M.Sc Thesis

M.Sc StudentFarajun Itay
SubjectQuantitative Correlation between Strains Measurement and
Damage Severity in a Structure with Local Opening
DepartmentDepartment of Aerospace Engineering
Supervisors PROFESSOR EMERITUS David Durban
DR. Baruch Karp
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


While structural health monitoring (SHM) science and engineering have matured in recent decades, by now indeed a coherent and well-established branch of structural mechanics, most practicalities are of qualitative nature. Common health monitoring procedures are governed by the fundamental axiom that any change in structural response, under identical controlled loading, indicates damage deterioration. The present work aims at suggesting a simple, user friendly, static-loading method for assessing both damage location and level of damage deterioration along service life.

Setting is within framework of plane stress isotropic elasticity, focusing on a representative configuration of a large rectangular plate that contains a small hole type damage, at a distance from the boundaries, with a-priori unknown size, shape, or location. Health monitoring is based on applying a remote uniform static tension field and measuring strains at selected points. The underlying assumption is that, according to Saint-Venant principle, at sufficient distance from the hole, but not too far, the strain field characteristics are reasonably approximated by the classical Kirsch solution for a hypothetical circular hole (the equivalent hole).

By way of introduction, we discuss the Lame solution for a circular plate, containing a small concentric circular hole, under remote uniform radial tension. We show how just a few strain measurements can expose the hole characteristics and identify a universal strain distribution along any straight fiber. Useful practical algebraic relations are then derived, aiming at connecting strain measurements with hole geometry. Next, we examine the Kirsch solution for an infinite rectangular plate, with a central circular hole, under remote uniform axial tension. Here again, a universal strain pattern (with invariant properties) is identified along any straight fiber coaxial with the direction of remote axial tractions. That pattern facilitates strain-based monitoring of hole geometry and age induced damage deterioration. The Saint-Venant principle is then invoked as a theoretical framework that inspires the notion of an equivalent circular hole, for monitoring damage in presence of non-circular holes. Among other real-life situations, the envisaged scenario is service life corrosion that deforms the original circular hole boundary. Detailed finite element calculations have been performed for the strain field, as in-silico substitute for test data, over a range of hole shapes and dimensions (circular, elliptical and rectangular).

The numerically obtained strain data has been used, in conjunction with the simple formulae derived from Kirsch solution, to monitor structural damage characteristics due to presence of holes. We show that the damage “fingerprints” obtained from the ideal infinite plate solution are in good agreement with numerical findings for the finite plate with non-circular holes. It appears that the suggested method, even though of approximate nature, and limited to isotropic homogeneous plates, provides a practical and simple tool for a quantitative SHM procedure. The newly defined parameter of an equivalent circular hole is investigated in some detail, including sensitivities, reliability, and limits of validity. It is argued that the predictive power of the proposed method provides a simple and reliable tool for quantitative health monitoring of thin plates with local damage.