טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentEitan Shani
SubjectLow Probability Characteristics in Heterogeneous Mechanical
Structures
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Eli Altus
Full Thesis textFull thesis text - English Version


Abstract

Heterogeneity exists in many types of structures and in different scales. For example, isotropic homogeneous macro metals are usually made of anisotropic crystal grains with variable phase grain boundaries.

Predicting the mechanical behavior of heterogeneous structures becomes complicated when size characteristics of heterogeneity are in the same order of the entire structure. For these structures, assumptions like macro-homogeneity or effective properties are not precise and often non-applicable. Moreover, for stochastic heterogeneity, the response of the structure is also stochastic - a feature which does not exist in macro-homogeneous structures.

Micro and nano-beams are widely used in sensors and N-MEMS actuators. These structures are linear elastic, brittle and their mechanical behavior depend mainly on surface properties. In addition, their basic element size (grain) is not negligible in comparison with an overall typical dimension (length, width).

In many cases, ordinary statistical properties (mean, variance) are less critical for design. For example, in strength analysis, the behavior around low probabilities, like around minimal values is the most important. In other cases probabilities for minimal deflections (maximum stiffness) are important. The complexity of the problem in low probabilities is greater than in ordinary statistical properties, and little research has been done on the subject. Developing solution methods for this problem is of great interest to researchers today.

In this research, an approximated analytical model to describe the low probability behavior of microbeams with longitude stochastic heterogeneity in grain sizes and stiffness, is suggested. Low probability sections of Cumulative distribution functions were obtained by MCS and compared to the suggested model. Morphology distributions, which produce low probability values of the reaction force were analytically derived leading to a power law relation. Clear connections have been found between the power parameters and the beam morphology. This approximation enables us to make a prediction of the low probability regime of the reaction force exerted on a microbeam.

In the second part of this research, shapes of moduli distributions in the beam which create the lowest reactions were found analytically. These results were verified with MCS. These distributions enable us to make an optimal design of microbeams even when the only information we have on the beam is statistical.

Info-Gap theory was used to calculate the robustness of microbeams, which are designed with the suggested model with respect to the beam response. This can help designers to easily estimate the allowed deviations in the model parameters.