Showing papers on "Finite element method published in 2020"
TL;DR: This contribution focuses in mechanical problems and analyze the energetic format of the PDE, where the energy of a mechanical system seems to be the natural loss function for a machine learning method to approach a mechanical problem.
721 citations
TL;DR: In this paper, an alternative method based on Fourier series which avoids meshing and which makes direct use of microstructure images is proposed, which is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material.
Abstract: The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images. It is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material. First, the case of elastic nonhomogeneous constituents is considered and an iterative procedure is proposed to solve the Lippman-Schwinger equation which naturally arises in the problem. Then, the method is extended to non-linear constituents by a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The flexibility of the method allows it to serve for a large variety of microstructures. (C) 1998 Elsevier Science S.A.
219 citations
TL;DR: This paper converts the problem of finding the weak solution of PDEs into an operator norm minimization problem induced from the weak formulation, and parameterized as the primal and adversarial networks respectively, which are alternately updated to approximate the optimal network parameter setting.
214 citations
TL;DR: In this article, a combination of principal component analysis (PCA) and convolutional neural networks (CNN) is used to predict the entire stress-strain behavior of binary composites evaluated over the entire failure path.
186 citations
TL;DR: In this article, free vibration analysis of embedded carbon and silica carbide nanotubes lying on an elastic matrix is performed based on Eringen's nonlocal elasticity theory.
Abstract: In this study, free vibration analyses of embedded carbon and silica carbide nanotubes lying on an elastic matrix are performed based on Eringen’s nonlocal elasticity theory. These nanotubes are modeled as nanobeam and nanorod. Elastic matrix is considered as Winkler–Pasternak elastic foundation and axial elastic media for beam and rod models, respectively. The vibration formulations of the beam and rod are derived by utilizing Hamilton’s principle. The obtained equations of motions are solved by the method of separation of variables and finite element-based Hermite polynomials for various boundary conditions. The effects of boundary conditions, system modeling, structural sizes such as length, cross-sectional sizes, elastic matrix, mode number, and nonlocal parameters on the natural frequencies of these nanostructures are discussed in detail. Moreover, the availability of size-dependent finite element formulation is investigated in the vibration problem of nanobeams/rods resting on an elastic matrix.
157 citations
TL;DR: In this paper, the authors investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling, and propose a new adaptive time increment scheme to further reduce the computational cost while allowing to accurately resolve sudden changes in material behavior.
136 citations
TL;DR: The results show that the simulated fault features of the proposed dynamic model for spalled gear pairs agree well with that obtained from the experiment, which indicates that the proposed model is a promising tool for the fault mechanism study of gears with realistic spalling patterns.
127 citations
TL;DR: In this article, the conjugate flow and heat transfer of phase change materials (PCMs)-metal foam confined between two annuli is addressed, where a pulse heat load is employed at the inner surface of annuli, while the outer surface is subject to convection cooling.
117 citations
TL;DR: In this paper, the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure were investigated.
Abstract: The purpose of the current study is to numerically investigate the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure. A numerical method called the control volume-based finite element method is implemented for solving the governing equations. The modified flow and thermal structures and corresponding heat transfer features are investigated. Numerical outcomes reveal very good grid independency and excellent agreement with the existing studies. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt number. Further, enhancement of Rayleigh number increases the velocity of nanofluid, while that of aspect ratio of the elliptical cylinder shows the opposite trend.
112 citations
TL;DR: This article considers a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples, and provides extensive discussions about numerical methods for determining approximate solutions of the nonlocal models considered.
Abstract: Partial differential equations (PDEs) are used with huge success to model phenomena across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDEs fail to adequately model observed phenomena, or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. In this article we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modelling and algorithmic extensions, which serve to show the wide applicability of nonlocal modelling.
109 citations
TL;DR: The presented approach is very simple to implement and requires only a few lines of code within the open-source machine learning framework such as Tensorflow or Pytorch.
Abstract: We present a deep energy method for finite deformation hyperelasticitiy using deep neural networks (DNNs). The method avoids entirely a discretization such as FEM. Instead, the potential energy as a loss function of the system is directly minimized. To train the DNNs, a backpropagation dealing with the gradient loss is computed and then the minimization is performed by a standard optimizer. The learning process will yield the neural network's parameters (weights and biases). Once the network is trained, a numerical solution can be obtained much faster compared to a classical approach based on finite elements for instance. The presented approach is very simple to implement and requires only a few lines of code within the open-source machine learning framework such as Tensorflow or Pytorch. Finally, we demonstrate the performance of our DNNs based solution for several benchmark problems, which shows comparable computational efficiency such as FEM solutions.
TL;DR: The effects of thermal relaxation times and porosity in a poro-thermoelastic medium are studied and numerical computations for temperatures, displacements and stresses for the liquid and the solid are presented graphically.
Abstract: The purpose of this study is to provide a method to investigate the effects of thermal relaxation times in a poroelastic material by using the finite element method. The formulations are applied under the Green and Lindsay model, with four thermal relaxation times. Due to the complex governing equation, the finite element method has been used to solve these problems. All physical quantities are presented as symmetric and asymmetric tensors. The effects of thermal relaxation times and porosity in a poro-thermoelastic medium are studied. Numerical computations for temperatures, displacements and stresses for the liquid and the solid are presented graphically.
TL;DR: In this article, the closed-form solutions of the forced transverse vibration of a coupled Timoshenko double-beam system under compressive axial load are presented and compared with other known results along with FEM solutions for verification.
TL;DR: In this article, a numerical simulation model is established by the finite element method to predict the meso-scale effective thermal conductivity of soil, and Monte Carlo simulation is employed to account for the random distribution of voids.
TL;DR: In this article, the vibrational behavior of porous functionally graded magneto-electro-elastic (P-FGMEE) circular and annular plates is explored through finite element procedures.
TL;DR: In this paper, the effect of shape parameter on the deformation mechanisms of the modified rhombic dodecahedron (RD) lattice structure was discussed, where three different deformation modes were observed.
Abstract: Dynamic compression properties of the modified rhombic dodecahedron (RD) lattice structures were investigated by using a Split Hopkinson Pressure Bar (SHPB) system. All the deformation processes were recorded and a digital image correlation (DIC) technique was employed to analyse the strain distribution during the compression process. Experimental results indicated that the modified lattice structure showed better compressive strength, plateau stress and energy absorption when compared with the original one under both quasi-static and dynamic loading conditions. The effect of the shape parameter on the deformation mechanisms of the RD lattice structure was discussed, where three different deformation modes were observed. Finite element analysis was also conducted to simulate the dynamic response of the modified lattice structure. The finite element results are in good agreement with the experimental results. Then, a mode classification map was plotted and discussed based on the numerical results.
TL;DR: In this article, the authors calculate the flow of stress of deforming metal as a function of temperature, strain and strain rate using a hybrid adaptive genetic algorithm and cuckoo search (ANN-AGCS) model.
TL;DR: In this article, the Non-Uniform Rational B-Splines (NURBS) based analysis of stiffened laminated composite plates is presented, where a first-order shear deformation theory is used to derive the governing equations by employing a variational formulation.
TL;DR: A literature review is conducted on induction motor fault diagnosis techniques using FEM and the state-of-the-art techniques reported in the literature are categorized into three streams: first, FEM-based fault diagnosis approach, second, F EM and signal processing-based approach, and third, Fem, machine learning, and other advanced techniques-based approaches.
Abstract: Condition monitoring and fault diagnosis of induction motors serve as essential techniques toward the reliable operation of critical industrial processes. The finite element method (FEM) offers a great insight into fundamental principle and physical operation of the machine. It can model complex magnetic circuit topology, discrete windings layouts, and nonlinear magnetic material properties of the machine. It determines the machine parameters (such as the magnetic field distribution, flux density, electromagnetic torques, and stator current) and can model localized magnetic saturation due to faults to a high degree of accuracy. Used as fault detection algorithms, the FEM can address the issues such as the lack of comprehensive fault databases through field measurements, and the difficulty in distinguishing fault severity. It can reduce the number of destructive tests required in the field/labs, simulate any faulty states of the machine. Although FEM has been widely used in induction motors’ design and analysis, its application in fault diagnosis is limited despite the promising potential. In this article, a literature review is conducted on induction motor fault diagnosis techniques using FEM. The state-of-the-art techniques reported in the literature are categorized into three streams: first, FEM-based fault diagnosis approach, second, FEM and signal processing-based approach, and third, FEM, machine learning, and other advanced techniques-based approach. The advantages of fault diagnosis techniques using the FEM are demonstrated and the future research direction is recommended.
TL;DR: In this paper, a finite element method (FEM) for phased array technology in ultrasonic time of flight diffraction (TOFD) for defect detection of two-dimensional (2-D) geometric materials was researched.
Abstract: In this study, the finite element method (FEM) for phased array technology in ultrasonic time of flight diffraction (TOFD) for the defect detection of two-dimensional (2-D) geometric materials was researched. The phased array technology generated the FEM model for the TOFD signal. We
have established the finite element model by the FEM software ANSYS based on the ultrasonic mechanism about the defects and the phased array transducer. A plane strain elements have simulated the reflected signal of the defect. We can compare the error ratio between simulation and experiment
by using the theoretical calculation value as the benchmark, and find the feasibility of the FEM detection.
TL;DR: The present work aims to provide a comprehensive review of the performed numerical researches using Comsol Multiphysics to solve the physical governing equations of the heat transfer in advanced ceramics.
Abstract: Numerical simulation is a powerful tool to predict the physical behavior of the designed devices. This method provides detailed information about the investigated phenomenon at each point of the device which is sometimes impossible by experiments. Comsol Multiphysics is a powerful tool that can cover a wide range of engineering fields. This software has employed the finite element method (FEM) to solve the physical governing equations. Owing to the importance of the heat transfer in advanced ceramics, and the potential of the numerical methods in the solution of the related problems, the present work aims to provide a comprehensive review of the performed numerical researches using Comsol Multiphysics.
TL;DR: In this article, the partial safety factor corresponding to the resistance model uncertainties in the use of nonlinear finite element analyses (NLFEAs) for reinforced concrete systems subjected to cyclic loads is assessed.
TL;DR: In this article, analytical solutions of coupled thermoelastic forced vibrations of micro-nano-beams based on Rayleigh beam theory and Eringen nonlocal elasticity theory are derived.
TL;DR: In this paper, the numerical approximation of solutions to stochastic partial differential equations with additive spatial white noise on bounded domains in R-d is considered, where the differential operator is given by the fractional power L-beta, beta is an element of (0, 1) of an integer-order elliptic differential operator L and is therefore nonlocal.
Abstract: The numerical approximation of solutions to stochastic partial differential equations with additive spatial white noise on bounded domains in R-d is considered. The differential operator is given by the fractional power L-beta, beta is an element of (0, 1) of an integer-order elliptic differential operator L and is therefore nonlocal. Its inverse L-beta is represented by a Bochner integral from the Dunford-Taylor functional calculus. By applying a quadrature formula to this integral representation the inverse fractional-order operator L-beta is approximated by a weighted sum of nonfractional resolvents (I + exp(2yl)L)(-1) at certain quadrature nodes t(j) > 0. The resolvents are then discretized in space by a standard finite element method. This approach is combined with an approximation of the white noise, which is based only on the mass matrix of the finite element discretization. In this way an efficient numerical algorithm for computing samples of the approximate solution is obtained. For the resulting approximation the strong mean-square error is analyzed and an explicit rate of convergence is derived. Numerical experiments for L = kappa(2) - Delta, kappa > 0 with homogeneous Dirichlet boundary conditions on the unit cube (0, 1)(d) in d = 1, 2, 3 spatial dimensions for varying beta is an element of (0, 1) attest to the theoretical results.
TL;DR: In this paper, the Johnson-Holmquist damage constitutive model was adopted, based on the LS-DYNA secondary development technology, and smooth particle hydrodynamics (SPH) was introduced to simulate the fluid.
TL;DR: This package includes geometrical and analytical routines for vectorizing bitmap image, computing geometric information statistics, and generating numerical models that have broad application prospect in mechanical behavior analysis for heterogeneous materials.
TL;DR: In this paper, a novel Galerkin-based numerical approach for simulating quasi-brittle fracture, named Global Cracking Elements Method (GCEM), is proposed, which is embedded in the standard framework of the FEM and uses disconnected element-wise crack openings for capturing crack initiation and propagation.
Abstract: Following the so-called Cracking Elements Method (CEM), recently presented in \cite{Yiming:14,Yiming:16}, we propose a novel Galerkin-based numerical approach for simulating quasi-brittle fracture, named Global Cracking Elements Method (GCEM). For this purpose the formulation of the original CEM is reorganized. The new approach is embedded in the standard framework of the Galerkin-based Finite Element Method (FEM), which uses disconnected element-wise crack openings for capturing crack initiation and propagation. The similarity between the proposed Global Cracking Elements (GCE) and the standard 9-node quadrilateral element (Q9) suggests a special procedure: the degrees of freedom of the center node of the Q9, originally defining the displacements, are "borrowed" to describe the crack openings of the GCE. The proposed approach does not need remeshing, enrichment, or a crack-tracking strategy, and it avoids a precise description of the crack tip. Several benchmark tests provide evidence that the new approach inherits from the CEM most of the advantages. The numerical stability and robustness of the GCEM are better than the ones of the CEM. However, presently only quadrilateral elements with nonlinear interpolations of the displacement field can be used.
TL;DR: An extended overview of the theory and applications of the particle finite element method is provided, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications and to confirm the flexibility and robustness of the method for a broad range of engineering applications.
Abstract: The particle finite element method (PFEM) is a powerful and robust numerical tool for the simulation of multi-physics problems in evolving domains. The PFEM exploits the Lagrangian framework to automatically identify and follow interfaces between different materials (e.g. fluid–fluid, fluid–solid or free surfaces). The method solves the governing equations with the standard finite element method and overcomes mesh distortion issues using a fast and efficient remeshing procedure. The flexibility and robustness of the method together with its capability for dealing with large topological variations of the computational domains, explain its success for solving a wide range of industrial and engineering problems. This paper provides an extended overview of the theory and applications of the method, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications. Moreover, this work aims to confirm the flexibility and robustness of the PFEM for a broad range of engineering applications. Furthermore, presenting the advantages and disadvantages of the method, this overview can be the starting point for improvements of PFEM technology and for widening its application fields.
TL;DR: In this paper, the authors apply the method of Maggi's equations to realize the assembly of the equations of motion for a planar mechanical systems using finite two-dimensional elements.
Abstract: An important stage in an analysis of a multibody system (MBS) with elastic elements by the finite element method is the assembly of the equations of motion for the whole system. This assembly, which seems like an empirical process as it is applied and described, is in fact the result of applying variational formulations to the whole considered system, putting together all the finite elements used in modeling and introducing constraints between the elements, which are, in general, nonholonomic. In the paper, we apply the method of Maggi’s equations to realize the assembly of the equations of motion for a planar mechanical systems using finite two-dimensional elements. This presents some advantages in the case of mechanical systems with nonholonomic liaisons.