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

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-p...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 15; p. 3275
Main Authors Padilla, José J., Chicharro, Francisco I., Cordero, Alicia, Hernández-Díaz, Alejandro M., Torregrosa, Juan R.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2023
Subjects
Analysis
Concrete
Constitutive models
Equilibrium
Iterative methods
Mathematical models
Methods
multiple roots
nonlinear constitutive models
Nonlinear equations
order of convergence
Reinforced concrete
Reinforcing steels
Robustness (mathematics)
Roots of equations
stability
Steel
unified parameter plane
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11153275