Article
Engineering, Mechanical
Zengyao Lv, Peng Liu, Yuanshuai Ding, Hangyu Li, Yongmao Pei
Summary: Metamaterials can control incident waves in the sub-wavelength range through the design of artificial structures, providing new possibilities for signal acquisition and processing, network computing, and driving new applications of sound waves. The development of computational metamaterials has opened up a new direction for analog computing, while the field of acoustic computing metamaterials is still in its early stages and requires further research.
ACTA MECHANICA SINICA
(2021)
Article
Mathematics, Applied
Simran Sokhal, Sag Ram Verma
Summary: This study discusses a new method for solving partial differential equations using Fourier wavelet series. It calculates the Fourier wavelet coefficients and uses them instead of Fourier coefficients to obtain solutions, while estimating the bounds of these coefficients. Convergence analysis and the existence of Fourier wavelet series are also explored.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Engineering, Multidisciplinary
Diab W. Abueidda, Qiyue Lu, Seid Koric
Summary: Deep learning and the collocation method are merged to solve partial differential equations describing structures' deformation, offering a meshfree approach that avoids spatial discretization and data generation bottlenecks.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Shams A. Ahmed, Tarig M. Elzaki, Mohamed Elbadri, Mohamed Z. Mohamed
Summary: The primary purpose of this research is to demonstrate the efficiency of a new double transform method, the double Laplace - Sumudu transform (DLST), in solving partial differential equations. The theorems handling fashionable properties of the DLST are proved, along with mentioning the convolution theorem, and using these results to solve partial differential equations efficiently.
AIN SHAMS ENGINEERING JOURNAL
(2021)
Article
Multidisciplinary Sciences
Tarig M. Elzaki, Shams A. Ahmed, Mounirah Areshi, Mourad Chamekh
Summary: In this study, we propose a combined expression based on the double transformation of Laplace and Sumudu. We develop some results associated with this proposed transformation. By applying this double transformation, interesting results can be obtained and used to solve fractional partial differential equations.
JOURNAL OF KING SAUD UNIVERSITY SCIENCE
(2022)
Article
Mathematics, Applied
Rania Saadeh, Bayan Ghazal, Aliaa Burqan
Summary: This research introduces the basic properties of single and double general transforms and investigates new interesting results related to fractional operators using the Caputo derivative. The study applies the general double transformation to special functions and Caputo's fractional derivative of different orders. It establishes new formulas and proves theories that can save time and effort for researchers studying the properties and applications of integral transformations on fractional operators. The results are tested by solving different types of fractional partial differential equations. The outcomes of this article are valuable to researchers and mathematicians interested in solving fractional partial differential equations via integral transforms, which are important techniques for handling these equations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Multidisciplinary Sciences
Abdelilah Kamal Sedeeg, Zahra. I. Mahamoud, Rania Saadeh
Summary: The main goal of this research is to propose a new approach called the double Laplace-ARA transform and apply it to several common partial differential equations. The new approach is simpler and requires less calculations.
Article
Computer Science, Artificial Intelligence
Adam R. Brink, David A. Najera-Flores, Cari Martinez
Summary: This paper introduces a meshfree collocation method that utilizes deep learning to determine basis functions and weights, capable of approximating various types of partial differential equations. By training homogeneous and particular networks separately, new forcing functions can be quickly approximated without retraining the entire network.
NEURAL COMPUTING & APPLICATIONS
(2021)
Article
Multidisciplinary Sciences
Ahmad Qazza, Aliaa Burqan, Rania Saadeh, Raed Khalil
Summary: In this article, we apply the double ARA-Sumudu transformation (DARA-ST) to the nonlocal fractional Caputo derivative operator and achieve interesting results. The new technique is efficient and accurate in solving certain classes of FPDEs, such as telegraph, Klein-Gordon and Fokker-Planck equations. Numerical examples, figures, and a symmetry analysis are used to verify the results.
Article
Mechanics
Diab W. Abueidda, Seid Koric, Rashid Abu Al-Rub, Corey M. Parrott, Kai A. James, Nahil A. Sobh
Summary: In this study, the potential energy formulation and deep learning are merged to introduce the deep energy method, which shows potential for solving deformation problems in hyperelastic and viscoelastic materials.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Mathematics, Applied
Yong Zhi Zhao, Zhi Yong Ai
Summary: This paper proposes a general framework of the transformed differential quadrature method (TDQM) for solving partial differential equations (PDEs). The TDQM introduces the integral transform theorem to decompose the solution process, reducing the difficulty of large-scale matrix inversion and improving computational efficiency. It also reduces the limitation and influence of boundary conditions on computational results, making it suitable for multi-dimensional problems with complex variables.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
M. Magri, S. Lucarini, G. Lemoine, L. Adam, J. Segurado
Summary: This paper presents a new algorithm for simulating gradient ductile damage, which effectively addresses issues in the spatial discretization of continuum ductile damage models. By iteratively solving the mechanical problem and the Helmhotz-type equation separately, the algorithm successfully simulates the failure process of complex 3D particle reinforced composites.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Zhen Chen, Victor Churchill, Kailiang Wu, Dongbin Xiu
Summary: This study introduces a numerical framework for deep neural network modeling of unknown time-dependent PDE using trajectory data. Unlike previous work, the learning and modeling take place in physical space without the need for geometric information of data nodes. The effectiveness of the proposed DNN modeling is demonstrated through a series of examples, including linear and nonlinear scalar PDE, system of PDEs, and discussion on extension to other equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Multidisciplinary Sciences
Abdul Hamid Ganie, Mashael M. AlBaidani, Adnan Khan
Summary: Compared to fractional-order differential equations, integer-order differential equations fail to explain various phenomena effectively in science and engineering. This article employs efficient analytical techniques utilizing the Caputo operator to investigate the solutions of fractional partial differential equations. The Adomian decomposition method, homotopy perturbation method, and Elzaki transformation are utilized to compute comprehensive results for the specified problems. The methods employed are simple, efficient, and provide a series-form solution with easily computable components and a higher convergence rate to the precise solution of the targeted problems. Graphs in two and three dimensions are used to visualize the solutions of the proposed fractional models. The results of this study serve as a valuable tool for solving fractional partial differential equations.
Article
Mathematics, Applied
Teekam Chand Mahor, Rajshree Mishra, Renu Jain
Summary: This paper discusses the analytical solutions of fractional partial differential equations using Integral Transform method, utilizing Fractional Fourier transform to solve various fractional equations. The proposed method is proven to be effective.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Engineering, Mechanical
Diab W. Abueidda, Seid Koric, Nahil A. Sobh, Huseyin Sehitoglu
Summary: This study applied sequence learning models to predict the history-dependent responses of materials, showing that gated recurrent unit and temporal convolutional network can accurately learn and instantly predict such phenomena, with TCN being more computationally efficient during the training process.
INTERNATIONAL JOURNAL OF PLASTICITY
(2021)
Article
Computer Science, Interdisciplinary Applications
Fereshteh A. Sabet, Seid Koric, Ashraf Idkaidek, Iwona Jasiuk
Summary: This study compared implicit and explicit methods in investigating the mechanical properties of trabecular bone using finite element analysis. The results indicated that the two methods gave comparable results, with the explicit method performing faster and consuming less memory.
COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE
(2021)
Article
Materials Science, Multidisciplinary
Seid Koric, Diab W. Abueidda
Summary: This study utilizes advanced numerical modeling techniques and deep learning methods to accurately capture and predict the nonlinear thermo-mechanical behavior of solidifying steel, even in unseen test data samples.
Article
Multidisciplinary Sciences
Patricia M. Gregg, Yan Zhan, Falk Amelung, Dennis Geist, Patricia Mothes, Seid Koric, Zhang Yunjun
Summary: By combining satellite InSAR data with numerical models using high-performance computing data assimilation, the prolonged unrest and eruption timing of the Sierra Negra volcano in the Galapagos were successfully predicted. The evolution of the stress state in the surrounding rock and a faulting event were found to be key factors in the eruption.
Article
Computer Science, Interdisciplinary Applications
Shantanu Shahane, Erman Guleryuz, Diab W. Abueidda, Allen Lee, Joe Liu, Xin Yu, Raymond Chiu, Seid Koric, Narayana R. Aluru, Placid M. Ferreira
Summary: Surrogate neural network models are used in cell phone camera systems to accurately evaluate lens configurations and analyze optical properties. They provide efficient handling of large amounts of data for sensitivity and uncertainty analysis, and are valuable tools for optimizing tolerance design and component matching.
COMPUTERS & STRUCTURES
(2022)
Article
Mechanics
Diab W. Abueidda, Seid Koric, Rashid Abu Al-Rub, Corey M. Parrott, Kai A. James, Nahil A. Sobh
Summary: In this study, the potential energy formulation and deep learning are merged to introduce the deep energy method, which shows potential for solving deformation problems in hyperelastic and viscoelastic materials.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Engineering, Multidisciplinary
Junyan He, Diab Abueidda, Seid Koric, Iwona Jasiuk
Summary: This paper investigates the application of graph convolutional networks in the deep energy method model for solving the momentum balance equation of linear elastic and hyperelastic materials in three-dimensional space. Numerical examples demonstrate that the proposed method achieves similar accuracy with shorter run time compared to traditional methods. The study also discusses two different spatial gradient computation techniques.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mechanics
Junyan He, Charul Chadha, Shashank Kushwaha, Seid Koric, Diab Abueidda, Iwona Jasiuk
Summary: This paper introduces a topology optimization framework based on physics-informed neural networks (PINNs) to solve the forward elasticity problem. It eliminates the need for an additional neural network for the inverse problem. The capabilities of the framework are demonstrated through numerical examples and compared to the finite element method.
Article
Engineering, Manufacturing
V. Perumal, D. Abueidda, S. Koric, A. Kontsos
Summary: Metal additive manufacturing (AM) involves complex multiscale and multiphysics processes. Deep learning-based approaches, specifically temporal convolutional networks (TCNs), have been proposed as a solution to the challenges faced by physics-based modeling methods in predicting thermal histories in AM. This study presents the use of TCNs for fast inferencing in directed energy deposition (DED) processes, achieving comparable accuracy to other deep learning methods with significantly reduced compute and training times.
JOURNAL OF MANUFACTURING PROCESSES
(2023)
Article
Thermodynamics
Seid Koric, Diab W. Abueidda
Summary: DeepONet approximates linear and nonlinear PDE solution operators by using parametric functions as inputs and mapping them to different PDE solution function output spaces. Unlike PINN, DeepONet models can predict parametric solutions in real-time without the need for retraining or transfer learning. It shows good performance in solving the heat conduction equation and is orders of magnitude faster than classical numerical solvers.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2023)
Article
Engineering, Mechanical
Daegun You, Orcun Koray Celebi, Ahmed Sameer Khan Mohammed, Diab W. Abueidda, Seid Koric, Huseyin Sehitoglu
Summary: A predictive model is developed to accurately predict the dislocation glide stress in FCC materials, considering the anisotropic continuum energy, the atomistic misfit energy, and the minimum energy path for the intermittent motion of Shockley partials. By generating a large material dataset and using machine learning, the model achieves a 94% accuracy in predicting the critical resolved shear stress for 1033 materials, revealing the sensitivity of material parameters to the predicted stress.
INTERNATIONAL JOURNAL OF PLASTICITY
(2023)
Article
Engineering, Civil
Junyan He, Shashank Kushwaha, Mahmoud A. Mahrous, Diab Abueidda, Eric Faierson, Iwona Jasiuk
Summary: This study characterizes the size-dependent properties of materials through experimental methods by manufacturing and testing flat dog-bone tensile specimens of different thicknesses. Approximate analytical expressions for material properties values as a function of specimen thickness are provided through curve-fitting to experimental data, creating a phenomenological size-dependent constitutive model. The application of the size-dependent material model is demonstrated through numerical simulations of axial crushing and topology optimization, showing improved performance compared to models that ignore size effects.
THIN-WALLED STRUCTURES
(2023)