Static and free vibration analysis of Timoshenko beam based on combined peridynamic-classical theory besides FEM formulation. (March 2019) - Jafari, Akbar; Ezzati, Meysam; Atai, Ali Asghar
Highlights: Governing equations of Timoshenko beam were developed based on peridynamic theory. A standard FEM formulation was constructed for peridynamic beam element. Effects of different peridynamic (non-local) characteristics on the numerical convergence were studied in detail. Influences of several parameters on the static and vibrational behavior of the beam were studied. Abstract: In this paper, combination of classical and peridynamic theories is implemented to study static and free vibrational behavior of a Timoshenko beam. Employing Hamilton's principle, the governing integro-differential equations are developed. Due to problematic analytical solution, FEM formulations are constructed and necessary computer codes are developed. Static and vibrational problems are numerically studied to reveal influential parameters. Mesh sensitivity analysis and comparison with relevant results reported in the open literature are done for verification of the methodology and ensuring reliable results. Effects of peridynamic parameters, boundary conditions, and the beam size are studied. Regarding each influencing factor, relevant illustration is presented and the results are discussed from the physical point of view.