A new version of boundary integral equations and their application to dynamic three-dimensional problems of the theory of elasticity |
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| Affiliation: | 1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;2. University of Chinese Academy of Sciences, Beijing 100049, China;3. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;4. College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, 450002, China;1. Department of Robotics and Mechatronics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland;2. Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK;3. Academic Computer Centre Cyfronet AGH, AGH University of Science and Technology, ul. Nawojki 11, 30-950 Krakow, Poland;1. School of Geosciences, China University of Petroleum (East China), Qingdao, China;2. Xinjiang Oilfield Company, CNPC, Karamay, China;1. Departmento de Ingeniería Matemática en Informática, Universidad Pública de Navarra, 31500 Tudela, Spain;2. Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA |
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| Abstract: | A version of boundary integral equations of the first kind in dynamic problems of the theory of elasticity is proposed, based on an investigation of the analytic properties of the Fourier transformant of the displacement vector, rather than on fundamental solutions. A system of three boundary integral equations of the first kind with Fredholm kernels is constructed, and the equivalence of the initial boundary-value problem on the vibrations of a bounded region and the system of boundary integral equations obtained is investigated. A version of the numerical realization, which combines the ideas of the classical method of boundary elements and the Tikhonov regularization method, is proposed. The results of numerical experiments are given. |
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