Abstract
Considering the coupling effect of axial force, bending moment and shear force, the displacement interpolation functions of the spatial beam-column element under axial tension and axial compression are derived respectively based on the differential equilibrium equations of the deformed member. The different displacement interpolation functions of the tension and compression elements are unified by replacing the stability integration functions with the Maclaurin series, and the unified functions are completely equivalent to those expressed by stability integration functions. The second-order element tangent stiffness matrix considering the effect of axial deformation, shear deformation, biaxial bending and torsion is derived. The number of series expansion terms in unified displacement interpolation functions is determined from aspects of calculation accuracy and positive definiteness of the structural general stiffness matrixes. Numerical calculation results by this element model accord well with the experimental data, and it indicates the accurateness of this element. Different element models are used in the analyses of a single layer lattice shell, and calculation results indicate that the geometrical nonlinearity of the structure is well exhibited with good efficiency by the refined spatial beam-column element proposed in this paper.
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