Nonlinear finite elements/Buckling of beams

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Nonlinear post-buckling[edit | edit source]

Buckling of beams.

Newton-Raphson[edit | edit source]

Standard Newton-Raphon methods perform poorly for bucking problems.

Predicting buckling with Newton_Raphson.

Arc length method[edit | edit source]

  • 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