Direct meshless local Petrov–Galerkin method for elastodynamic analysis

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• 作者：Davoud Mirzaei ; Kourosh Hasanpour
• 刊名：Acta Mechanica
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：227
• 期：3
• 页码：619-632
• 全文大小：1,020 KB
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• 作者单位：Davoud Mirzaei (1)
  Kourosh Hasanpour (2)
  
  1. Department of Mathematics, University of Isfahan, P.O.Box 81746-73441, Isfahan, Iran
  2. Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, P.O.Box 81746-73441, Isfahan, Iran
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Mechanics, Fluids and Thermodynamics
  Continuum Mechanics and Mechanics of Materials
  Structural Mechanics
  Vibration, Dynamical Systems and Control
  Engineering Thermodynamics and Transport Phenomena
  
• 出版者：Springer Wien
• ISSN：1619-6937

文摘

This article describes a new and fast meshfree method based on a generalized moving least squares (GMLS) approximation and the local weak forms for vibration analysis in solids. In contrast to the meshless local Petrov–Galerkin method, GMLS directly approximates the local weak forms from meshless nodal values, which shifts the local integrations over the low-degree polynomial basis functions rather than over the complicated MLS shape functions. Besides, if the method is set up properly, all local integrals have the same value if all local subdomains have the same shape. These features reduce the computational costs, remarkably. The new technique is called direct meshless local Petrov–Galerkin (DMLPG) method. In DMLPG, the stiff and mass matrices are constructed by integration against polynomials. This overcomes the main drawback of meshfree methods in comparison with the finite element methods (FEM). The Newmark scheme is adapted as a time integration method, and numerical results are presented for various dynamic problems. The results are compared with the exact solutions, if available, and the FEM solutions.