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Stress-Based Topology Optimization of Multi-Material Structures with Convolutional Neural Networks

Yaghoobi, Abolfazl | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57864 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. In this study, a novel approach is proposed for analyzing multi-material topology optimization problems with stress constraints. Instead of interpolating the stress tolerance of materials, the proposed method divides the stress exerted on each finite element among the existing materials within the element and directly compares it with the stress tolerance of each material. This method not only reduces computational load but also effectively prevents the occurrence of stress singularity phenomena. To evaluate the effectiveness of the proposed method, two problem formulations were investigated. In the first formulation, the structure's mass is considered as the objective function, with stress as the constraint. In the second formulation, maximizing stiffness is set as the objective function, with stress and the mass fraction as applied constraints. The optimization problems were solved using convolutional neural networks. The network architecture was inspired by the U-Net architecture, with minor modifications. Stress distribution and displacement were used as input features for the network. These features are closely related to the final structure and problem parameters, accelerating the optimization process and leading to desirable results. The efficiency of the proposed method was assessed through several numerical examples and experimental tests. The optimization process in all analyzed cases followed a suitable convergence path. Numerical results demonstrate that in structures designed using the proposed method, the stress experienced by each material is less than the material's stress tolerance. Additionally, it is observed that increasing the number of materials used in the design reduces the structure's mass by approximately 24% compared to the single-material case. Experimental results indicate that considering the structural stiffness alongside the stress constraints, improves the strength in the designed structures
  9. Keywords:
  10. Topology Optimization ; Convolutional Neural Network ; Multi-Material Design ; Stress Constraint ; U-Net Model

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