P1-Nonconforming shell element and its application to topology optimization

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• 作者：Chen Lei (1)
  Tae Hyun Baek (2)
  Gang-Won Jang (3)
  
• 关键词：P1 ; nonconforming element ; Shear locking ; Degenerated shell element ; Incompressible material ; Topology optimization
• 刊名：Journal of Mechanical Science and Technology
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：29
• 期：1
• 页码：297-308
• 全文大小：1,641 KB
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• 作者单位：Chen Lei (1)
  Tae Hyun Baek (2)
  Gang-Won Jang (3)
  
  1. Department of Mechanical Engineering, Xiangfan University, Xiangfan, Hubei, 441053, China
  2. School of Mechanical and Automotive Engineering, Kunsan National University, Gunsan, 573-701, Korea
  3. Faculty of Mechanical and Aerospace Engineering, Sejong University, 98 Gunja-Dong, Gwangjin-Gu, Seoul, 143-747, Korea
  
• 刊物类别：Engineering
• 刊物主题：Mechanical Engineering
  Structural Mechanics
  Control Engineering
  Industrial and Production Engineering
  
• 出版者：The Korean Society of Mechanical Engineers
• ISSN：1976-3824

文摘

The P1-nonconforming quadrilateral element developed by Park and Sheen [19] is employed for the formulation of a four-node degenerated shell element. The numerical stability of the P1-nonconforming quadrilateral element verified in plane elasticity problems and Stokes flow problems is investigated for the application of mitigating locking phenomena in shell problems. To facilitate the stiffness matrix computation for a non-flat general quadrilateral shell element, a nonparametric reference scheme using both affine transformation and bilinear transformation is adopted. Based on a field-consistency concept, the spurious constraints that cause locking are analyzed and an effective reduced integration scheme is found. The proposed shell element is applied to multi-physics topology optimization problems involving fluid analysis and shell analysis. For fluid analysis, the P1-nonconforming quadrilateral element is also adopted to utilize its volumetric locking-free property for incompressible materials. Vein layouts of leaves are designed by topology optimization and compared with natural vein layouts to verify the effectiveness of the proposed element.