Steel and Composite Structures

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Multi-material polygonal topology optimization for functionally graded isotropic and incompressible linear elastic structures

  • Thanh T. Banh (Department of Architectural Engineering, Sejong University) ;
  • Joowon Kang (Department of Architecture, Yeungnam University) ;
  • Soomi Shin (Research Institute of Industrial Technology, Pusan National University) ;
  • Dongkyu Lee (Department of Architectural Engineering, Sejong University)
  • Received : 2023.12.12
  • Accepted : 2024.04.22
  • Published : 2024.05.10
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Abstract

This paper proposes an effective method for optimizing the structure of functionally graded isotropic and incompressible linear elastic materials. The main emphasis is on utilizing a specialized polytopal composite finite element (PCE) technique capable of handling a broad range of materials, addressing common volumetric locking issues found in nearly incompressible substances. Additionally, it employs a continuum model for bi-directional functionally graded (BFG) material properties, amalgamating these aspects into a unified property function. This study thus provides an innovative approach that tackles diverse material challenges, accommodating various elemental shapes like triangles, quadrilaterals, and polygons across compressible and nearly incompressible material properties. The paper thoroughly details the mathematical formulations for optimizing the topology of BFG structures with various materials. Finally, it showcases the effectiveness and efficiency of the proposed method through numerous numerical examples.

Keywords

Acknowledgement

This research was supported by and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1003776).

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