﻿ Static analysis

# Static analysis

The ultimate goal of the statics calculation in OrcaFlex is to find positions and orientations for each element in the model such that all forces and moments are in equilibrium. This may be an end in itself, or it may be done to provide a starting configuration for a dynamic simulation. If the system were linear, then the equilibrium configuration could be calculated directly with a single matrix solve; in practice, however, OrcaFlex models are invariably nonlinear and so calculating statics requires an iterative approach using the multi-dimensional form of Newton’s method. The iterative stages OrcaFlex goes through are

1. fix the degrees of freedom (DOFs) of all objects (e.g. buoys, vessels, constraints etc.) other than lines
2. calculate the line statics to determine the equilibrium configuration for all the lines (itself a two-step iterative process)
3. release all DOFs and perform a whole system statics analysis for the entire system using Newton’s method, with the initial guess for the iteration coming from the previous two stages

For the majority of systems, the static analysis process is quick and reliable. Occasionally, and generally only for very complex systems with multiple free bodies and many inter-connections, convergence may be difficult to achieve. To help overcome this, OrcaFlex provides facilities to suppress some of the DOFs of the system and approach the true equilibrium in a series of easy stages.

In addition, model-wide control of line statics can be exerted through the line statics policies, fine-grained control is available for each line's statics methods, and the whole system statics stage can be disabled.

### Unstable equilibria

Sometimes statics may converge on an unstable equilibrium (think of, for example, a pencil balancing on its tip, or a coin on its edge). Typically, a dynamic run will excite the system enough to 'kick' it out of the unstable equilibrium, but you should not rely on this: statics and dynamics results from such unstable equilibria are invalid, and you will need to modify your statics analysis to obtain a stable equilibrium configuration.

### Starting velocity

Static analysis can be turned into a steady-state analysis by specifying a non-zero starting velocity on the general data form. This can be useful when modelling towed systems, for instance, or other systems which have a steady velocity.

 Note: Static analysis is considered to occur immediately before the actual first stage of the simulation; and, if the model is a restart analysis, then also after the final stage of the parent simulation. Having the concept of a stage in the static analysis is useful for defining release at stage data in a chain of restart models. Similarly, the static analysis conceptually occurs at precisely the actual start time specified on the general data form. This time is used to define the behaviour of those aspects of the model that are active in statics but are usually considered to have time-dependence, such as the value of the ramp factor when scaling the current velocity.