I wrote a finite element code (FEM Program) for two-dimensional analysis of elastic body using MATLAB programming language.
Here is a video of the results + its verification with Abaqus:
4-node elements ,4 Gauss points for numerical integration are used;.
*** Here is a solve example using both Abaqus and Code:
Normal Stress in X-direction, Abaqus result:
Normal Stress in X-direction, Code result:
Shear Stress in XY-direction, Abaqus result:
Shear Stress in XY-direction, Code result:
Normal Stress in Y-direction, Abaqus result:
Normal Stress in Y-direction, Code result: