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Steel and Composite Structures
  Volume 47, Number 5, June 10 2023 , pages 569-585
DOI: https://doi.org/10.12989/scs.2023.47.5.569
 


The smooth topology optimization for bi-dimensional functionally graded structures using level set-based radial basis functions
Wonsik Jung, Thanh T. Banh, Nam G. Luuc and Dongkyu Lee

 
Abstract
    This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.
 
Key Words
    continuum functionally graded steel; exponential spline; Gaussians; level set; micro-mechanical functionally graded; multiquadric; radial basis functions; thin plate spline; topology optimization
 
Address
Wonsik Jung, Thanh T. Banh, Nam G. Luuc and Dongkyu Lee:Department of Architectural Engineering, Sejong University, Seoul 05006, Republic of Korea
 

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