Study On Nonlinear Spatial Beam Element Model Based On Theory Of Deformation And Displacement

Spatial element structures are extensively applied in practical projects. In order to implement the historical nonlinear analysis of the spatial elements structures under external force, it is necessary to develop the precise analytical model. In order to get more precise model of beam element, the assumption of constant longitudinal strain is abandoned, the shear displacement is adopted, and Bernoulli-Euler assumption of beam is modified when the material is at the elastic stage, based on the exiting displacement model of beam.Firstly, the numerical relationship between the rotation of section and the rate of grade of line of deflection is derived. Moreover the sectional warp angle and its numerical relationship with torsion angle are introduced. With this foundation, the axial displacement and lateral displacement of any point in the space member are found, which consider coupled effects of multifactor, such as pull and press, bend, shear, torsion. It gives the theory for spatial beam finite element analysis.Then a new spatial beam element mechanics model of two nodes with twenty-two degrees of freedom is presented. This model can be used for elastic analysis, geometrical nonlinear analysis and material nonlinear analysis of spatial element structures. Some effects can be considered in the model such as two-way bending deformation, warping deformation on axial displacement of beam, transverse shearing deformation, warping deformation and quadratic shearing stress. The stiffness matrix of element is nearly full which can reflect the coupled effects of different deformation.Finally, using the proposed analytical model, the nonlinear analytical program is developed. It gives the element stiffness and strain stress calculation process.The incremental Newton-Rapson method is adopted. Using a framework for an example, this paper analyzes the simple loads bar stress strain rule, through the change section height, the shear displacement of the influence of vertical displacement.