Static Analysis can be used to calculate static equilibrium position and force while considering all non-linear effects. The Motion Solver supports three types for Static Analysis. The first is the linear static analysis without a rigid mode. This method is useful to solve the static equilibrium of a structural system without rigid motion.
The second method is non-linear static analysis with a rigid mode. This method has two steps for finding the solution. The first step is to find a local solution with Newton Raphson method while satisfying the governing equation as follows.
 | (9–7) |
 | (9–8) |
These variables are introduced in Initial Analysis. The second step is
to find a global solution while minimizing the position change of 
in Equation 9–7. The static
equilibrium position refers to the positions and orientations of bodies at which the
equation of motion is zero when velocity and acceleration are zero.
The third and final method is non-linear analysis without a rigid mode. This method can be solved while ignoring the mass term in Equation 9–7. This is useful to solve the static equilibrium of structural system with non-linear material or a large deformation, but the method has a disadvantage for systems with rigid motion or contact.
Remarks
Since the mass matrix is used to avoid a singular problem in Equation 9–7, this analysis is numerically stable for a system in which bodies or nodes have a non-zero mass.
For neutral equilibrium, unstable or a free-falling problem as shown in the figure above, static bush force can be useful to avoid this problem.
Most contact problems are typical examples of an unstable static problem because of zero stiffness in the tangential direction at the contact point. When contact does not occur, the governing equation has zero stiffness for the contact normal direction. For these cases, it is difficult to find the static position in static analysis. It is better to use dynamic analysis to find the steady state solution.
