Nonlinear Analysis Of Space Beam Based On Shear Displacement And Multi-Factors Coupling Influence

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 and analytical method. 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 geometrical relationship and physical relationship of spatial element structures are researched; 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 displacement and strain expression of any point in the space member are found, which consider coupled effects of multifactor, such as pull and press, bend, shear, torsion. In addition, according to basic plastic theory, the constitutive relation of this kind of structure is derived, incorporating the particular stress state of micro-unite in spatial element structures. It gives the theory for spatial member structures' elastic-plastic nonlinear analysis.Then a new spatial beam element mechanics model of two nodes with twenty 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. The stiffness matrix can be used in arbitrary cross-section of the thin-walled beam. By introducing geometric stiffness matrix on basis of the elastic stiffness matrix, the geometrical nonlinear analyses of this model is realized. By introducing elastic-plastic constitutive matrix, it will get spatial member structures' accuracy elastic-plastic analytical mechanical model.Finally, using the proposed analytical model, the nonlinear analytical program is developed. The incremental Newton-Rapson method is adopted. Two numerical examples are analyzed. The numerical result illustrates the analytical model and analytical methods presented in this paper are accurate and effect.