PROGRAMMING USING SEIDEL AND NEWTON METHODS TO SOLVE CURVILINEAR NODAL STRESS EQUATIONS IN PYTHON

Abstract

The Seidel and Newton methods discussed in this article provide solutions for solving curvilinear nodal stress equations in Python. The Seidel method is an iterative technique that updates nodal displacements sequentially until convergence is achieved, while the Newton method utilizes linearization and solves a linear system of equations to obtain the update in nodal displacements.These methods are widely used in engineering fields such as structural analysis and finite element analysis to analyze the stress distribution within complex structures. By implementing the Seidel or Newton method in Python, engineers and analysts can efficiently solve the nonlinear equations and obtain converged nodal displacements. It is important to note that the accuracy and convergence of these methods depend on the nature of the stress equations, the initial guess for nodal displacements, and the chosen convergence criteria. Sensitivity to the initial guess and appropriate convergence criteria should be considered to ensure reliable results. Additionally, validation and verification of the computational model using analytical solutions, experimental data, or benchmark examples are essential steps to ensure the accuracy and reliability of the implemented methods and the numerical model itself. Overall, the Seidel and Newton methods provide powerful tools for solving curvilinear nodal stress equations and can aid in the accurate analysis of structural systems. By understanding the concepts and considerations of these methods, engineers and analysts can make informed decisions and obtain valuable insights into the behavior and performance of the structures under study.