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|Title:||Solutions of some elastodynamic problems with application to crack propagation|
|Doctoral Committee Chair(s):||Robinson, Arthur R.|
|Department / Program:||Civil and Environmental Engineering|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||The purpose of this study is to develop a range of elastodynamic solutions that will be applicable to the investigation of crack growth and to non-destructive evaluation. A number of problems of dynamic crack propagation in brittle solids are solved by applying the Smirnov and Sobolev method of self-similar potentials and extending the method in several ways. The method of self-similar potentials in conjunction with function-theoretic approach leads to a direct approach to the solutions of two-dimensional problems of mode-I, mode-II, and mode-III cracks in homogeneous solids as well as to the solution of problem of the mode-III interface crack. The technique of self-similar with a new application of rotational superposition was used to solve dynamic problems of an expanding penny-shaped crack under torsional loading. The problem of sudden arrest of a crack is treated by the method of self-similar potentials with the aid of appropriate time delays and origin shifts and by using a scheme of weighted superposition of fundamental problems. The solutions of fundamental problems require a full of the function-theoretic approach.
In all the problems considered, it is assumed that the crack-tip speed is less than that of the Rayleigh-wave speed for inplane problems and less than that of the shear-wave speed for antiplane problems. For the sub-Rayleigh cases, the singularities of velocities and stresses occurring at crack tips are always of inverse square root type. The dynamic stress intensity factor is used to describe the square root singularities at the crack tips. The asymptotic solutions at wave fronts are also obtained for some problems.
|Rights Information:||Copyright 1989 Chung, Yen-Ling|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9010834|
This item appears in the following Collection(s)
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Civil and Environmental Engineering