Exact geometric nonlinear analysis of frames modeled with nonprismatic shear-deformable elements defined by noncentroidal axes

Abstract

This paper provides an explicit closed-form expression for geometric-stiffness coefficients for nonprismatic frame elements defined by their noncentroidal axes. The proposed formulation uses the element’s exact elastic stiffness coefficients and exact Timoshenko’s shape functions. One advantage of working with exact stiffness values is the obvious quality of the resulting tangent stiffness matrix, which is expected to be highly accurate. In addition, adopting frame elements based on noncentroidal axes enables the modeling of complex nonprismatic frame elements using simple, straight-line segments. Hence, beams having cross sections that vary asymmetrically around their straight centerlines can be consistently modeled in a simplified process. The formulation takes into consideration the correct interaction between axial and flexural effects. To validate the formulation’s robustness, we evaluate the geometric nonlinear in-plane response of several metal frames possessing nonprismatic elements with variable thin-walled monosymmetric cross sections. We compare these results with highly accurate 3D responses obtained using the ANSYS software.