincided is taken as the object of this paper,which uses the finite element method for stationary potential energy principle,and starts from expressions of deformation and strain for beam column structures,and studies and discusses the space beam structure considering the flexural torsional coupling effect.At first,the stationary potential principle is applied to the finite element analysi s of plane pure bending members,by replacing the displacement field of the element by interpolation function,then the flexural stiffness matrix of the plane beam element is obtained.Then,we study the plane beam element considering the bending effect,a nd obtain the stiffness matrix of the element,which is composed of the pure bending stiffness matrix and the geometric stiffness matrix related to the axial force.As a result,the tension,compression and bending effects in the plane can be coupled,thus to solve the geometrically nonlinear analysis of the planar beam system under small displacements.Then,a biaxial curved beam with unsymmetrical cross section is studied considering the flexural torsional coupling effect,by analysing the expressions of stress and strain at any point,the strain energy of the micro section at this point is obtained,so the total potential energy of the beam rod is obtained by integrating.The simplified method is derived according to the finite element method of the stati onary potential principle,and the element stiffness matrix of beam and bar considering the coupling effect of bending and torsion is obtained,so that the bending and torsion effect can be coupled in space.MATLAB program is written to realize the assembly of stiffness matrix,and the setting up 1 and giving 0 method to deal with the constraints of structure is used.According to the special nonlinear computational model in this paper,an approximate numerical method is proposed.Analyse two cantilever bea ms with different cross-sections by MATLAB programming,and compare the results with ANSYS,the advance of this method is proved in many ways.Then,the spatial beam bar considering the coupling effect of bending and torsion is studied,on the basis of the foregoing,strain and stress expressions at any point are rederived,and the bending torsion coupling effect and the spatial beam element stiffness matrix.The compression,bending and torsion effects of the component are fully coupled in space.At last,the accuracy of the method is proved by a numerical example.At last,the theoretical results of this paper are applied to the nonlinear analysis of a certain type of high-altitude working vehicle,by programming in MATLAB,the displacement of the boom system is calculated.The results are compared with those of ANSYS software,The practicability of the method in engineering practice is proved.