The wave field generated by a centre of rotation in an unbounded elastic medium with a semi-infinite conical crack |
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| Authors: | ND Vaisfel’d GYa Popov |
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| Institution: | 1. School of Finance, Nankai University, China;2. Department of Mathematics and Department of Statistics, University of Illinois at Urbana–Champaign, United States of America;3. Department of Actuarial Mathematics and Statistics, Heriot–Watt University, United Kingdom;4. Department of Mathematics, University of Illinois at Urbana–Champaign, United States of America;1. Department of Sociology, University of Groningen, Inter-University Center for Social Science Theory and Methodology (ICS), Groningen, The Netherlands;2. Department of Developmental Psychology, University of Groningen, Groningen, The Netherlands;1. National Science Foundation, 4201 Wilson Blvd. #1025, Arlington, VA 22230, United States;2. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Hungary;3. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, United States;1. School of Materials, University of Manchester, Oxford Road, Manchester M13 9PL, UK;2. Eurolens Research, Faculty of Life Sciences, University of Manchester, Oxford Road, Manchester M13 9PL, UK |
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| Abstract: | The dynamic stress intensity factor at the edge of a semi-infinite conical crack when the medium is loaded by a non-stationary centre of rotation is determined. A centre of rotation is understood to be a set of four forces of equal magnitude that act in the same plane and form pairs having the same direction of rotation.1 If the magnitude of these forces is time dependent, i.e., their application is non-stationary, they form a non-stationary centre of rotation. The solution of the problem required the use of methods of integral transformations and discontinuous solutions, which reduced the problem to an integral differential equation in Laplace transform space. The combined use of the orthogonal polynomial method and time discretization to solve the equation enabled a formula for the stress intensity factor to be obtained. |
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