Nonlinear finite elements/Buckling of beams

Nonlinear post-buckling edit

Buckling of beams.

Newton-Raphson edit

Standard Newton-Raphon methods perform poorly for bucking problems.

Predicting buckling with Newton_Raphson.

Arc length method edit

  • Also called Modified Riks Method.
  • Control the size of the load step using a parameter  .
  • Solve for both   and   in each Newton iteration.

Assume   = independent of geometry. Then


  can be thought of as a normalized load parameter.

Arc-length method

The load increment is computed using


The reference arc length