In the “Example pdf” file embedded below I present a finite element method application to a three-dimensional elastostatics problem. I approximate a spherical domain by a reunion of 3-simplexes which is generated from a laticial three-dimensional grid. The “Finite elements” figure above was obtained from a size 5x5x5 grid. For a size 3x3x3 grid, the total number of elements which are within the sphere, each element having 10 nodes, turns out to be 24. Choosing a larger size for the grid was not possible because the program which I have created to solve the example problem, when running on my laptop computer, rised a memory error, the system matrix of the problem being to large. Even for size 3x3x3 grid, the matrix comes out with 1692×1692 size.
The “Import pdf” and “Main program pdf” files embedded below contain the Python code (import code and respective main program code) I have written for modeling the elastostatics problem which is described in “Example pdf” file. The program computes the displacements field for the elastostatics problem and plots an example of displaced surface section of the considered elastic body.
Also I give the description and derivation of the conjugate residual gradient method which is used to solve the equations system of the problem.