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| 1 | Artificial Neural Network Methods for the Solution of Second Order Boundary Value Problems显示文摘We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy.In this procedure,a coarse grid of training points is used at the initial training stages,while more points are added at later stages based on the value of the residual at a larger set of evaluation points.This method increases the robustness of the neural network approximation and can result in significant computational savings,particularly when the solution is non-smooth.Numerical results are presented for benchmark problems for scalar-valued PDEs,namely Poisson and Helmholtz equations,as well as for an inverse acoustics problem. | Cosmin Anitescu Elena Atroshchenko Naif Alajlan Timon Rabczuk | 2019 | Computers, Materials & Continua2019，，4： | 72 |
| 2 | A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate显示文摘In this paper,a deep collocation method(DCM)for thin plate bending problems is proposed.This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning.Besides,the proposed DCM is based on a feedforward deep neural network(DNN)and differs from most previous applications of deep learning for mechanical problems.First,batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries.A loss function is built with the aim that the governing partial differential equations(PDEs)of Kirchhoff plate bending problems,and the boundary/initial conditions are minimised at those collocation points.A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters.In Kirchhoff plate bending problems,the C^1 continuity requirement poses significant difficulties in traditional mesh-based methods.This can be solved by the proposed DCM,which uses a deep neural network to approximate the continuous transversal deflection,and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries. | Hongwei Guo Xiaoying Zhuang Timon Rabczuk | 2019 | Computers, Materials & Continua2019，，5： | 53 |
| 3 | A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem显示文摘A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems. | Timon Rabczuk Huilong Ren Xiaoying Zhuang | 2019 | Computers, Materials & Continua2019，，4： | 28 |
| 4 | Computational model generation and RVE design o self-healing concrete显示文摘Computational homogenization is a versatile tool that can extract effective properties of heterogeneous or composite material through averaging technique. Self-healing concrete (SHC) is a heterogeneous material which has different constituents as cement matrix, sand and healing agent carrying capsules. Computational homogenization tool is applied in this paper to evaluate the effective properties of self-healing concrete. With this technique, macro and micro scales are bridged together which forms the basis for multi-scale modeling. Representative volume element (RVE) is a small (microscopic) cell which contains all the microphases of the microstructure. This paper presents a technique for RVE design of SHC and shows the influence of volume fractions of different constituents, RVE size and mesh uniformity on the homogenization results. | Md. Shahriar QUAYUM Xiaoying ZHUANG Timon RABCZUK | 2015 | Frontiers of Structural and Civil Engineering2015，9，4： | 5 |
| 5 | Computational Machine Learning Representation for the Flexoelectricity Effect in Truncated Pyramid Structures显示文摘In this study,machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression.A Non-Uniform Rational B-spline(NURBS)based IGA formulation is employed to model the flexoelectricity.We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements.Six input parameters are selected to construct a deep neural network(DNN)model.They are the Young's modulus,two dielectric permittivity constants,the longitudinal and transversal flexoelectric coefficients and the order of the shape function.The outputs of interest are the strain in the stress direction and the electric potential due flexoelectricity.The dataset are generated from the forward analysis of the flexoelectric model.80%of the dataset is used for training purpose while the remaining is used for validation by checking the mean squared error.In addition to the input and output layers,the developed DNN model is composed of four hidden layers.The results showed high predictions capabilities of the proposed method with much lower computational time in comparison to the numerical model. | Khader M.Hamdia Hamid Ghasemi Xiaoying Zhuang Naif Alajlan Timon Rabczuk | 2019 | Computers, Materials & Continua2019，，4： | 5 |
| 6 | Optimizing the neural network hyperparameters utilizing genetic algorithm显示文摘Neural networks(NNs),as one of the most robust and efficient machine learning methods,have been commonly used in solving several problems.However,choosing proper hyperparameters(e.g.the numbers of layers and neurons in each layer)has a significant influence on the accuracy of these methods.Therefore,a considerable number of studies have been carried out to optimize the NN hyperpaxameters.In this study,the genetic algorithm is applied to NN to find the optimal hyperpaxameters.Thus,the deep energy method,which contains a deep neural network,is applied first on a Timoshenko beam and a plate with a hole.Subsequently,the numbers of hidden layers,integration points,and neurons in each layer are optimized to reach the highest accuracy to predict the stress distribution through these structures.Thus,applying the proper optimization method on NN leads to significant increase in the NN prediction accuracy after conducting the optimization in various examples. | Saeid NIKBAKHT Cosmin ANITESCU Timon RABCZUK | 2021 | Journal of Zhejiang University-Science A(Applied Physics & Engineering)2021，22，6： | 5 |
| 7 | A Dual-Support Smoothed Particle Hydrodynamics for Weakly Compressible Fluid Inspired By the Dual-Horizon Peridynamics显示文摘A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspired by the dual-support,a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed.Conventionally,the SPH formulation employs either the influence domain or the support domain.The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH formulation when variable smoothing lengths are used.The DS-SPH formulation can be implemented into conventional SPH codes with minimal changes and also without compromising the computational efficiency.A number of numerical examples involving weakly compressible.fluid are presented to demonstrate the capability of the method. | Huilong Ren Xiaoying Zhuang Timon Rabczuk | 2019 | Computer Modeling in Engineering & Sciences2019，，11： | 4 |
| 8 | High velocity impact of metal sphere on thin metallic plate using smooth particle hydrodynamics(SPH)method显示文摘The modeling of high velocity impact is an important topic in impact engineering.Due to various constraints,experimental data are extremely limited.Therefore,detailed numerical simulation can be considered as a desirable alternative.However,the physical processes involved in the impact are very sophisticated;hence a practical and complete reproduction of the phenomena involves complicated numerical models.In this paper,we present a smoothed particle hydrodynamics(SPH)method to model two-dimensional impact of metal sphere on thin metallic plate.The simulations are applied to different materials(Aluminum,Lead and Steel);however the target and projectile are formed of similar metals.A wide range of velocities(300,1000,2000,and 3100 m/s)are considered in this study.The goal is to study the most sensitive input parameters(impact velocity and plate thickness)on the longitudinal extension of the projectile,penetration depth and damage crater. | Hossein ASADI KALAMEH Arash KARAMALI Cosmin ANITESCU Timon RABCZUK | 2012 | Frontiers of Structural and Civil Engineering2012，6，2： | 4 |
| 9 | Machine-learning-driven on-demand design of phononic beams显示文摘The development of phononic crystals, especially their interaction with topological insulators, allows exploration of the anomalous properties of acoustic/elastic waves for various applications. However, rapidly and inversely exploring the geometry of specific targets remains a major challenge. In this work, we show how machine learning can address this challenge by studying phononic crystal beams using two different inverse design schemes. We first develop the theory of phononic beams using the transfer matrix method. Then, we use the reinforcement learning algorithm to effectively and inversely design the structural parameters to maximize the bandgap width. Furthermore, we employ the tandem-architecture neural network to solve the training-difficulty problem caused by inconsistent data and complete the task of inverse structure design with the targeted topological properties. The two inverse-design schemes have different adaptabilities, and both are characterized by high efficiency and stability. This work provides deep insights into the combination of machine learning, topological property,and phononic crystals and offers a reliable platform for rapidly and inversely designing complex material and structure properties. | Liangshu He Hongwei Guo Yabin Jin Xiaoying Zhuang Timon Rabczuk Yan Li | 2022 | Science China(Physics,Mechanics & Astronomy)2022，65，1： | 3 |
| 10 | Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model显示文摘We present a cohesive zone model for delamination in thin shells and composite structures.The isogeometric(IGA)thin shell model is based on Kirchhoff-Love theory.Non-Uniform Rational B-Splines(NURBS)are used to discretize the exact mid-surface of the shell geometry exploiting their C 1-continuity property which avoids rotational degrees of freedom.The fracture process zone is modeled by interface elements with a cohesive law.Two numerical examples are presented to test and validate the proposed formulation in predicting the delamination behavior of composite structures. | Tran Quoc THAI Timon RABCZUK Xiaoying ZHUANG | 2020 | Frontiers of Structural and Civil Engineering2020，14，2： | 2 |
| 11 | Three-Dimensional Isogeometric Analysis of Flexoelectricity with MATLAB Implementation显示文摘Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect.We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup.Besides educational purposes,this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy.The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem,which requires higher order approximations,numerically.The complete MATLAB code which is available as source code distributed under a BSD-style license,is provided in the part of Supplementary Materials of the paper. | Hamid Ghasemi Harold S.Park Xiaoying Zhuang Timon Rabczuk | 2020 | Computers, Materials & Continua2020，，11： | 2 |
| 12 | Evaluation of a novel Asymmetric Genetic Algorithm to optimize the structural design of 3D regular and irregular steel frames显示文摘We propose a new algorithm,named Asymmetric Genetic Algorithm(AGA),for solving optimization problems of steel frames.The AGA consists of a developed penalty function,which helps to find the best generation of the population.The objective function is to minimize the weight of the whole steel structure under the constraint of ultimate loads defined for structural steel buildings by the American Institute of Steel Construction(AISC).Design variables are the cross-sectional areas of elements(beams and columns)that are selected from the sets of side-flange shape steel sections provided by the AISC.The finite element method(FEM)is utilized for analyzing the behavior of steel frames.A 15-storey three-bay steel planar frame is optimized by AGA in this study,which was previously optimized by algorithms such as Particle Swarm Optimization(PSO),Particle Swarm Optimizer with Passive Congregation(PSOPC),Particle Swarm Ant Colony Optimization(HPSACO),Imperialist Competitive Algorithm(ICA),and Charged System Search(CSS).The results of AGA such as total weight of the structure and number of analyses are compared with the results of these algorithms.AGA performs better in comparison to these algorithms with respect to total weight and number of analyses.In addition,five numerical examples are optimized by AGA,Genetic Algorithm(GA),and optimization modules of SAP2000,and the results of them are compared.The results show that AGA can decrease the time of analyses,the number of analyses,and the total weight of the structure.AGA decreases the total weight of regular and irregular steel frame about 11.1%and 26.4%in comparing with the optimized results of SAP2000,respectively. | Mohammad Sadegh ES-HAGHI Aydin SHISHEGARAN Timon RABCZUK | 2020 | Frontiers of Structural and Civil Engineering2020，14，5： | 2 |
| 13 | The effects of mismatch fracture properties in encapsulation-based self-healing concrete using cohesive-zone model显示文摘Finite element analysis is developed to simulate the breakage of capsule in capsule-based self-healing concrete.A 2D circular capsule with different core-shell thickness ratios embedded in the mortar matrix is analyzed numerically along with their interfacial transition zone.Zero-thickness cohesive elements are pre-inserted into solid elements to represent potential cracks.This study focuses on the effects of mismatch fracture properties,namely fracture strength and energy,between capsule and mortar matrix into the breakage likelihood of the capsule.The extensive simulations of 2D specimens under uniaxial tension were carried out to investigate the key features on the fracture patterns of the capsule and produce the fracture maps as the results.The developed fracture maps of capsules present a simple but valuable tool to assist the experimentalists in designing appropriate capsule materials for self-healing concrete. | Luthfi Muhammad MAULUDIN Chahmi OUCIF Timon RABCZUK | 2020 | Frontiers of Structural and Civil Engineering2020，14，3： | 1 |
| 14 | 基于PHT-样条加强等几何分析配置方法显示文摘结合传统等几何分析配置法和传统等几何分析伽辽金法,提出一种基于PHT-样条函数的加强等几何分析配置方法.对于一个偏微分方程问题,基于具有局部细分特性的PHT-样条基础函数,应用传统等几何分析配置法在问题域内配置点定义线性方程组,并应用传统等几何分析伽辽金法施加边界条件,以保证多片结构连接的稳定;再将2组线性方程组及施加的边界条件合成一个整体系统.实例计算结果表明,该方法既具有配置法固有的计算效率高的优点,又改善了边界计算出现的不稳定问题,可有效地用于局部细分和多片结构的计算. | 贾悦 Cosmin Anitescu Yongjie Jessica Zhang 徐岗 李春 Timon Rabczuk | 2018 | 计算机辅助设计与图形学学报2018，30，4： | 1 |
| 15 | Parkinson’s Disease Detection Using Biogeography-Based Optimization显示文摘In recent years,Parkinson’s Disease(PD)as a progressive syndrome of the nervous system has become highly prevalent worldwide.In this study,a novel hybrid technique established by integrating a Multi-layer Perceptron Neural Network(MLP)with the Biogeography-based Optimization(BBO)to classify PD based on a series of biomedical voice measurements.BBO is employed to determine the optimal MLP parameters and boost prediction accuracy.The inputs comprised of 22 biomedical voice measurements.The proposed approach detects two PD statuses:0-disease status and 1-good control status.The performance of proposed methods compared with PSO,GA,ACO and ES method.The outcomes affirm that the MLP-BBO model exhibits higher precision and suitability for PD detection.The proposed diagnosis system as a type of speech algorithm detects early Parkinson’s symptoms,and consequently,it served as a promising new robust tool with excellent PD diagnosis performance. | Somayeh Hessam Shaghayegh Vahdat Irvan Masoudi Asl Mahnaz Kazemipoor Atefeh Aghaei Shahaboddin Shamshirband Timon Rabczuk | 2019 | Computers, Materials & Continua2019，，7： | 1 |
| 16 | Biodegradation of Medicinal Plants Waste in an Anaerobic Digestion Reactor for Biogas Production显示文摘Glycyrrhiza glabra,Mint,Cuminum cyminum,Lavender and Arctium medicinal are considered as edible plants with therapeutic properties and as medicinal plants in Iran.After extraction process of medicinal plants,residual wastes are not suitable for animal feed and are considered as waste and as an environmental threat.At present there is no proper management of waste of these plants and they are burned or buried.The present study discusses the possibility of biogas production from Glycyrrhiza Glabra Waste(GGW),Mentha Waste(MW),Cuminum Cyminum Waste(CCW),Lavender Waste(LW)and Arctium Waste(AW).250 g of these plants with TS of 10%were digested in the batch type reactors at the temperature of 35℃.The highest biogas production rate were observed to be 13611 mL and 13471 mL for CCW and GGW(10%TS),respectively.While the maximum methane was related to GGW with a value of 9041 mL(10%TS).The highest specific biogas and methane production were related to CCW with value of 247.4 mL.(g.VS)-1 and 65.1 mL.(g.VS)-1,respectively.As an important result,it was obvious that in lignocellulose materials,it cannot be concluded that the materials with similar ratio of C/N has the similar digestion and biogas production ability. | Kabir Fardad Bahman Najafi Sina Faizollahzadeh Ardabili Amir Mosavi Shahaboddin Shamshirband Timon Rabczuk | 2018 | Computers, Materials & Continua2018，，6： | 1 |
| 17 | Tension-induced phase transition of single-layer molybdenum disulphide (MoS2) at low temperatures显示文摘 | Junhua Zhao Liangzhi Kou Jin-Wu Jiang Timon Rabczuk | 2014 | Nanotechnology2014，，： | 1 |
| 18 | Computational modeling of fracture in capsule-based self-healing concrete: A 3D study显示文摘We present a three-dimensional(3D)numerical model to investigate complex fracture behavior using cohesive elements.An efficient packing algorithm is employed to create the mesoscale model of heterogeneous capsulebased self-healing concrete.Spherical aggregates are used and directly generated from specified size distributions with different volume fractions.Spherical capsules are also used and created based on a particular diameter,and wall thickness.Bilinear traction-separation laws of cohesive elements along the boundaries of the mortar matrix,aggregates,capsules,and their interfaces are pre-inserted to simulate crack initiation and propagation.These pre-inserted cohesive elements are also applied into the initial meshes of solid elements to account for fracture in the mortar matrix.Different realizations are carried out and statistically analyzed.The proposed model provides an effective tool for predicting the complex fracture response of capsule-based self-healing concrete at the meso-scale. | Luthfi Muhammad MAULUDIN Timon RABCZUK | 2021 | Frontiers of Structural and Civil Engineering2021，15，6： | 1 |
| 19 | A Bio-Inspired Global Finite Time Tracking Control of Four-Rotor Test Bench System显示文摘A bio-inspired global finite time control using global fast-terminal sliding mode controller and radial basis function network is presented in this article,to address the attitude tracking control problem of the three degree-of-freedom four-rotor hover system.The proposed controller provides convergence of system states in a predetermined finite time and estimates the unmodeled dynamics of the four-rotor system.Dynamic model of the four-rotor system is derived with Newton’s force equations.The unknown dynamics of four-rotor systems are estimated using Radial basis function.The bio-inspired global fast terminal sliding mode controller is proposed to provide chattering free finite time error convergence and to provide optimal tracking of the attitude angles while being subjected to unknown dynamics.The global stability proof of the designed controller is provided on the basis of Lyapunov stability theorem.The proposed controller is validated by(i)conducting an experiment through implementing it on the laboratory-based hover system,and(ii)through simulations.Performance of the proposed control scheme is also compared with classical and intelligent controllers.The performance comparison exhibits that the designed controller has quick transient response and improved chattering free steady state performance.The proposed bioinspired global fast terminal sliding mode controller offers improved estimation and better tracking performance than the traditional controllers.In addition,the proposed controller is computationally cost effective and can be implanted on multirotor unmanned air vehicles with limited computational processing capabilities. | Rooh ul Amin Irum Inayat Li Aijun Shahaboddin Shamshirband Timon Rabczuk | 2018 | Computers, Materials & Continua2018，，12： | 1 |
| 20 | A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics显示文摘 | Timon Rabczuk Stéphane Bordas Goangseup Zi | 2007 | Computational Mechanics2007，，3： | 1 |
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