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Bending of a thin plate containing a rigid inclusion and a crack
Affiliation:1. Multi-Scale Additive Manufacturing Lab, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada;2. Hot Deformation & Thermomechanical Processing Laboratory of High-Performance Engineering Materials, School of Metallurgy and Materials Engineering, College of Engineering, University of Tehran, Tehran, Iran;1. Department of Mechanical Engineering, University of California, Berkeley, CA, 94720, USA;2. Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Maslak, 34469, Istanbul, Turkey;3. Turkish Airlines General Management Building Ataturk Airport, Yesilkoy, 34149, Istanbul, Turkey;1. School of Math. Sci., University of Electronic Science and Technology of China, Chengdu, 611731, China;2. Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan, 641100, China;1. Department of Mathematics & Statistics, Texas Tech University, USA;2. Department of Scientific Computing, Florida State University, USA
Abstract:The bending of a thin infinite plate with a line crack and an arbitrarily shaped rigid inclusion is analyzed. The superposition principle is used to reduce the original formulation to two subsidiary problems. A distribution of dislocation is assumed along the crack line. The solution is obtained in an integral form by using the Green function of a point dislocation. The stress functions for both subsidiary problems are obtained by employing the rational mapping function technique. The stress intensity factors are obtained in terms of the dislocation density function. Numerical results are demonstrated for the plate containing a square rigid inclusion and a line crack.
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