Tejas Bendre To calculate the nodal stresses for a 2D linear quadrilateral mesh from element stress values calculated at Gauss points, you can use a process called stress recovery. This process involves interpolating the element stresses to the nodes of the mesh.

One common stress recovery approach is using the least squares (MLS) method. This method involves fitting a polynomial function to the element stresses in the vicinity of each node, and then evaluating the polynomial at the node to obtain the nodal stresses.

The MLS method typically involves fitting a quadratic polynomial to the element stresses, although higher-order polynomials can also be used. The polynomial coefficients are determined by minimizing the sum of the squared differences between the element stresses and the polynomial values at the Gauss points.

Once the polynomial coefficients have been determined, the nodal stresses can be calculated by evaluating the polynomial at the nodal coordinates.

There are many resources available online that provide more detailed explanations of the MLS method for stress recovery, along with examples and MATLAB code. Here are a few that you might find helpful:

• "A simple introduction to the Method of least squares for solving problems in Science and Engineering" by Carl W. Helstrom (available online as a PDF)
• "Finite Element Analysis of Solids and Fluids I" course notes by Prof. Sukumar (available online as a PDF)
• "FEA Stress Recovery for Linear Triangular Elements using Least Squares" by Abhijit Jadhav (available online as a PDF with MATLAB code)

I hope this helps! Let me know if you have any further questions.

Thank you for a detailed response. I could not find the resources you've mentioned but I did find other papers on the MLS method.