Finite Elements Analysis Basics

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Finite Elements Analysis Basics
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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.
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FEA Analogy Area

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

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FEA Analogy Area

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

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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.

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FEA Mesh Elements

• Each element is a simple solid.
• Elements are connected together at locations
  called NODES.

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FEA Mesh Elements

• A BRICK element model often must be created
  MANUALLY.
• A TETRA element can be created AUTOMATICALLY.

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Brick Elements vs. Tetra Elements

• Brick Models
• Usually have many fewer elements than a Tetra
  model (Quicker Solution).
• - Time-consuming to generate.
• - Very difficult to create a brick model for
  complex parts.
• Tetra Models
• Quick to generate the model (with Automatic
  meshing).
• The same accuracy can be achieved as with
  Bricks.
• Can mesh very complex parts.
• - Usually have more elements than a Brick model.

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Brick Elements vs. Tetra Elements
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Brick Elements vs. Tetra Elements
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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.

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Accuracy vs Mesh Size
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Accuracy vs Mesh Size
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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.

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Design Analysis Steps

• Geometry definition.
• Define component materials.
• Define physical situation with boundary
  conditions.
• Mesh the model.
• Run the analysis (solve the system of equations).
• View and evaluate the results.