Advanced Non Linearities
This module explored the complexities of nonlinear finite element analysis, where structures no longer respond proportionally to applied loads. Nonlinearities can arise from large deformations, instabilities, or material behavior, and they often control the safe operating limits of engineering designs
The assignments focused on column buckling and material hardening:
Geometrical nonlinearities: I compared linear buckling predictions with nonlinear simulations using the arc-length method. The study showed how linear models provide only a critical load estimate, while nonlinear solvers can capture post-buckling paths and snap-through behavior.
Sensitivity to imperfections: Introducing small initial deviations (1–10% of column length) reduced the critical load dramatically, underlining why real structures never reach the “perfect” buckling load predicted by theory.
Material nonlinearities: I compared linear elastic models with isotropic and kinematic hardening. The results highlighted different unloading behaviors, the Bauschinger effect, and how plasticity influences residual stresses.
Path-following methods: I tested displacement control, energy-stabilized force control, and arc-length methods, evaluating which approaches converge reliably for nonlinear problems.
This module demonstrated why nonlinear FEM is essential for realistic engineering analysis. Even minor imperfections or material assumptions can change results significantly, and mastering solver strategies is key to obtaining meaningful answers