A multilevel iterative algorithm for robust nonlinear dynamic analysis of force-based beam structure
by Ausama Mohamed Ali; Jame Alexander; Tathagata Ray
International Journal of Structural Engineering (IJSTRUCTE), Vol. 14, No. 1, 2024

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.

Online publication date: Mon, 26-Feb-2024

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