r3.06.03 Calculation of node stresses by local smoothing

Summary:

A local method for calculating node stresses from the constraints at the points in GAUSS is presented. It is used in options SIGM_ELNO and SIEF_ELNO.

This method boils down to calculating the constraints at the vertices of an element by multiplying the constraints at the points of GAUSS by a smoothing matrix, which is constant for each type of element.

For isoparametric elements of degree 2, the stresses at the middle nodes are obtained by averaging the values of the stresses at the 2 vertices of the edge.

This straightening method has two advantages:

• the nodal stresses obtained have an order of precision higher than by the direct calculation at the nodes,

• the method is inexpensive in time CPU.

This method has been generalized:

• to the calculations of deformations (option EPSI_ELNO) and internal variables (option VARI_ELNO) at mechanical nodes,

• to the calculation of flows (option FLUX_ELNO) at the thermal nodes.

• 1. Foreplay
• 2. Local method of minimization by least squares
• 3. Local smoothing methods (ref [bib2] and [bib3])
  • 3.1. Continuous local smoothing
  • 3.2. Discreet local smoothing
• 4. Application of the method to the calculation of node stresses for various elements
  • 4.1. Square passage matrices
  • 4.2. Rectangular \({M}^{\text{-1}}P\) passage matrices
• 5. Other calculation options using the same method
• 6. Other stress smoothing methods
• 7. Bibliography
• 8. Description of document versions