Applying Potra-Pt & aacute;k Iterative Cycle for Solving Highly Nonlinear Structural Problems

When solving nonlinear algebraic equations that arise from discretization using the finite element method (FEM), it is often observed that the standard Newton-Raphson (N-R) iteration either fails to converge or necessitates a large number of iterations in the vicinity of critical points. This work proposes an additional numerical strategy, known as the Potra-Ptak iterative cycle, to improve the efficiency of solving highly nonlinear structural problems. Therefore, the focus here is on making the nonlinear solver more robust and efficient, allowing the analysis of more complex nonlinear structures. In the Potra-Ptak iterative cycle, two corrections of the objective function (energy function) are performed. The introduction of a second correction in the iterative cycle makes the Potra-Ptak strategy more efficient than the standard or modified N-R iterations. This numerical strategy was implemented in the homemade Computational System for Advanced Structural Analysis (CS-ASA) program. The program is based on the FEM and is capable of performing static and dynamic nonlinear analysis of steel, concrete, and composite structures, and its efficiency is then verified through the analysis of slender frames and arches. The algorithm details for solving the nonlinear structural problem, characterized by the Potra-Ptak scheme, are provided.

Automated summary

This research proposes the Potra-Ptak iterative cycle as a numerical strategy to improve the efficiency of solving highly nonlinear structural problems. By introducing a second correction in the iterative cycle, the Potra-Ptak strategy is more efficient than the standard or modified Newton-Raphson iterations. The algorithm details for solving the nonlinear structural problem using the Potra-Ptak scheme are provided.