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

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