About Static Riks Steps

A static Riks step is an effective approach to find solutions for unstable static response, such as postbuckling or collapse behavior.

You can use this method for solving ill-conditioned problems, such as limit load problems or almost unstable problems that exhibit softening.

See Also
Defining Static Riks Steps
In Other Guides
Unstable Collapse and Postbuckling Analysis
Solving Nonlinear Problems
Matrix Storage and Solution Scheme in Abaqus/Standard

This method is appropriate for cases where the loading is proportional; that is, where the load magnitudes are governed by a single scalar parameter. The method can provide solutions even in cases of complex, unstable response such as that shown in the following figure:



The Riks method uses the load magnitude as an additional unknown; it solves simultaneously for loads and displacements. Therefore, the solver requires another quantity to measure the progress of the solution. Abaqus/Standard uses the “arc length” along the static equilibrium path in load-displacement space. This approach provides solutions regardless of whether the response is stable or unstable.

You can define a stop condition for a static Riks analysis by specifying a maximum load proportionality factor, a maximum displacement at a node, or both. The solver ends the analysis if the computed solution crosses either of these limits. If the solution does not exceed one of these limits, the analysis ends after executing the maximum number of increments for the step.