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Author Patel, Jigarkumar S
Title Elastic structures with defects
book jacket
Descript 154 p
Note Source: Dissertation Abstracts International, Volume: 72-06, Section: B, page: 3512
Adviser: Janos Turi
Thesis (Ph.D.)--The University of Texas at Dallas, 2011
Defects in elastic structures may cause catastrophic failures if undetected, and can lead to the high maintenance costs or replacement of whole structure in case of their late detection. A simple, fast, and inexpensive method for the detection of defects in elastic structures is vibration testing. The underlying assumption is that any changes in the structure (i.e. developments of defects) may result in changes in its dynamic properties e.g. natural frequency, amplitude, stresses, modes of vibration, etc
In this dissertation the dynamics of a simple elastic structure (cantilever beam) with extreme defects (surface cracks) are studied. We start with the direct problem where the locations and the sizes of the cracks are known. In the special case of no cracks we have an ideal beam and standard techniques can be used for the solution of the direct problem. For the defective beam we consider a variational inequality framework based on Hamilton's least action principle
We first focus our attention on the static problem. Hamilton's least action principle provides a displacement field, corresponding to a load, which minimizes the potential energy of the beam. We consider various types of cracks at various locations and solve the corresponding static problems. In consideration of the dynamic problem we know that, during vibrations cracks can open and close. Appearance of the crack(s) at the various locations in the cantilever beam gives rise to non penetration (contact) type boundary conditions
We describe a computational framework to study the influence of the crack(s) on the dynamics of the beam. To perform a numerical study we replace the infinite dimensional continuous problem by a finite dimensional discrete problem using Galerkin type projections. Discretization of the contact conditions leads to a linear complementarity problem (LCP). We propose a very effective method to solve this LCP. The time dependent solution of an LCP obtained from the variational inequality with initial and contact boundary conditions is evaluated which approximates the displacement field for the cantilever beam. We obtained a LCP obtained from the variational inequality with initial and contact boundary conditions
The result section of this study includes: numerical solution of the static problem with different sizes of crack(s) at various locations; comparison of vibrations for an ideal beam and beams with cracks at the wall and in the middle, respectively; cracks at various locations with different sizes, comparison for the Von-Mises and principal stresses in the deformed cracked, and ideal beams with different types and sizes of cracks. All these comparisons indicate changes in the natural frequency, amplitude, period, and stresses distribution
School code: 0382
Host Item Dissertation Abstracts International 72-06B
Subject Applied Mathematics
Engineering, Civil
Engineering, Mechanical
Alt Author The University of Texas at Dallas. Mathematical Sciences
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