Optimal balance between mass and smoothed stiffness in simulation of acoustic problems |
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| Institution: | 1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082 PR China;2. School of Science, Engineering & Design, Teesside University, Middlesbrough, UK;1. Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtzplatz 1, Eggenstein-Leopoldshafen 76344, Germany;2. State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences, Changchun 130033, China;3. Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences, Changchun 130033, China;4. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;1. Department of Mathematics, Al-Azhar University, Nasr City, Cairo 11884, Egypt;2. Department of Mathematics, Al-Baha University, Saudi Arabia;3. Department of Mathematics, The University of Jordan, Amman 11942, Jordan;4. King Abdulaziz University, Jeddah, Saudi Arabia;1. School of Aeronautics, Northwestern Polytechnical University, Xi''an 710072, Shaanxi, China;2. Air and Missile Defense School, Air Force Engineering University, Xi''an 710051, Shaanxi, China;3. School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China;4. School of Naval Engineering, Wuxi Institute of Communications Technology,Wuxi 214151, China |
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| Abstract: | The Finite Element Method (FEM) is known to behave overly-stiff, which leads to an imbalance between the mass and stiffness matrices within discretized systems. In this work, for the first time, a model is developed that provides optimal balance between discretized mass and smoothed stiffness—the mass-redistributed alpha finite element method (MR-αFEM). This new method improves on the computational efficiency of the FEM and Smoothed Finite Element Methods (S-FEM). The rigorous research conducted ensures that stiffness with the parameter, α, optimally matches the mass with a flexible integration point, q. The optimal balance system significantly reduces the dispersion error of acoustic problems, including those of single and multi-fluids in both time and frequency domains. The excellent properties of the proposed MR-αFEM are validated using theoretical analyses and numerical examples. |
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