Modeling Friction Effects - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II
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CAESAR II Version
13

There are two methods to solving friction problems:

  • Insert a force at the node which must be overcome for motion to occur.

  • Insert a stiffness which applies an increasing force up to the value of Mu * Normal Force.

CAESAR II uses the stiffness method.

If there is motion at the node under evaluation then the friction force is equal to Mu * Normal force. However, because there is a non-rigid stiffness placed at that location to resist the initial motion; the node could experience some displacement. The force at the node is the product of the displacement and the stiffness. If the resultant force is less than the maximum friction force (Mu * Normal Force) the node is assumed to be not sliding. As a result, you might see displacements at nodes that have not achieved the "sliding" friction force in the output report.

The maximum value of the force at the node is the friction force (Mu * Normal force). After the system reaches this value, the reaction at the node stops increasing. This constant force value is then applied to the global load vector during the next iteration to determine the nodal displacements. The example below explains what happens in a "friction" problem.

  1. The default friction stiffness is 1,000,000 lb./in. To solve convergence problems, consider decreasing this value.

  2. Until the calculated load at the node equals (Mu * Normal force), the restraint load is the product of the displacement multiplied by the friction stiffness.

  3. Should the calculated load exceed the maximum value of the friction force, the friction force stops increasing because a constant effort force opposite the sliding direction is inserted in the model in place of the friction stiffness.

If you increase the friction stiffness in the setup file, the displacements at the node may decrease slightly. Usually, this causes a re-distribution of the loads throughout the system that could have an adverse effect on the solution convergence.

If problems arise during the solution of a job with friction at supports, reducing the friction stiffness typically improves convergence. You must do several runs with varying values of the friction stiffness to ensure the behavior of the system is consistent.

For more information on this subject, see "Inclusion of a Support Friction into a Computerized Solution of a Self-Compensating Pipeline" by J. Sobieszczanski, published in the Transactions of the ASME, Journal of Engineering for Industry, August 1972. A summary of the major points of this paper is below.

Summary of J. Sobieszczanski’s ASME Paper

  • For dry friction, the friction force magnitude is a step function of displacement. This discontinuity means the problem as intrinsically nonlinear and eliminates the possibility of using the superposition principle.

  • The friction loading on the pipe can be represented by an ordinary differential equation of the fourth order with a variable coefficient that is a nonlinear function of both dependent and independent variables. No solution in closed form is known for an equation of this type. The solution has to be sought by means of numerical integration to be carried out specifically for a particular pipeline configuration.

  • Dry friction can be idealized by a fictitious elastic foundation, discretized to a set of elastic spring supports.

  • A well-known property of an elastic system with dry friction constraints is that it may attain several static equilibrium positions within limits determined by the friction forces.

  • The whole problem then has clearly not a deterministic, but a stochastic character.