Parametric Iterative Method for Addressing an Embedded-Steel Constitutive Model with Multiple Roots

José J. Padilla, Francisco I. Chicharro, Alicia Cordero, Alejandro M. Hernández-Díaz and Juan R. Torregrosa ()
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José J. Padilla: Department of Ingeniería Civil, UCAM Universidad Católica de Murcia, 30107 Murcia, Spain
Francisco I. Chicharro: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 Valencia, Spain
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 Valencia, Spain
Alejandro M. Hernández-Díaz: Área de Mecánica de Medios Continuos y Teoría de Estructuras, Universidad de La Laguna, 38200 La Laguna, Spain
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2023, vol. 11, issue 15, 1-15

Abstract: In this paper, an iterative procedure to find the solution of a nonlinear constitutive model for embedded steel reinforcement is introduced. The model presents different multiplicities, where parameters are randomly selected within a solvability region. To achieve this, a class of multipoint fixed-point iterative schemes for single roots is modified to find multiple roots, achieving the fourth order of convergence. Complex discrete dynamics techniques are employed to select the members with the most stable performance. The mechanical problem referred to earlier, as well as some academic problems involving multiple roots, are solved numerically to verify the theoretical analysis, robustness, and applicability of the proposed scheme.

Keywords: nonlinear constitutive models; iterative methods; stability; order of convergence; unified parameter plane; multiple roots (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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