Nonlinear finite elements/Buckling of beams

Nonlinear post-bucklingEdit

 
Buckling of beams.

Newton-RaphsonEdit

Standard Newton-Raphon methods perform poorly for bucking problems.

 
Predicting buckling with Newton_Raphson.

Arc length methodEdit

  • 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