This problem shows the deformation of a tension bar with a hole. FlexPDE solves two simultaneous Partial Differential Equations for the X- and Y- displacements within the bar.
dx(Sx) + dy(Txy) + Fx = 0
dx(Txy) + dy(Sy) + Fy = 0
where Sx and Sy are the stresses in the X- and Y- directions, Txy is the shear stress, and Fx and Fy are the body forces in the X- and Y- directions.
Sx = C11*dx(U) + C12*dy(V) + C13*[dy(U) + dx(V)]
Sy = C12*dx(U) + C22*dy(V) + C23*(dy(U) + dx(V))
Txy = C13*dx(U) + C23*dy(V) + C33*(dy(U) + dx(V))
Here the Cnn are the constitutive relations of the material.
![final-adaptively-refined-grid final-adaptively-refined-grid](http://pdesolutions.com/wp-content/uploads/2024/06/final-adaptively-refined-grid.gif)
The Final Adaptively Refined Grid
![vector-displacement-field Vector displacement field - stress analysis equations graph](http://pdesolutions.com/wp-content/uploads/2024/06/vector-displacement-field.gif)
The Vector Displacement Field
![x-directed-stress X Directed Stress Analysis](http://pdesolutions.com/wp-content/uploads/2024/06/x-directed-stress.gif)
The X-Directed Stress
![x-stress-tension-analysis x-stress-tension-analysis](http://pdesolutions.com/wp-content/uploads/2024/06/x-stress-tension-analysis.gif)