THEORY: Linear vs Nonlinear Displacement


Just a quick reminder on some of the limitations of Linear Elastic Analyses
Linear Elastic Analyses produce wrong results (to differing and variable degrees) when:
  1. Defining ν >= 0.49 to simulate the incompressibility found in elastomers. It is easily verified that the resulting stress-strain law is singular as ν approaches 0.5. If it is attempted to enforce incompressibility in an approximate manner by using a high bulk modulus, there is not only a risk of singularity, but there is also a risk of volume locking. Special techniques have to be employed to overcome the difficulties that arise as a result of the incompressibility or near incompressibility constraint
  2. When the total elastic strain at any gauss point exceeds 5% (later blog)
  3. When the rotation of ANY element exceeds 0.5 degrees
    • Assuming an arbitrary rigid body rotation (φ) using small displacement assumptions, then φ=0.5° gives about 1% non-physical elastic strain which limits the maximum rotation to nearer 0.05 degrees in reality
    • This is really important for:
      • GAPS
      • CBUSH
      • BARS
      • RBEs (eg rotation about independent node enlarges hole diameter!)
      • Offsets
      • CWELD / CFAST
As a graphic example of the last point, here is a bar undergoing a free 90 degree rotation…

 Large Displacement On:

Large Displacement Off (showing the non-physical elastic strain being calculated):


More to come!

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