Topology Optimization for Several Boundary Conditions in Statically Loaded Structures

Abstract In topology optimization using deep learning, load and boundary conditions represented as vectors or sparse matrices often miss the opportunity to encode a rich view of the design problem, leading to less than ideal generalization results. We propose a new data-driven topology optimization model called TopologyGAN that takes advantage of various physical fields computed on the original, unoptimized material domain, as inputs to the generator of a conditional generative adversarial network (cGAN). Compared to a baseline cGAN, TopologyGAN achieves a nearly 3× reduction in the mean squared error and a 2.5× reduction in the mean absolute error on test problems involving previously unseen boundary conditions. Built on several existing network models, we also introduce a hybrid network called U-SE(Squeeze-and-Excitation)-ResNet for the generator that further increases the overall accuracy. We publicly share our full implementation and trained network.

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Checking the Automated Construction of Finite Element Simulations From Dirichlet Boundary Conditions

Volume 2A: 45th Design Automation Conference ◽

10.1115/detc2019-98000 ◽

2019 ◽

Author(s):

Kevin N. Chiu ◽

Mark D. Fuge

Keyword(s):

Finite Element ◽

Topology Optimization ◽

Boundary Conditions ◽

Dirichlet Boundary ◽

Fem Simulation ◽

Computational Design ◽

Dirichlet Boundary Conditions ◽

Governing Equations ◽

Variational Form ◽

Key Issues

Abstract From engineering analysis and topology optimization to generative design and machine learning, many modern computational design approaches require either large amounts of data or a method to generate that data. This paper addresses key issues with automatically generating such data through automating the construction of Finite Element Method (FEM) simulations from Dirichlet boundary conditions. Most past work on automating FEM assumes prior knowledge of the physics to be run or is limited to a small number of governing equations. In contrast, we propose three improvements to current methods of automating the FEM: (1) completeness labels that guarantee viability of a simulation under specific conditions, (2) type-based labels for solution fields that robustly generate and identify solution fields, and (3) type-based labels for variational forms of governing equations that map the three components of a simulation set — specifically, boundary conditions, solution fields, and a variational form — to each other to form a viable FEM simulation. We implement these improvements using the FEniCS library as an example case. We show that our improvements increase the percent of viable simulations that are run automatically from a given list of boundary conditions. This paper’s procedures ultimately allow for the automatic — i.e., fully computer-controlled — construction of FEM multi-physics simulations and data collection required to run data-driven models of physics phenomena or automate the exploration of topology optimization under many physics.

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Topology optimization of self-sensing nanocomposite structures with designed boundary conditions

Smart Materials and Structures ◽

10.1088/1361-665x/ab1179 ◽

2019 ◽

Vol 28 (7) ◽

pp. 074006

Author(s):

Ryan Seifert ◽

Mayuresh Patil ◽

Gary Seidel

Keyword(s):

Topology Optimization ◽

Boundary Conditions ◽

Nanocomposite Structures

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Robust Fluid Topology Optimization Using Polynomial Chaos Expansions: TOffee

Volume 2D: Turbomachinery ◽

10.1115/gt2018-75761 ◽

2018 ◽

Author(s):

A. Gaymann ◽

F. Montomoli ◽

M. Pietropaoli

Keyword(s):

Topology Optimization ◽

Boundary Conditions ◽

Gas Turbines ◽

Real Life ◽

Optimization Method ◽

Robust Topology Optimization ◽

Pressure Losses ◽

Polynomial Chaos Expansions ◽

The Impact ◽

Optimized Geometries

The paper presents an innovative solution to robust topology optimization developed for components that can be manufactured by additive manufacturing. Topology optimization has been used in fluid dynamics to optimize geometries based on a target set of performances required for the flow paths. These target performances can be defined as pressure losses or heat exchanges for example, and multiple optimized geometries can be found in the literature. However, none of these cases considered the impact of stochastic variations and are based on a deterministic optimization. It means the optimization has been done for a single boundary condition value. Would this boundary be random, as it is the case in real life gas turbines, then the optimized geometry, optimized for a single set of boundary conditions, will underperform. Robust topology optimization obtains a geometry able to cope with these random variations. The robust optimization method has been implemented in an in-house solver TOffee and relies on a multi-objective function. 2D and 3D robust optimized geometries are obtained and their performance compared to deterministic cases over a range of boundary conditions. Superiority of robust geometries as compared to deterministic geometries is shown. Robust topology optimization presents a great interest in the gas turbine industry due to the greater performance obtained by the optimized geometries while taking into consideration random variations of boundary conditions, making the simulations closer to real life conditions. For the first time in this work it is shown a fluid topology optimization solution with sedimentation that are inherently able to cope with uncertainty.

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Consistent boundary conditions for PDE filter regularization in topology optimization

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-020-02556-w ◽

2020 ◽

Vol 62 (3) ◽

pp. 1299-1311

Author(s):

Mathias Wallin ◽

Niklas Ivarsson ◽

Oded Amir ◽

Daniel Tortorelli

Keyword(s):

Topology Optimization ◽

Boundary Conditions

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Periodic structures stiffness topology optimization

Revista dos Trabalhos de Iniciação Científica da UNICAMP ◽

10.20396/revpibic262018683 ◽

2019 ◽

Author(s):

Joao Victor Watanabe Nunes ◽

Renato Pavanello

Keyword(s):

Topology Optimization ◽

Boundary Conditions ◽

Periodic Structures ◽

Computational Costs ◽

Evolutionary Structural Optimization ◽

Low Weight ◽

Uniform Medium ◽

Refined Meshes ◽

Optimum Topology ◽

Periodic Materials

Stiffness topology optimization aims to determine the best material arrangement, capable of conciliating high structural stiffness and low weight, which handles certain loading conditions subjected to predefined boundary conditions. The imposed periodic constrain is fundamented on the fact that structures made of periodic materials behave as a homogeneous continuum, because the macro-structure cells are modeled as a uniform medium composed by periodic material. The optimization algorithm used in this work is the BESO (Bi-directional Evolutionary Structural Optimization), which analyzes the structure, under its loadings and boundary conditions, and generates the optimum topology through addition and removal of material. However, in order to reduce the high computational costs of this method when applied to very refined meshes, which is the case with most periodic structures, emphasis was placed on the integration between Matlab and Ansys softwares, with promising results.

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TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain

Journal of Mechanical Design ◽

10.1115/1.4049533 ◽

2021 ◽

pp. 1-13

Author(s):

Zhenguo Nie ◽

Tong Lin ◽

Haoliang Jiang ◽

Levent Burak Kara

Keyword(s):

Topology Optimization ◽

Boundary Conditions ◽

Mean Squared Error ◽

Sparse Matrices ◽

Hybrid Network ◽

Generative Adversarial Networks ◽

Test Problems ◽

Generative Adversarial Network ◽

The Mean ◽

Physical Fields

Abstract In topology optimization using deep learning, load and boundary conditions represented as vectors or sparse matrices often miss the opportunity to encode a rich view of the design problem, leading to less than ideal generalization results. We propose a new data-driven topology optimization model called TopologyGAN that takes advantage of various physical fields computed on the original, unoptimized material domain, as inputs to the generator of a conditional generative adversarial network (cGAN). Compared to a baseline cGAN, TopologyGAN achieves a nearly 3x reduction in the mean squared error and a 2.5x reduction in the mean absolute error on test problems involving previously unseen boundary conditions. Built on several existing network models, we also introduce a hybrid network called U-SE(Squeeze-and-Excitation)-ResNet for the generator that further increases the overall accuracy. We publicly share our full implementation and trained network.

Download Full-text