M.Sc Student | Edelstein Yair |
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Subject | Loading of Structures for Maximal Sensitivity to Local Stiffness Change |

Department | Department of Mechanical Engineering |

Supervisor | Professor Emeritus Eli Altus |

Full Thesis text |

Development of tools for assessing local variations of stiffness in structures is important in discovering cracks in structures, lumps in the body with exceptional stiffness suspected as malignant and more. Most diagnostic instruments are based on collecting waves reflected or penetrating from several places, e.g. X-ray and ultrasound. For these methods, density changes are detected rather than moduli changes.

In continuum mechanics, external loading of a body would cause deformations which are function of the moduli. The objective of our research is to study the optimal distribution of external static loads to find the structure's extremal sensitivities for heterogeneity. We define sensitivity as the rate of change in the structure's response due to compliance inhomogeneity. Sensitivity is represented as the ratio between the energy of a heterogeneous problem to the energy of a homogenous one for the same set of external loads. Heterogeneity is defined as a local variation in the structure's compliance.

A couple of simple beam and truss problems were solved, for which the structure's response was examined and heterogeneity's characteristics were found. Information received from a zero sensitivity case enables us to reveal the location of the heterogeneity. Those former comprehensions brought us to formulate a generalized parametric study of the problem, from which an analytical study of the relationship between heterogeneity characteristics and changes in sensitivity was developed.

The numerically solved problems and a detailed parametric description lead to mathematical model of a generalized eigenvalue problem, which represents eigenvalues as the extremal sensitivities and eigenvectors as the set of loads yielding those sensitivities. As well, the dimension of the problem is defined by the number of external loads. Adding more loads will provide more information regarding the characteristics of the heterogeneity. There is a limitation on the amount of local heterogeneities with regard to the number of loads in order to be able to reveal heterogeneity's characteristics.

The presented model offers an analytical examination of optimal sensitivity, which has a great potential in many emerging fields of engineering.