### Minimum Constraints in FEA – 4. Inertia Relief Application by Kotur Raghavan

General

Many analysis packages have provision for applying “inertia relief”. This is a highly specialized operation which is applicable to objects in flight. Objects in flight such as rockets are always in dynamic equilibrium. Any manoeuvre load applied to them will be in equilibrium with the inertia forces. Stress analysis of an aircraft or a rocket under the action of manoeuvre loads requires that the loads be applied in the normal way and that the inertia relief operation be invoked. The programs internally computes inertia forces and moments which are equal and opposite to the applied loads. An important requirement is that just the minimum constraints be imposed on the structure.

This is demonstrated by way of a simple example problem. The author has experienced that this capability has often been incorrectly used leading to erroneous results. As stated already, the command concerned is for a special application.

Example Problem

The example is that of a rocket-like object in 2D plane shown Fig. 1.

Fig. 1

It is acted upon by two manoeuvre forces F as shown. There is a net anti-clockwise moment acting about the Z- axis. Three displacement constraints are imposed as shown. The FE model is analyses after invoking inertia relief.

Fig. 2

The contours of lateral displacement and bending stress are shown in Fig. 2.  Due to locations of applied constraints the object is behaving like a supported beam. Constraints at different locations will result in different deformed shapes. The stress field would however remain the same.

The reaction forces at three constraint degrees of freedom are as in the box above. The total as well as the individual reaction forces are zero. This indicates that the constraints are properly applied and that the the program has generated the inertia forces correctly.

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1. During our DRDL work we had a case of Aerodynamic Bending in which there were no apparent constraints.. I think we had used similar approach there. We had solved that problem using three approaches. One of them being the pseudo dynamic analysis (which can be solved without constraints) and extracted elastic response by suppressing rigid body.

1. Yes. Transient dynamic analysis implicitly accounts for dynamic equilibrium. Inertia relief is a better option.

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