Date of Award

Spring 1986

Document Type


Degree Name

Doctor of Engineering Science in Mechanical Engineering


Mechanical Engineering

First Advisor

Martin J. Linden

Second Advisor

Michael Pappas

Third Advisor

Harold Alexander

Fourth Advisor

Roman I. Andrushkiw

Fifth Advisor

Rafaat Hussein


A computer aided analysis method, utilizing computed tomography (CT) has been developed, which together with a finite element program determines the stress-displacement pattern in a long bone section. The CT data file provides the geometry, the density and the material properties for the generated finite element model.

A three-dimensional finite element model of a tibial shaft is automatically generated from the CT file by a pre-processing procedure for a finite element program. The developed pre-processor includes an edge detection algorithm which determines the boundaries of the reconstructed cross-sectional images of the scanned bone. A mesh generation procedure then automatically generates a three-dimensional mesh of a user-selected refinement. The elastic properties needed for the stress analysis are individually determined for each model element using the radiographic density (CT number) of each pixel within the element borders. The elastic modulus is determined from the CT radiographic density by using an empirical relationship from the literature. The generated finite element model, together with applied loads, determined from existing gait analysis and initial displacements, comprise a formatted input for the SAP IV finite element program. The output of this program, stresses and displacements at the model elements and nodes, are sorted and displayed by a developed post-processor to provide maximum and minimum values at selected locations in the model.

The model generation method is verified by applying the model generation procedures to an object of simple geometry and material properties, and comparing the computer aided analysis results with the analutical solution of the same model with the same boundary conditions. A convergence test was conducted to check the convergence of nodal displacements to asymptotic results as a function of refinements, and to determine an optimal number of selected elements for the three-dimensional mesh. A sample problem was modeled and analyzed to demonstrate the capabilities of the pre- and post-processors, using the scanned tibia section for the model. The analysis results were sorted, printed and displayed by the designated post-processor, and compared with tibia stress analysis results from the literature obtained by other methods.

This computer aided analysis method provides an automatic, versatile, noninvasive procedure for long bone modeling for finite element stress analysis.