Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Mechanical Engineering

First Advisor

Judy M. Vance


This research combines virtual reality with fast stress re-analysis/approximation methods, meshless stress analysis, and free-form deformation (FFD) to produce a virtual design environment that allows interactive stress re-analysis. The interactive stress re-analysis program allows designers to visualize the initial stresses in their design, then modify the design while watching the stresses update as the design is changed.;The primary objective of this research is to find the best stress re-analysis method for use in the virtual design environment. The pre-conditioned conjugate gradient (PCG) iterative method is compared with respect to accuracy and speed with the combined approximation (CA) method, simple iteration method, and linear Taylor series approximation. The PCG method was found to have the best accuracy over a large range of design changes and to be faster than the CA method.;However, the PCG method is not fast enough to perform stress re-analysis at frame-rate speed (10--30 Hz), which is required to update the stresses as the user interactively changes the design. A two-level stress approximation approach is used to solve this problem. Linear Taylor series approximations are used while performing interactive design modifications using free form deformation of the model. At intervals during the design process, PCG re-analysis and the meshless stress analysis method are used to provide the designer with accurate stresses. These accurate stresses are then used as the starting point for a new Taylor series approximation. Parallel processing is utilized to make the accurate stresses available as quickly as possible and meshless stress analysis avoids re-meshing and/or mesh distortion inaccuracies after large design changes.



Digital Repository @ Iowa State University,

Copyright Owner

Kurt Anthony Chipperfield



Proquest ID


File Format


File Size

122 pages