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Document Type

Open Access

Degree Program

Mechanical Engineering

Degree Type

Master of Science (M.S.)

Year Degree Awarded


Month Degree Awarded



Finite element analysis, Femur, Bone curvature, Shape eccentricity, Bending predictability, Load carrying capacity


The femur is the longest limb bone found in humans. Almost all the long limb bones found in terrestrial mammals, including the femur studied herein, have been observed to be loaded in bending and are curved longitudinally. The curvature in these long bones increases the bending stress developed in the bone, potentially reducing the bone’s load carrying capacity, i.e. its mechanical strength. Therefore, bone curvature poses a paradox in terms of the mechanical function of long limb bones. The aim of this study is to investigate and explain the role of longitudinal bone curvature in the design of long bones. In particular, it has been hypothesized that curvature of long bones results in a trade-off between the bone’s mechanical strength and its bending predictability. This thesis employs finite element analysis of human femora to address this issue. Simplified human femora with different curvatures were modeled and analyzed using ANSYS Workbench finite element analysis software. The results obtained are compared between different curvatures including a straight bone. We examined how the bone curvature affects the bending predictability and load carrying capacity of bones. Results were post processed to yield probability density functions (PDFs) for circumferential location of maximum equivalent stress for various bone curvatures to assess the bending predictability of bones. To validate our findings on the geometrically simplified ANSYS Workbench femur models, a digitally reconstructed femur model from a CT scan of a real human femur was employed. For this model we performed finite element analysis in the FEA tool, Strand7, executing multiple simulations for different load cases. The results from the CT scanned femur model and those from the CAD femur model were then compared. We found general agreement in trends but some quantitative differences most likely due to the geometric differences between the digitally reconstructed femur model and the simplified CAD models. As postulated by others, our results support the hypothesis that the bone curvature is a trade-off between the bone strength and its bending predictability. Bone curvature increases bending predictability at the expense of load carrying capacity.

First Advisor

Ian R. Grosse