Special Topics: Inertia Relief Analysis

Description

A set of external forces on a free body will cause it to move with constant acceleration in space if these forces are not in static equilibrium. However, if the external forces do not change with time, or the rate of change is negligibly small, the free body may be considered to be in a quasi-static state (i.e., the inertia force on the body and the external forces are in equilibrium). The Linear Static solver can be used to determine the deformation and stresses within this free body by setting the Inertia Relief option on the Freedom Case.

The solver executes a number of steps to produce the inertia relief result:

  1. Assembles the mass matrix of the structure and the applied load vector for all the included load cases.
  2. Calculates the translational and rotational accelerations on the structure's mass matrix that will generate inertia forces that balance the applied loads. The inertia forces are calculated assuming the structure is a rigid body.
  3. Assembles the structural stiffness matrix.
  4. Calculates the inertia load vector due to the application of the translational and rotational accelerations acting on the mass matrix and adds this vector to the applied load vector to form a combined load vector that has a zero resultant force and moment (numerically it will not be perfectly zero).
  5. Solves the model as a linear static analysis. As inertia relief models are typically unrestrained, the stiffness matrix will be approximately singular, so during the matrix reduction process it may be necessary to add some very small stiffness to ensure the matrix can be factorised.
  6. The displacement vector produced by this solution can sometimes have large rigid body translations and/or rotations, depending on how well-balanced the assembled load vector is, and how much restraining stiffness is added. To reduce the large displacements, Straus7 offers the option of removing the global rigid motion at the completion of the analysis. In any case, the rigid body motions do not affect the element stresses.

To conduct an inertia relief analysis, the freedom case is designated as being an inertia relief freedom case by setting the Freedom Case Type option under CASES: Freedom Cases; the option to remove rigid body motion is also set there.

Inertia relief analysis in Straus7 can be conducted on completely unrestrained models, and on symmetric models that have the appropriate symmetry boundary conditions.

See Also