Auth: Kjell Magne Mathisen
Book Summary: This technical lecture document, presented at the Geilo Winter School, focuses on the specialized numerical techniques required to solve problems in Nonlinear Finite Element Analysis (NFEA). It addresses scenarios where structural behavior cannot be accurately modeled with linear assumptions due to large deformations (geometric nonlinearity), complex material behaviors like plasticity (material nonlinearity), or changing boundary conditions such as contact.
The text outlines the mathematical frameworks behind incremental-iterative solution strategies necessary for tracking structural equilibrium paths. Key topics typically covered include the classic Newton-Raphson and Modified Newton-Raphson iteration schemes, convergence criteria, and advanced path-following techniques like Arc-Length methods, which are critical for capturing complex structural instabilities such as snap-through and snap-back behaviors.
