Spring 2020
Femur Bone FEM
During the Spring 2020 semester, I took Computation & Design. Through this class, I learned the math behind Finite Element Analysis hand calculations and software. At the end of the semester, we were assigned a final project that required us to analyze a human femur bone under static loading. It consisted of two parts: ANSYS Analysis and a MATLAB program. I converted a 3-D model made from organic structures to a finite element model. Using this model, I performed a mesh convergence study and identified stress, strain, and displacement under given conditions.
The goal of the second part of this project was to model the bone via its underlying structural fibers. I created a MATLAB program in which I modeled the bone as a 2-D truss using databases assign node number and location. Using the mathematical techniques I learned in class, I set up an iterative loop over my elements to assemble local and global stiffness matrices and calculate stress, strain, and displacements of given nodes.
PROBLEM
1. Perform a mesh convergence study and identified stress, strain, and displacement under given conditions.
2. Model the bone via its underlying structural fibers and calculate stress, strain, and displacements of given nodes.
Figure 3.1: Organic Femur Bone Model
Part 1: ANSYS
Mesh Convergence Study
PROBLEM
The first problem I had to approach was creating a mesh convergence study. A mesh convergence studying is a type of analysis that you can perform which adjusts the number of elements until the values of two consecutive maximum nodal principal stresses fall within a certain percentage of each other. In my case, that value was 3%.
ACTION
I imported the given file in Ansys and set the key parameters such as static load and point of application. I ran a mesh convergence study by generating a mesh a few times until I achieved consecutive nodal stress values within 3% of each other.
RESULTS
My findings are displayed in Figure 3.2 and Table 3.1
Figure 3.2 is a plot of the largest maximum nodal principal stresses and the number of solutions. It took 3 iterations to generate a solution compliant with our 3% gap.
Figure 3.2 Mesh Convergence Data
Table 3.1 Mesh Convergence Data
Table 3.1 is a data table that collects the important values generated during each iteration of the mesh convergence study.
Identifying Values
PROBLEM
An additional goal of the project was to identify values for max principal stress, displacement, and stress at specific locations under given positions.
ACTION
I applied the static force in the appropriate position. In order to get a better representation, I applied the force as a pressure distributed over the area of the top of the bone (left side). Then, I set the given displacements specific nodes. After applying the conditions and suitable mesh, I ran a static structural analysis on the bone looking for directional deformation
RESULTS
The figure below shows the deformation along the x-axis of nodes within the model. The gradient conveys the severity of the deformation values.
Figure 3.3 Directional Deformation of Femur Bone
Part 2: MATLAB
Modeling the Underlying System
PROBLEM
As mentioned before, the purpose of the second part of this project was to look deeper into the composition of a system at a molecular level.
ACTION
To do so, I created a MATLAB program that called on information from a series of databases to establish the framework of my system. From here, I created an iterative loop designed to pass through each element, generate a local stiffness matrix, and add it to a global stiffness matrix. Using this information, I applied the penalty method to obtain nodal displacement values to use for elemental stress and strain calculations.
Once complete I called two additional data sets describing anisotropic nodal networks compare to my results.
Results
Elemental Strain
Looking at the legend you can see that bars correspond to the strain in the horizontal anisotropic network, the green to the isotropic network, and blue to the vertical anisotropic network.
This graph is a visualization of the effect of elemental shape and the resulting strain.
Figure 3.4 Elemental strains of isotropic, horizontal anisotropic, and vertical anisotropic nodal networks
Nodal Displacement
To the right, you will find the code I used to generate the displacement depictions.
Below, you will see three figures which depict the undeformed and deformed structures of a given nodal network.
Figure 3.5 Snippet of MATLAB script used to generate Figures 3.6-3.8
