Title: A multilevel iterative algorithm for robust nonlinear dynamic analysis of force-based beam structure

Authors: Ausama Mohamed Ali; Jame Alexander; Tathagata Ray

Addresses: Engineering and Industrial Technology, North Shore Community College, 300 Broad Street, Lynn, MA 01905, USA ' H2B Inc., 1225 N Loop W #800, Houston, TX 77008, USA ' Construction and Civil Engineering Technology, Morehead State University, 105 A Llyod Cassity Building, Morehead, KY 4035, USA

Abstract: Modelling material nonlinearity is imperative in structural analysis, especially for earthquake, blast, impact, and environment-driven chemical deteriorations. Stiffness-based beams are primarily used in commercial software for simulating such nonlinearity. This paper presents several improvements of the flexibility-based method to make it better than the stiffness-based method. The specific developments proposed here are: 1) the iterative convergence for updating the state of the element sections, and solution of the multi-axial smooth hysteretic equation; 2) the derivation of consistent tangent stiffness of the smooth hysteretic model; 3) the semi-implicit iteration for determining the incremental corotational stress resultants. The proposed solution is verified satisfactorily with existing stiffness-based solutions for global and local nonlinear dynamic responses. The proposed solution performs better than the existing stiffness-based solutions regarding coarser element discretisation and larger time-step. The chief reasons for this superior performance are: 1) the multilevel iterative algorithm; 2) the consistent tangent operator.

Keywords: nonlinear dynamic analysis; flexibility-based beam; stiffness-based beam; implicit solution algorithm.

DOI: 10.1504/IJSTRUCTE.2024.136894

International Journal of Structural Engineering, 2024 Vol.14 No.1, pp.25 - 41

Received: 18 Nov 2022
Accepted: 15 Aug 2023
Published online: 26 Feb 2024 *

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