In our previous blog, we introduced common CAD-related “myths,” explored typical geometric issues, and highlighted the importance of geometry cleanup along with its advantages. We also outlined a CAE analyst’s workflow for debugging such issues and discussed modeling strategies using an aircraft example.

Building on that foundation, engineers at Designfusion will now use the cleaned aircraft geometry prepared in Simcenter HyperMesh 2026 to perform advanced simulations in Simcenter OptiStruct.

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Background Theory

Any structure that we evaluate must be mathematically stable; that is, the applied constraints must sufficiently resist all translations and rotations. This stability is commonly observed in structures that are fixed to the ground or bolted to other structures.

Have you ever considered how we evaluate structures that move through the air, like an aircraft, or those freely floating in outer space, like a satellite?

In these cases, external forces such as aerodynamic loads (arising from pressure differences), thrust, and self-weight act on the structure. However, since these systems are not physically constrained, conventional static analysis leads to instability due to unconstrained rigid body motion. For systems like these, when we analyze deflections and the stress on the body due to applied mechanical forces, they must satisfy the equilibrium condition. Since the systems are flying or floating in the air and space, we cannot constrain them to maintain their attitudes; thus, the equation becomes unstable.

To address this, engineers at Designfusion adapted a special form of Linear Static analysis called “Inertia Relief Analysis”. This analysis allows the simulation of unconstrained or partially constrained structures. It calculates the stress and deformations that we expect in a steady-state, mathematically stable simulation.

In “Inertia Relief Analysis”, the applied mechanical forces are balanced by rigid body accelerations and forces. These accelerations and forces are distributed over the structure in such a way that the total of the applied forces on the structure is zero, achieving equilibrium.

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Model Setup

Referring to the aircraft model from the previous blog, we will demonstrate the setup and results of this inertia relief analysis.

1. This model is meshed appropriately for demonstration purposes
2. Assigned material properties and element properties are modified for demonstration purposes
3. The thrust force from the engine is not considered; instead, a 2.04G pull-up force is applied.

We meshed the model with 1D, 2D, and 3D elements to represent the geometry and capture features. Material data was used from ASM Aerospace Specification Metals Inc. The 2.04G pull-up force was applied in an elliptical form to represent the forces. The major contribution of the force is close to the root of the wing in the form of an elliptical force, as shown below.

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Results

1. The maximum displacement is 13mm
2. The scale of the stress developed in the structure has changed for visualization purposes.

Note: The scale of the displacement contour in images 5 and 6 is enhanced for better visualization.

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Verification

Equilibrium can be evaluated in another way.

A force of 2.04G is applied along the Z axis, and the resulting rigid body forces are computed with respect to the model’s center of gravity. The corresponding moments of the X and Y axes are also calculated.

To compute rigid body accelerations, we need to extract the rigid body mass matrix at the center of the gravity position. So, we have forces and moments acting at the center of gravity and the rigid body mass matrix at the center of gravity.

Using the formula F=Mass*Acceleration , and by performing rigid body mass matrix inversion, we can determine the rigid body accelerations.

Below is an image of the rigid body acceleration and forces that were calculated using Simcenter Optistruct.

If the system must be in equilibrium, the difference between the external force and the product of mass and rigid body accelerations should be zero.

F_(applied mechanical force)-{M_(mass matrix at center of gravity)*A_(rigid body accelerations) }=0

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Conclusion

Certified engineers at Designfusion can perform such complex simulations for companies in the aerospace and mechanical industries. Along with advanced simulations, we can help organizations with their design optimization and 3D printing needs.

We are here to help – feel free to reach out anytime.