Computational Mechanics with Neural Networks

ISBN-13: 9783030661137 / Angielski / Miękka / 2022 / 242 str.

Genki Yagawa;Atsuya Oishi

Opis

This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning method in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.

Spis treści

Part I Preliminaries: Machine Learning Technologies for Computational Mechanics

1. Computers and Network

1.1 Computers and Processors

1.2 Network Technologies

1.3 Parallel Processing

1.4 Numerical Precision

2. Feedforward Neural Networks

2.1 Bases

2.2 Various Types of Layers

2.3 Regularization

2.4 Acceleration for Training

2.5 Initialization of Connection Weights

2.6 Model Averaging and Dropout

3. Deep Learning

3.1 Neural Network vs. Deep Learning

3.2 Pretraining: Autoencoder

3.3 Pretraining: Restricted Boltzmann Machine

4. Mutually Connected Neural Networks

4.1 Hopfield Network

4.2 Boltzmann Machine

5. Other Neural Networks

5.1 Self-Organizing Maps

5.2 Radial Basis Function Networks

6. Other Algorithms and Systems

6.1 Genetic Algorithms

6.2 Genetic Programming

6.3 Other Bio-inspired Algorithms

6.4 Support Vector Machines

6.5 Expert Systems

6.6 Software Tools

Part II Applications

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7. Introductory Remarks

8. Constitutive Models

8.1 Parameter Determination of Viscoplastic Constitutive Equations

8.2 Implicit Constitutive Modelling for Viscoplasticity

8.3 Autoprogressive Algorithm

8.4 Others

9. Numerical Quadrature

9.1 Optimization of Number of Quadrature Points

9.2 Optimization of Quadrature Parameters

10. Identifications of Analysis Parameters

10.1 Time Step Evaluation of Pseudo Time-dependent Stress Analysis

10.2 Parameter Identification of Augmented Lagrangian Method

10.3 Predictor-Corrector Method for Structural Nonlinear Analysis

10.4 Contact Stiffness Estimation

11. Solvers and Solution Methods

11.1 Finite Element Solutions through Direct Minimization of Energy Functionals

11.2 Neurocomputing Model for Elastoplasticity

11.3 Structural Re-analysis

11.4 Simulations of Global Flexibility and Element Stiffness

11.5 Solutions based on Variational Principle

11.6 Boundary Conditions

11.7 Hybrid Graph-Neural Method for Domain Decomposition

11.8 Wavefront Reduction

11.9 Contact Search

11.10 Physics-informed Neural Networks

11.11 Dynamic Analysis with Explicit Time Integration Scheme

11.12 Reduced Order Model for Improvement of Solutions using Coarse Mesh

12. Structural Identification

12.1 Identification of Defects with Laser Ultrasonics

12.2 Identification of Cracks

12.3 Estimation of Stable Crack Growth

12.4 Failure Mechanisms in Power Plant Components

12.5 Identification of Parameters of Non-uniform Beam

12.6 Prediction of Beam-Mass Vibration

12.7 Others

12.7.1 Nondestructive Evaluation with Neural Networks

12.7.2 Structural Identification with Neural Networks

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12.7.3 Neural Networks Combined with Global Optimization Method

12.7.4 Training of Neural Networks

13. Structural Optimization

13.1 Hole Image Interpretation for Integrated Topology and Shape Optimization

13.2 Preform Tool Shape Optimization and Redesign

13.3 Evolutionary Methods for Structural Optimization with Adaptive Neural Networks

13.4 Optimal Design of Materials

13.5 Optimization of Production Process

13.6 Estimation and Control of Dynamic Behaviors of Structures

13.7 Subjective Evaluations for Handling and Stability of Vehicle

13.8 Others

14. Some Notes on Applications of Neural Networks to Computational Mechanics

14.1 Comparison among Neural Networks, and Other AI Technologies

14.2 Improvements of Neural Networks in terms of Applications to

Computational Mechanics

15. Other AI Technologies for Computational Mechanics

15.1 Parameter Identification of Constitutive Model

15.2 Constitutive Material Model by Genetic Programming

15.3 Data-driven Analysis without Material Modelling

15.4 Numerical Quadrature

15.5 Contact Search using Genetic Algorithm

15.6 Contact Search using Genetic Programming

15.7 Solving Non-linear Equation Systems using Genetic Algorithm

15.8 Nondestructive Evaluation

15.9 Structural Optimization

15.10 Others

16. Deep Learning for Computational Mechanics

16.1 Neural Networks versus Deep Learning

16.2 Applications of Deep Convolutional Neural Networks to Computational Mechanics

16.3 Applications of Deep Feedforward Neural Networks to Computational Mechanics

16.4 Others

Appendix

A1 Bases of Finite Element Method

A2 Parallel Processing for Finite Element Method

A3 Isogeometric Analysis

A4 Free Mesh Method

A5 Other Meshless Methods

A6 Inverse Problems

Blurb

This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning methods in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.

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