Finite Elements Analysis Basics

Analysis Foundation

In designing the gear shafts below, what quantities would we examine?

– Stress– Strain– Displacement– Rotation– Temperatures

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Analysis Foundation

In designing a valve, burner, or heat sink, what quantities would we examine?

– Pressure drop– Temperatures– Mass flow rate– Velocities– Fluid mixing

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Analysis Foundation

• Hand calculations are easily applied to simple geometries.– Cylinders– Blocks– Beam structures

They are not easily or accurately applied to general (complex) shapes.

To analyze complex shapes we break them into many simple shapes and compute the combined response.

FEA Analogy: Area

Suppose we want to compute the area of a generic shape.

FEA Analogy: Area

What do we do to improve the accuracy of the area measurement?

FEA Mesh

The pieces we divide the model into are called ELEMENTS. Equations are generated for each element. These are combined into a system of equations for the entire structure. Matrix algebra is used to solve the system of equations.

FEA Mesh: Elements

• Each element is a simple solid.

• Elements are connected together at locations called NODES.

Analysis Accuracy

• Fewer elements will solve more quickly.

• More elements will be more accurate.

You need to strike a balance between model size and run time.

Coarse Mesh:1773 nodes

Moderate Mesh:7009 nodes

Fine Mesh:16,107 nodes

Accuracy vs Mesh Size

Moderate Mesh:7009 nodes

Sol. Time: 5 sec.Max. Stress: 27.8 ksi

Coarse Mesh:1773 nodes

Sol. Time: 2 sec.Max. Stress: 25.8 ksi

Fine Mesh:16,107 nodes

Sol. Time: 10 sec.Max. Stress: 27.6 ksi

Accuracy vs Mesh Size

Mesh Transition

– Many times different locations in the model do not require the same accuracy.

– Use mesh control and transition capabilities to focus the computational effort in the areas where the most accuracy is required.

Design Analysis Steps

1. Geometry definition.

2. Define component materials.

3. Define physical situation with boundary conditions.

4. Mesh the model.

5. Run the analysis (solve the system of equations).

6. View and evaluate the results.

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