|M.Sc Student||Zarrouk David|
|Subject||Solution Convergence of the Functional Perturbation Method|
for Problems of Nonhomogeneous Structures
|Department||Department of Mechanical Engineering||Supervisor||Professor Emeritus Eli Altus|
|Full Thesis text|
Micro-sized beams, routinely used in sensors and actuators, present non-homogeneities in dimensions and properties. Morphology simulations are usually based on pre-determined Two Point Correlation (C2) functions, while higher correlations are neglected. There are several commonly used C2-based methods for modeling such fields, for comparing analytical methods with Monte-Carlo Simulations (MCS). In this study, different “linear” methods which satisfy S’=Lη are studied. S’ is the deviation of the property, L is a matrix and η is the uncorrelated random variables. It has been found that each method leads to different high order statistical correlation values and that they do not ensure high order statistical homogeneity. These higher order terms become important in predicting strength reliability especially in problems with high heterogeneity. A new method (HVM) that ensures homogeneity in all orders is presented herein.
The present study proposes a more effective utilization of the one and two point morphological data by finding their contributions to the higher order terms and adding them to the solution.
The research includes:
The 4th order FPM solution is calculated for the first time. The comparison between the 2nd and 4th FPM solutions to the MCS shows that 4th order FPM solution reduced the error by at least 50% and sometimes up to 90% .