Session: 12-03-03: Data-Enabled Predictive Modeling, Scientific Machine Learning, and Uncertainty Quantification in Computational Mechanics

Paper Number: 109442

109442 - Topology Optimization Using Neural Network for Stress Constrained Problems 

Lightweight designs are highly desirable in many industrial applications, such as aerospace, automotive, and transportation, due to their ability to reduce weight while maintaining or even improving the technical performance of the structure. Achieving lightweight designs involves the use of advanced materials and engineering methods to enable structural elements to deliver the same or enhanced technical performance while using less material. One of the powerful tools for achieving lightweight designs is Topology Optimization (TO), which is a conceptual design method that generates optimal material layouts within a given design domain to maximize performance under relevant design specifications. Over the last few years, there has been rapid development and extensive application of topology optimization in various engineering fields. Different topology optimization methods, such as density-based, level set, evolutionary, phase field, and topological sensitivity, have been implemented to solve these problems [1]. The finite element method (FEM) is commonly used to calculate the unknown structural response and to evaluate the design performance against the designed criteria set by the user. Generally, topology optimization has been used to determine the stiffest structure by minimizing compliance for a prescribed amount of material. However, traditional topology optimization often results in designs with high-stress concentrations and even geometrical shapes causing stress singularities. It is not practical for use as it can lead to structural failure. Stress singularities are areas within the structure where the stress is concentrated, with high stress gradients. Sharp corners, high gradients in the material density, or other factors can cause these areas. The stress singularities can cause premature failure of the structure, and it is crucial to address it. Therefore, it is essential to take into account stress-related objectives or constraints in the mass minimization problem (which is the traditional objective in topology optimization) in order to produce safe, reliable, and efficient designs.

 

Recently a technique for using neural networks in topology optimization is proposed [2]. In this study, stress constraints are incorporated into the optimization process by using this neural network approach. This allows the optimization to be carried out in real-time, making it more efficient and accurate. The neural network is used to execute topology optimization directly from a finite element solver. The activation function of the neural network represents the popular density field function, Solid Isotropic Material with Penalization (SIMP), which is widely used in the field of topology optimization. The density function is parametrized by the network's learning parameters, which is a key feature of this approach. This approach improves the optimization process and allows for an efficient and accurate determination of the optimal material layout within a given design domain, maximizing performance based on user-specified criteria. An important aspect of this method is the inclusion of a Fourier space projection in the framework. This projection allows for control over the length scale of the features in the final design, which is crucial for meeting the manufacturer's design requirements. The ability to comply with these specifications ensures that the final design is suitable for its intended application. The whole model is built using the high-performance library JAX to implement this method, which enables an end-to-end differentiability. This means that the sensitivity computations for stress-related objectives and constraints of topology optimization are automated by expressing the computations through the built-in backpropagation of the neural network model. This feature makes it more efficient and accurate as it eliminates the need for explicit calculation of sensitivity and allows for real-time optimization.

  [1] Sigmund, Ole, and Kurt Maute. "Topology optimization approaches." Structural and Multidisciplinary Optimization 48, no. 6 (2013): 1031-1055.

  [2] Chandrasekhar, Aaditya, and Krishnan Suresh. "TOuNN: topology optimization using neural networks." Structural and Multidisciplinary Optimization 63, no. 3 (2021): 1135-1149.

Presenting Author: MD IMRUL REZA SHISHIR The University of North Carolina at Charlotte

Presenting Author Biography: Md Imrul Reza Shishir received B.Sc. in Mechanical Engineering from Bangladesh University of Engineering and Technology, Bangladesh, in 2012 and M. Eng. in Mechanical Engineering at Inha University in 2017. In 2022, He completed his Ph.D. in Mechanical Engineering at the University of North Carolina at Charlotte. Currently, He is doing research at North Carolina State University as a post-doctoral researcher. His research interest is machine learning, molecular dynamics, topology optimization, finite element method, fracture mechanics, 2D materials, cohesive zone models, cellulose-based bio-materials, etc.

Authors:

MD IMRUL REZA SHISHIR The University of North Carolina at Charlotte
Alireza Tabarraei The University of North Carolina at Charlotte