Time-domain analysis of framed structures based on "exact" structural-property matrices for nonprismatic Timoshenko’s elements

Abstract

This paper applies a unified process to calculate ”exact” (consistent) finite-element (FE) matrices for framed structures having nonprismatic elements and including shear-deformation and rotational-inertia effects. In this process, the exact expressions for the element stiffness and nodal-load coefficients result from applying the principle of virtual forces (PVF) at the element level. Rigidity values, determined at a certain number of cross sections in the frame element, are employed to describe how the corresponding rigidities vary along its length. For that, interpolation polynomials of different orders are considered. Exact Timoshenko’s shape functions, built under the most general cases of rigidity variation, are used for evaluating the mass matrix coefficients. In the applications, complex 2D frames with nonprismatic elements are considered to simulate bridge structures under seismic excitation and a generic harmonic load. Comparisons with highly accurate response time-histories obtained by employing ANSYS (3D) solid-FE models are effected to verify the robustness of the proposed formulation.