Open Access

ARTICLE

Topology Optimization of Orthotropic Materials Using the Improved Element-Free Galerkin (IEFG) Method

Wenna He, Yichen Yang, Dongqiong Liang, Heng Cheng^*

School of Applied Science, Taiyuan University of Science and Technology, Taiyuan, 030024, China

* Corresponding Author: Heng Cheng. Email:

(This article belongs to the Special Issue: Optimization Design for Material Microstructures)

Computers, Materials & Continua 2025, 83(1), 1415-1414. https://doi.org/10.32604/cmc.2025.059839

Received 17 October 2024; Accepted 06 February 2025; Issue published 26 March 2025

Abstract

In this paper, we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods. The approximation function is established based on the improved moving least squares (IMLS) method, which enhances the efficiency and stability of the numerical solution. The numerical solution formulas are derived using the improved element-free Galerkin (IEFG) method. We introduce the solid isotropic microstructures with penalization (SIMP) model to formulate a mathematical model for topology optimization, which effectively penalizes intermediate densities. The optimization problem is defined with the numerical solution formula and volume fraction as constraints. The objective function, which is the minimum value of flexibility, is optimized iteratively using the optimization criterion method to update the design variables efficiently and converge to an optimal solution. Sensitivity analysis is performed using the adjoint method, which provides accurate and efficient gradient information for the optimization algorithm. We validate the proposed framework through a series of numerical examples, including clamped beam, cantilever beam, and simply supported beam made of orthotropic materials. The convergence of the objective function is demonstrated by increasing the number of iterations. Additionally, the stability of the iterative process is analyzed by examining the fluctuation law of the volume fraction. By adjusting the parameters to an appropriate range, we achieve the final optimization results of the IEFG method without the checkerboard phenomenon. Comparative studies between the Element-Free Galerkin (EFG) and IEFG methods reveal that both methods yield consistent optimization results under identical parameter settings. However, the IEFG method significantly reduces computational time, highlighting its efficiency and suitability for orthotropic materials.

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Keywords

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