Example: Stress Analysis

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.

The final adaptively refined grid

The vector displacement Field

The X-directed Stress