Geometric nonlinear analysis of space frames constituted of nonprismatic Timoshenko-like elements referred to noncentroidal and nonprincipal axes

Resumo

This paper proposes a geometric nonlinear space frame formulation considering nonprismatic Timoshenko-like elements with heterogeneous cross sections. The kinematics of deformation of the element and the cross-sectional constitutive relationships are referenced to an arbitrary reference frame. The element axis may be any simple straight-line segment intersecting the element’s cross-sections at any position, regardless of the position of their centroid. Such an arbitrary element axis requires consistent consideration of the interaction between axial and flexural effects. This paper uses a flexibility-type method based on the principle of virtual forces to obtain the structural property coefficients. This method avoids solving the complex differential equations that govern the nonprismatic space frame problem. In addition, it allows obtaining the corresponding exact Timoshenko’s Shape Functions (TSFs) for nonprismatic space frame elements. The Euler-Rodriguez’s finite rotation transformation is adopted to determine the natural rotations associated with the nodes of the frame elements along the nonlinear incremental-iterative process. Polynomials of different orders may be used to interpolate the variable rigidities along the element length. Moreover, boundary integrals are adopted to compute the cross-sectional rigidities, which facilitates the modeling of heterogeneous cross sections of complex shapes. All resulting integrals are evaluated using low-order Gauss-Legendre quadrature (3-4 points). The proposed formulation is validated by comparing the results with the ones determined by using highly refined 3D ANSYS models. Nonlinear equilibrium paths, stresses, and internal forces are observed in the comparison of results.