Learning Forum

[greg2835]

Trying to wrap my head around how Ansys solves the equation of motion.

Let's keep it simple and say I'm doing a linear static analysis. When Ansys solves F=Ku, does it directly solve the nodal forces and displacements, or does it solve at the Gauss points and then extrapolates to the nodes? I understand that stress and strain are evaluated at the Gauss points and are extrapolated, but not too sure on displacement.

All my references say F=Ku is solved for the nodes. If that's the case then I gotta dig deeper as to why/how stress and strain are evaluated at the Gauss points. I understand there's a bit of numerical integration happening at the Gauss points, but the whole process isn't so clear to me yet.

Thank you!

[danielshaw]

The FEM procedure for a linear static analysis is:
The equation of motion ( F=KU for linear static) is solved to determine the nodal DOF results (U matrix). For a structural analysis using 3D solid elements, the nodal DOFs are the directional displacements (UX, UY, and UZ), so each node has 3 DOFs.
The nodal displacements are used to determine the component stress/strain at the Gauss points (SX, SY, ... etc.). You can study the exact numerical integration procedure in any FEM text.
The Gaussian stress/strain results are extrapolated to the nodes using the shape functions. Those values would be the unaveraged element nodal stress/strain results.
The unaveraged element nodal stress/strains are usually averaged to obtain the averaged nodal stress/strain results.
Either the averaged nodal stress/strain results or the unaveraged element nodal stress/strain results can be used to derive other stress/strain quantities (principals, vonMises, etc.).

[greg2835]

Amazing, Thank you ! That confirms a lot of info for me.