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Time-domain analysis of framed structures based on “exact” structural-property matrices for nonprismatic Timoshenko’s elements.
(2022) Pillon, Fenando R.; Ribeiro, Iara Souza; Araújo, Francisco Célio de; Degenhardt, Richard
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 consid- ered. 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, com- plex 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.