Mathematics, Interdisciplinary Applications

Article Engineering, Multidisciplinary

Orientation optimization via topological derivatives in combination with multi-material topology optimization based on extended level set method

Masaki Noda, Kei Matsushima, Takayuki Yamada

Summary: This paper presents an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The method utilizes a topological derivative to measure the sensitivity of the objective function with respect to a topological change in anisotropic materials and incorporates this sensitivity into a gradient-based optimization algorithm to obtain better optimal candidates. The effectiveness of the proposed method is verified through numerical examples.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

SS-MASVM: An advanced technique for assessing failure probability of high-dimensional complex systems using the multi-class adaptive support vector machine

Hua-Ping Wan, Jia-Rui Gan, Yi-Kai Zhu, Zeng Meng

Summary: The study focuses on accurately calculating the failure probabilities of high-dimensional complex systems using surrogate models and subset simulation (SS), with the aim of enhancing computational efficiency and accuracy through the use of multi-class adaptive support vector machine (MASVM). The proposed SS-MASVM method proves to be efficient and accurate for assessing the reliability of complex systems.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

An improved sufficient dimension reduction-based Kriging modeling method for high-dimensional evaluation-expensive problems

Zhouzhou Song, Zhao Liu, Hanyu Zhang, Ping Zhu

Summary: The study proposes an improved Kriging modeling method (KISDR) based on sufficient dimension reduction for addressing the challenge of high-dimensional evaluation-expensive problems. The method introduces martingale difference divergence and ladle estimator for more accurate and stable dimension reduction and dimensionality determination. By integrating the dimension reduction information into the correlation structure, the number of hyperparameters to be estimated is significantly reduced. A local optimization approach is devised for fine-tuning the Kriging hyperparameters. Experimental results show that KISDR can accurately identify and utilize the low-dimensional linear structure in high-dimensional evaluation-expensive problems.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Phasor noise for dehomogenisation in 2D multiscale topology optimisation

Rebekka Woldseth, J. Andreas Baerentzen, Ole Sigmund

Summary: This paper presents an alternative approach to dehomogenisation of elastic Rank-N laminate structures based on the computer graphics discipline of phasor noise. The proposed methodology offers an improvement of existing methods, where high-quality single-scale designs can be obtained efficiently without the utilisation of any least-squares problem or pre-trained models. Numerical tests verifies the performance of the proposed methodology compared to state-of-the-art alternatives, and the dehomogenised designs achieve structural performance within a few percentages of the optimised homogenised solution.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Investigating an extended multiphase flow model that includes specific interfacial area

Mohammad Ebadi, James Mcclure, Peyman Mostaghimi, Ryan T. Armstrong Australia

Summary: In this study, an extended model for multiphase flow in porous media based on first principles is proposed. The advantages of the extended model, including real-time tracking of specific interfacial area, are demonstrated through comparisons with traditional models and analytical solutions. Sensitivity and stability analyses reveal the importance of the balance between permeability of the porous media and interfacial permeability. The extended model offers a better understanding of the evolution of specific interfacial area during multiphase flow.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Adaptive task decomposition physics-informed neural networks

Jianchuan Yang, Xuanqi Liu, Yu Diao, Xi Chen, Haikuo Hu

Summary: In this paper, the advantages and limitations of physics-informed neural networks (PINNs) are discussed, and a strategy of task decomposition and progressive learning is proposed to overcome the limitations and improve performance. Through task decomposition and decomposition of loss terms, they successfully overcome the limitations of existing methods and demonstrate better performance in experiments.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

An active sparse polynomial chaos expansion approach based on sequential relevance vector machine

Yangtian Li, Yangjun Luo, Zheng Zhong

Summary: In this paper, a new sparse PCE approach is proposed by introducing active learning technique and sequence relevance vector machine to address the curse of dimensionality issue in full PCE. The experimental results demonstrate that the proposed method outperforms the classical sparse PCE method in terms of both accuracy and efficiency.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Solving seepage equation using physics-informed residual network without labeled data

Shuaijun Lv, Daolun Li, Wenshu Zha, Luhang Shen, Yan Xing

Summary: This paper proposes a physics-informed residual network (PIResNet) to solve the single-phase seepage equation without labeled data. It adds physical constraints to the neural network, constructs the loss function based on the residuals of the discretized seepage equation, and embeds the boundary conditions as hard constraints. PIResNet has a simple network structure, fast convergence, and easy optimization.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Open-source complex-geometry 3D fluid dynamics for applications with unpredictable heterogeneous dynamic high-performance-computing loads

J. Bakosi

Summary: This paper discusses the software implementation of a finite element method for simulating complex-geometry 3D flows. It effectively utilizes hardware resources and addresses issues such as a priori unknown, heterogeneous, and dynamic parallel computational load. The authors' choices of data structures, algorithms, and software design are specifically aimed at meeting engineering resolution and accuracy requirements. They also utilize Charm++ as the runtime system to effectively manage hardware heterogeneities and dynamic application requirements.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal-dual gap estimators

Francois Fevotte, Ari Rappaport, Martin Vohralik

Summary: In this paper, we study nonsmooth partial differential equations related to the minimization of an energy functional. We adaptively regularize the nonsmooth nonlinearity in order to apply the usual Newton linearization. The finite element method is used for discretization. The choice of regularization parameter is focused on and adjusted based on a posteriori error estimate. The article presents an algorithm that uses adaptive stopping criteria with parameters for regularization, linearization, and discretization levels.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Physics informed WNO

N. Navaneeth, Tapas Tripura, Souvik Chakraborty

Summary: Deep neural operators are effective for learning solution operators of complex PDEs. The Wavelet Neural Operator is able to capture spatial manifolds effectively. However, relying on conventional solvers for data generation is challenging in practical applications.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

A digital twin framework for civil engineering structures

Matteo Torzoni, Marco Tezzele, Stefano Mariani, Andrea Manzoni, Karen E. Willcox

Summary: The digital twin concept provides an appealing opportunity for the maintenance and management of civil engineering systems, with the potential to reduce costs and improve safety and availability. This work proposes a predictive digital twin approach that combines dynamic Bayesian networks and deep learning models for real-time structural health diagnostics and maintenance planning.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

A coupled 3D thermo-mechanical peridynamic model for cracking analysis of homogeneous and heterogeneous materials

W. K. Sun, B. B. Yin, Arslan Akbar, V. K. R. Kodur, K. M. Liew

Summary: This paper proposes a variable timestep-strategy to accelerate the peridynamic modeling of thermomechanical cracking, and demonstrates its advantages in various aspects.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Shape sensitivity of thermoacoustic oscillations in an annular combustor with a 3D adjoint Helmholtz solver

Ekrem Ekici, Stefano Falco, Matthew P. Juniper

Summary: In this study, we developed a solver to calculate the effect of shape changes on the growth rate and frequency of thermoacoustic oscillations using finite element discretization and modal decomposition. By comparing two different shape modification strategies, we found that small geometry changes can significantly alter the growth rate and frequency of thermoacoustic oscillations. The framework of this study can handle complex three-dimensional geometries and is important for the design of industrial combustion systems.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Two-phase two-layer SNS-PFEM for hydromechanical geotechnical large deformation problems

Yin-Fu Jin, Zhen-Yu Yin, Xi-Wen Zhou

Summary: An improved two-phase two-layer SNS-PFEM method is proposed in this study for simulating water-soil coupling. By using two overlapping mesh layers to represent the two phases, this method can accurately simulate large deformation multi-phase problems.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Extended tensor decomposition model reduction methods: Training, prediction, and design under uncertainty

Ye Lu, Satyajit Mojumder, Jiachen Guo, Yangfan Li, Wing Kam Liu

Summary: This paper introduces an extended tensor decomposition (XTD) method that can improve approximation accuracy and reducibility in highly nonlinear and singular cases. The proposed method has been successfully applied to parametric problems and real-time stress predictions with uncertainty quantification. Additionally, a combined XTD-SCA strategy enables real-time multi-scale multi-parametric simulations. The method offers a novel framework for fast manufacturing and material design with uncertainties.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Adaptive Isogeometric Analysis using optimal transport and their fast solvers

M. Bahari, A. Habbal, A. Ratnani, E. Sonnendruecker

Summary: In this work, we propose a solution for the Monge-Ampere Equation within the Isogeometric Analysis framework using B-Splines Finite Elements. We address the challenge of constructing a bijection mapping and overcome the limitations of standard B-Splines Finite Elements when dealing with high variations near the boundary. Our approach includes a new formulation based on a discrete DeRham sequence and a fast solver using the Fast Diagonalization method. Various tests demonstrate the effectiveness of our new approach.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

A computational approach to obtain nonlinearly elastic constitutive relations of strips modeled as a special Cosserat rod

Roushan Kumar, Vivek Agarwal, Ajeet Kumar

Summary: This study presents a computational approach to obtain nonlinearly elastic constitutive relations for strip/ribbon-like structures. The approach utilizes the Helical Cauchy-Born rule and vector variables to model the deformation and strain field of the strip. By solving a set of ordinary differential equations using a nonlinear finite element formulation, the stored energy, internal force, moment, and stiffness of the strip can be determined. The proposed scheme demonstrates a wider range and greater accuracy compared to existing schemes in the literature.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Engineering, Multidisciplinary

Peridynamic modeling of elastic-plastic ductile fracture

Heng Zhang, Dan Huang, Xiong Zhang

Summary: A peridynamics-based framework is developed for elastic-plastic ductile fracture analysis. A new state-based peridynamic elastic-plastic model is proposed, along with methods for computing nonlinear energy release rate and modeling ductile crack growth. The results demonstrate that the proposed peridynamic models accurately capture the characteristics of elastic-plastic deformation and ductile fracture.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

Article Thermodynamics

Numerical modeling and parametric analysis of performance of a monopropellant thruster using a single-part catalyst bed model

Mohammad Reza Salimi, Hadiseh Karimaei, Mostafa Gholampour Yazdi

Summary: In this study, the decomposition chamber of a monopropellant hydrazine thruster is numerically simulated, and the effects of parameters such as catalyst granule diameter, catalyst bed porosity coefficient, and inlet pressure on the performance are investigated. The results show that the porosity coefficient is the most influential parameter, and decreasing it improves the specific impulse and temperature while enhancing the thrust force and mass flow rate. The size of the catalyst granules and the inlet pressure also have an impact on the performance.

COMBUSTION THEORY AND MODELLING (2024)