**Inertia Relief Analysis **

This document explains how inertia relief works and validation.

The static analysis of structures with rigid body modes needs to include inertia relief calculations in the solution process. Structures with non-structural masses may be significantly influenced by inertia relief effects.

In finite element analysis, inertia relief forces are calculated based on the rigid body modes and the global mass matrix of the model. If **Φ** represents the set of all the rigid body modes that satisfy the boundary conditions on the model, **M** represents the global mass matrix and **F** represents the load vector, then the corrected load vector **F’** is calculated as follows:

**F’** = **F** – **MΦ**u

**Example:**

**Model Details:**

Consider an example of simply supported plate of weight **4.52896E-01 Tonnes. **

This weight will be applied through Centre of gravity (C.G).

The force of Total 400 N applied on 4 nodes. (100N each).

**Calculating Mass and center of gravity in HyperWorks**

- Go to Validate panel
- Click on Mass.
- Click on option and choose between Mass or Mass with Centre of gravity computation.
- Click on compute to calculate mass and Centre of gravity.

**Inertia relief Analysis:**

- After solving with OptiStruct we will get calculated reference point, Rigid body force and Rigid body acceleration in .out file.

**1.Reference point output:**

**PARAM,REFPNT,CG**is used to set reference point as center of gravity

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Matched well with HyperWorks.

**2.** **Rigid Body Forces**

- Imposed 100N of force in the direction of Z on 4 nodes.
- Therefore “Rigid body force 3 0.400000E+03” as total force at CG.

**3.Rigid body acceleration **

- Mass of model is Mass(M) = 4.52896E-01 tonnes.
- Input force(F) is 400 N .
- Z direction Acceleration(A) derived from F=MA.
- Acceleration(A) = 883.205 mm/sec2
- Which matching well with Rigid body acceleration 3.

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