Relevant bibliographies by topics / Finite element methods (FEMs)

Academic literature on the topic 'Finite element methods (FEMs)'

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Published: 14 March 2023

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Journal articles on the topic "Finite element methods (FEMs)"

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Cen, Song, Cheng Jin Wu, Zhi Li, Yan Shang, and Chenfeng Li. "Some advances in high-performance finite element methods." Engineering Computations 36, no. 8 (October 7, 2019): 2811–34. http://dx.doi.org/10.1108/ec-10-2018-0479.

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Purpose The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time. Design/methodology/approach Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions. Findings The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate. Originality/value These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.
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Nair, M. Thamban, and Devika Shylaja. "Conforming and nonconforming finite element methods for biharmonic inverse source problem." Inverse Problems 38, no. 2 (December 20, 2021): 025001. http://dx.doi.org/10.1088/1361-6420/ac3ec5.

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Abstract This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and nonconforming finite element methods (FEMs). The inverse problem is analysed through the forward problem. Error estimate for the forward solution is derived in an abstract set-up that applies to conforming and Morley nonconforming FEMs. Since the inverse problem is ill-posed, Tikhonov regularization is considered to obtain a stable approximate solution. Error estimate is established for the regularized solution for different regularization schemes. Numerical results that confirm the theoretical results are also presented.
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Rong, Xin, Ruiping Niu, and Guirong Liu. "Stability Analysis of Smoothed Finite Element Methods with Explicit Method for Transient Heat Transfer Problems." International Journal of Computational Methods 17, no. 02 (October 24, 2019): 1845005. http://dx.doi.org/10.1142/s0219876218450056.

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In this paper, transient heat transfer problems are analyzed using the smoothed finite element methods (S-FEMs) with explicit time integration. For a numerical method with spatial discretization, the computational cost per time step in the explicit method is less than that in the implicit method, but the time step is much smaller in the explicit analysis than that in the implicit analysis when the same mesh is used. This is because the stability is of essential importance. This work thus studies the stability of S-FEMs, when applied to transient heat transfer problems. Relationships are established between the critical time steps used in S-FEMs with the maximum eigenvalues of the thermal stiffness (conduction) matrix and mass matrix. It is found that the critical time step relates to the “softness” of the model. For example, node-based smoothed finite element method (NS-FEM) is softer than edge-based smoothed finite element method (ES-FEM), which leads to that the critical time step of NS-FEM is larger than that of ES-FEM. Because computing the eigenvalues and condition numbers of the stiffness matrices is very expensive but valuable for stability analysis, we proposed a concise and effective algorithm to estimate the maximum eigenvalue and condition number. Intensive numerical examples show that our scheme for computing the critical time step can work accurately and stably for the explicit method in FEM and S-FEMs.
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D’Elia, Marta, Max Gunzburger, and Christian Vollmann. "A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems." Mathematical Models and Methods in Applied Sciences 31, no. 08 (June 19, 2021): 1505–67. http://dx.doi.org/10.1142/s0218202521500317.

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The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms involving double integrals which lead to discrete systems having higher assembly and solving costs due to possibly much lower sparsity compared to that of FEMs for PDEs. In addition, one may encounter nonsmooth integrands. In many nonlocal models, nonlocal interactions are limited to bounded neighborhoods that are ubiquitously chosen to be Euclidean balls, resulting in the challenge of dealing with intersections of such balls with the finite elements. We focus on developing recipes for the efficient assembly of FEM stiffness matrices and on the choice of quadrature rules for the double integrals that contribute to the assembly efficiency and also posses sufficient accuracy. A major feature of our recipes is the use of approximate balls, e.g. several polygonal approximations of Euclidean balls, that, among other advantages, mitigate the challenge of dealing with ball-element intersections. We provide numerical illustrations of the relative accuracy and efficiency of the several approaches we develop.
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Mackerle, Jaroslav. "Finite element analyses and simulations in biomedicine: a bibliography (1985‐1999)." Engineering Computations 17, no. 7 (November 1, 2000): 813–56. http://dx.doi.org/10.1108/02644400010352270.

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Gives a bibliographical review of the finite element methods (FEMs) applied in biomedicine from the theoretical as well as practical points of view. The bibliography at the end of the paper contains 748 references to papers, conference proceedings and theses/dissertations dealing with the finite element analyses and simulations in biomedicine that were published between 1985 and 1999.
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Wu, Jilian, Xinlong Feng, and Fei Liu. "Pressure-Correction Projection FEM for Time-Dependent Natural Convection Problem." Communications in Computational Physics 21, no. 4 (March 8, 2017): 1090–117. http://dx.doi.org/10.4208/cicp.oa-2016-0064.

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AbstractPressure-correction projection finite element methods (FEMs) are proposed to solve nonstationary natural convection problems in this paper. The first-order and second-order backward difference formulas are applied for time derivative, the stability analysis and error estimates of the semi-discrete schemes are presented using energy method. Compared with characteristic variational multiscale FEM, pressure-correction projection FEMs are more efficient and unconditionally energy stable. Ample numerical results are presented to demonstrate the effectiveness of the pressure-correction projection FEMs for solving these problems.
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He, Yanfei, Xingwu Zhang, Jia Geng, Xuefeng Chen, and Zengguang Li. "Two Kinds of Finite Element Variables Based on B-Spline Wavelet on Interval for Curved Beam." International Journal of Applied Mechanics 11, no. 02 (March 2019): 1950017. http://dx.doi.org/10.1142/s1758825119500170.

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Curved beam structure has been widely used in engineering, due to its good load-bearing and geometric characteristics. More common methods for analyzing and designing this structure are the finite element methods (FEMs), but these methods have many disadvantages. Fortunately, the multivariable wavelet FEMs can solve these drawbacks. However, the multivariable generalized potential energy functional of curved beam, used to construct this element, has not been given in previous literature. In this paper, the generalized potential energy functional for curved beam with two kinds of variables is derived initially. On this basis, the B-spline wavelet on the interval (BSWI) is used as the interpolation function to construct the wavelet curved beam element with two kinds of variables. In the end, several typical numerical examples of thin to thick curved beams are given, which show that the present element is more effective in static and free vibration analysis of curved beam structures.
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Jiang, Chen, Xu Han, G. R. Liu, Zhi-Qian Zhang, Gang Yang, and Guang-Jun Gao. "Smoothed finite element methods (S-FEMs) with polynomial pressure projection (P3) for incompressible solids." Engineering Analysis with Boundary Elements 84 (November 2017): 253–69. http://dx.doi.org/10.1016/j.enganabound.2017.07.022.

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CHIEN, C. S., H. T. HUANG, B. W. JENG, and Z. C. LI. "SUPERCONVERGENCE OF FEMS AND NUMERICAL CONTINUATION FOR PARAMETER-DEPENDENT PROBLEMS WITH FOLDS." International Journal of Bifurcation and Chaos 18, no. 05 (May 2008): 1321–36. http://dx.doi.org/10.1142/s0218127408021014.

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We study finite element approximations for positive solutions of semilinear elliptic eigenvalue problems with folds, and exploit the superconvergence of finite element methods (FEM). In order to apply the superconvergence of FEM for Poisson's equation in [Chen & Huang, 1995; Huang et al., 2004, 2006; Lin & Yan, 1996] to parameter-dependent problems with folds, this paper provides the framework of analysis, accompanied with the proof of the strong monotonicity of the nonlinear form. It is worthy to point out that the superconvergence of the nonlinear problem in this paper is different from that in [Chen & Huang, 1995]. A continuation algorithm is described to trace solution curves of semilinear elliptic eigenvalue problems, where the Adini elements are exploited to discretize the PDEs. Numerical results on some sample test problems with folds and bifurcations are reported.
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Hu, Jun, and Mira Schedensack. "Two low-order nonconforming finite element methods for the Stokes flow in three dimensions." IMA Journal of Numerical Analysis 39, no. 3 (April 19, 2018): 1447–70. http://dx.doi.org/10.1093/imanum/dry021.

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Abstract In this paper, we propose two low-order nonconforming finite element methods (FEMs) for the three-dimensional Stokes flow that generalize the nonconforming FEM of Kouhia & Stenberg (1995, A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow. Comput. Methods Appl. Mech. Eng, 124, 195–212). The finite element spaces proposed in this paper consist of two globally continuous components (one piecewise affine and one enriched component) and one component that is continuous at the midpoints of interior faces. We prove that the discrete Korn inequality and a discrete inf–sup condition hold uniformly in the mesh size and also for a nonempty Neumann boundary. Based on these two results, we show the well-posedness of the discrete problem. Two counterexamples prove that there is no direct generalization of the Kouhia–Stenberg FEM to three space dimensions: the finite element space with one nonconforming and two conforming piecewise affine components does not satisfy a discrete inf–sup condition with piecewise constant pressure approximations, while finite element functions with two nonconforming and one conforming component do not satisfy a discrete Korn inequality.
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Dissertations / Theses on the topic "Finite element methods (FEMs)"

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Kleditzsch, Stefan, and Birgit Awiszus. "Modeling of Cylindrical Flow Forming Processes with Numerical and Elementary Methods." Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-97124.

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With flow forming – an incremental forming process – the final geometry of a component is achieved by a multitude of minor sequential forming steps. Due to this incremental characteristic associated with the variable application of the tools and kinematic shape forming, it is mainly suitable for small and medium quantities. For the extensive use of the process it is necessary to have appropriate simulation tools. While the Finite-Element-Analysis (FEA) is an acknowledged simulation tool for the modeling and optimization of forming technology, the use of FEA for the incremental forming processes is associated with very long computation times. For this reason a simulation method called FloSim, based on the upper bound method, was developed for cylindrical flow forming processes at the Chair of Virtual Production Engineering, which allows the simulation of the process within a few minutes. This method was improved by the work presented with the possibility of geometry computation during the process.
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Breslavsky, D. V., V. O. Mietielov, O. K. Morachkovsky, S. O. Pashchenko, and О. А. Tatarinova. "Asymptotic methods and finite element method in cyclic creep-damage problems." Thesis, Львівський національний університет ім. І. Франка, 2015. http://repository.kpi.kharkov.ua/handle/KhPI-Press/19395.

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Camacho, Fernando F. "A Posteriori Error Estimates for Surface Finite Element Methods." UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/21.

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Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases. In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△Γ u = f . The two sources of errors for Surface Finite Elements are a Galerkin error, and a geometric error that comes from replacing the original surface by a computational mesh. A posteriori error estimates on flat domains only have a Galerkin component. We use residual type error estimators to measure the Galerkin error. The geometric component of our error estimate becomes zero if we consider flat domains, but otherwise has the same order as the residual one. This is different from the available energy norm based error estimates on surfaces, where the importance of the geometric components diminishes asymptotically as the mesh is refined. We use our results to implement an Adaptive Surface Finite Element Method. An important tool for proving a posteriori error bounds for non smooth functions is the Scott-Zhang interpolant. A refined version of a standard Scott-Zhang interpolation bound is also proved during our analysis. This local version only requires the interpolated function to be in a Sobolev space defined over an element T instead of an element patch containing T. In the last section we extend our elliptic results to get estimates for the surface heat equation ut − △Γ u = f using the elliptic reconstruction technique.
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Wang, Sili. "An ABAQUS Implementation of the Cell-based Smoothed Finite Element Method Using Quadrilateral Elements." University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1416233762.

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Witkowski, Thomas. "Software concepts and algorithms for an efficient and scalable parallel finite element method." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-141651.

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Software packages for the numerical solution of partial differential equations (PDEs) using the finite element method are important in different fields of research. The basic data structures and algorithms change in time, as the user\'s requirements are growing and the software must efficiently use the newest highly parallel computing systems. This is the central point of this work. To make efficiently use of parallel computing systems with growing number of independent basic computing units, i.e.~CPUs, we have to combine data structures and algorithms from different areas of mathematics and computer science. Two crucial parts are a distributed mesh and parallel solver for linear systems of equations. For both there exists multiple independent approaches. In this work we argue that it is necessary to combine both of them to allow for an efficient and scalable implementation of the finite element method. First, we present concepts, data structures and algorithms for distributed meshes, which allow for local refinement. The central point of our presentation is to provide arbitrary geometrical information of the mesh and its distribution to the linear solver. A large part of the overall computing time of the finite element method is spend by the linear solver. Thus, its parallelization is of major importance. Based on the presented concept for distributed meshes, we preset several different linear solver methods. Hereby we concentrate on general purpose linear solver, which makes only little assumptions about the systems to be solver. For this, a new FETI-DP (Finite Element Tearing and Interconnect - Dual Primal) method is proposed. Those the standard FETI-DP method is quasi optimal from a mathematical point of view, its not possible to implement it efficiently for a large number of processors (> 10,000). The main reason is a relatively small but globally distributed coarse mesh problem. To circumvent this problem, we propose a new multilevel FETI-DP method which hierarchically decompose the coarse grid problem. This leads to a more local communication pattern for solver the coarse grid problem and makes it possible to scale for a large number of processors. Besides the parallelization of the finite element method, we discuss an approach to speed up serial computations of existing finite element packages. In many computations the PDE to be solved consists of more than one variable. This is especially the case in multi-physics modeling. Observation show that in many of these computation the solution structure of the variables is different. But in the standard finite element method, only one mesh is used for the discretization of all variables. We present a multi-mesh finite element method, which allows to discretize a system of PDEs with two independently refined meshes
Softwarepakete zur numerischen Lösung partieller Differentialgleichungen mit Hilfe der Finiten-Element-Methode sind in vielen Forschungsbereichen ein wichtiges Werkzeug. Die dahinter stehenden Datenstrukturen und Algorithmen unterliegen einer ständigen Neuentwicklung um den immer weiter steigenden Anforderungen der Nutzergemeinde gerecht zu werden und um neue, hochgradig parallel Rechnerarchitekturen effizient nutzen zu können. Dies ist auch der Kernpunkt dieser Arbeit. Um parallel Rechnerarchitekturen mit einer immer höher werdenden Anzahl an von einander unabhängigen Recheneinheiten, z.B.~Prozessoren, effizient Nutzen zu können, müssen Datenstrukturen und Algorithmen aus verschiedenen Teilgebieten der Mathematik und Informatik entwickelt und miteinander kombiniert werden. Im Kern sind dies zwei Bereiche: verteilte Gitter und parallele Löser für lineare Gleichungssysteme. Für jedes der beiden Teilgebiete existieren unabhängig voneinander zahlreiche Ansätze. In dieser Arbeit wird argumentiert, dass für hochskalierbare Anwendungen der Finiten-Elemente-Methode nur eine Kombination beider Teilgebiete und die Verknüpfung der darunter liegenden Datenstrukturen eine effiziente und skalierbare Implementierung ermöglicht. Zuerst stellen wir Konzepte vor, die parallele verteile Gitter mit entsprechenden Adaptionstrategien ermöglichen. Zentraler Punkt ist hier die Informationsaufbereitung für beliebige Löser linearer Gleichungssysteme. Beim Lösen partieller Differentialgleichung mit der Finiten Elemente Methode wird ein großer Teil der Rechenzeit für das Lösen der dabei anfallenden linearen Gleichungssysteme aufgebracht. Daher ist deren Parallelisierung von zentraler Bedeutung. Basierend auf dem vorgestelltem Konzept für verteilten Gitter, welches beliebige geometrische Informationen für die linearen Löser aufbereiten kann, präsentieren wir mehrere unterschiedliche Lösermethoden. Besonders Gewicht wird dabei auf allgemeine Löser gelegt, die möglichst wenig Annahmen über das zu lösende System machen. Hierfür wird die FETI-DP (Finite Element Tearing and Interconnect - Dual Primal) Methode weiterentwickelt. Obwohl die FETI-DP Methode vom mathematischen Standpunkt her als quasi-optimal bezüglich der parallelen Skalierbarkeit gilt, kann sie für große Anzahl an Prozessoren (> 10.000) nicht mehr effizient implementiert werden. Dies liegt hauptsächlich an einem verhältnismäßig kleinem aber global verteilten Grobgitterproblem. Wir stellen eine Multilevel FETI-DP Methode vor, die dieses Problem durch eine hierarchische Komposition des Grobgitterproblems löst. Dadurch wird die Kommunikation entlang des Grobgitterproblems lokalisiert und die Skalierbarkeit der FETI-DP Methode auch für große Anzahl an Prozessoren sichergestellt. Neben der Parallelisierung der Finiten-Elemente-Methode beschäftigen wir uns in dieser Arbeit mit der Ausnutzung von bestimmten Voraussetzung um auch die sequentielle Effizienz bestehender Implementierung der Finiten-Elemente-Methode zu steigern. In vielen Fällen müssen partielle Differentialgleichungen mit mehreren Variablen gelöst werden. Sehr häufig ist dabei zu beobachten, insbesondere bei der Modellierung mehrere miteinander gekoppelter physikalischer Phänomene, dass die Lösungsstruktur der unterschiedlichen Variablen entweder schwach oder vollständig voneinander entkoppelt ist. In den meisten Implementierungen wird dabei nur ein Gitter zur Diskretisierung aller Variablen des Systems genutzt. Wir stellen eine Finite-Elemente-Methode vor, bei der zwei unabhängig voneinander verfeinerte Gitter genutzt werden können um ein System partieller Differentialgleichungen zu lösen
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Pacheco, Roman Oscar. "Evaluation of Finite Element simulation methods for High Cycle Fatigue on engine components." Thesis, Linköpings universitet, Mekanik och hållfasthetslära, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-148779.

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This document reflects the results of evaluating three computational methods to analyse the fatigue life of components mounted on the cylinder block; two currently in use at Scania and one that has been further developed from its previous state. Due to the cost of testing and the exponential increase in computational power throughout the years, the cheaper computational analyses have gained in popularity. When a component is mounted in a fairly complex assembly such as an engine, simplifications need to be made in order to make the analysis as less expensive as possible while keeping a high degree of accuracy. The methods of Virtual Vibrations, VROM and VFEM have been evaluated and compared in terms of accuracy, computational cost, user friendliness and general capacities. Additionally, the method VFEM has been further developed and improved from its previous state. A in-depth investigation regarding the differences of the methods has been conducted and improvements to make them more efficient are suggested herein. The reader can also find a decision matrix and recommendations regarding which method to use depending on the general characteristics of the component of interest and other factors. Two components, which differ in complexity and mounting nature, have been used to do the research.
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Cascio, Michele. "Coupled Molecular Dynamics and Finite Element Methods for the simulation of interacting particles and fields." Doctoral thesis, Università di Catania, 2019. http://hdl.handle.net/10761/4120.

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The dynamical simulation of many particle systems is currently a widespread technique in many fields: e.g. nuclear and atomic physics, computational material science, computational chemistry, molecular biology and pharmacology. Under the locution Molecular Dynamics (MD) we can regroup a variety of approaches and numerical codes, whereas the commonalities are: 1) the atomistic (or nuclear) resolution (i.e. particles are atoms or nucleons), 2) the force derivation, starting from the systems configuration, through semi-classical (also called semi-empirical) or quantum mechanics based theoretical frameworks, 3) the (generally explicit) numerical integration of the Newton-like equations of the motions to simulate the system kinetics. Within this scheme methodology variations can be found in the literature, but it is undoubtedly valid to qualify the MD meaning in the field of the scientific computation. The general scope of this Thesis work is the extension of the MD methods to the study of kinetics of larger particle (i.e. from mesoscopic dimensions and above), where effective particle-particle interactions are mediated by a field evolving self-consistently with the many particles system. This objective is mainly motivated by the applications of the method to control and predict the manipulation of mesoscopic (electrically) neutral particles by means of electromagnetic (e.m.) interactions: i.e. exploiting the so called dielectrophoresis (DEP) phenomena in the systems of electromechanical particles (EMPs). This is the specific case of study here considered, but in principle the methodology can applied after suitable adaptation to also other systems.
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Szegda, Damian. "Experimental investigation and computational modelling of the thermoforming process of thermoplastic starch." Thesis, Brunel University, 2009. http://bura.brunel.ac.uk/handle/2438/3445.

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Plastic packaging waste currently forms a significant part of municipal solid waste and as such is causing increasing environmental concerns. Such packaging is largely non-biodegradable and is particularly difficult to recycle or to reuse due largely to its complex compositions. Apart from limited recycling of some easily identifiable packaging wastes that can be separated economically, such as bottles, most packaging waste ends up in landfill sites. In recent years, in an attempt to address this problem in plastic packaging, the development of packaging materials from renewable plant resources has received increasing attention and a wide range of bioplastic materials based on starch are now available. Environmentally these bioplastic materials also reduce reliance on oil resources and have the advantage that they are biodegradable and can be composted upon disposal to reduce the environmental impact. Many food packaging containers are produced by thermoforming processes in which thin sheets are inflated under pressure into moulds to produce the required thin -wall structures. Hitherto these thin sheets have almost exclusively been made of oilbased polymers and it is for these that computational models of thermoforming processes have been developed. Recently, in the context of bioplastics, commercial thermoplastic starch sheet materials have been developed. The behaviour of such materials is influenced both by temperature and, because of the inherent hydrophilic characteristics of the materials, by moisture content. Both of these aspects affect the behaviour of bioplastic sheets during the thermoforming process. This thesis describes experimental work and work on the computational modelling of thermoforming processes for thermoplastic starch sheets using a commercially available material. The experimental work has been carried in order to characterise the deformation behaviour of the material with regard to different temperature, moisture contents and strain rates. Thermoforming of the material was performed and samples produced were used for comparison and verification of the computational modelling of the thermoforming process. In the first attempt to model the thermoforming process, a hyperelastic constitutive equation was established to approximate the material behaviour taking account of the combined effects of temperature and moisture content and a simple ii membrane model with constrained deformation was used to model an axisymmetric case of thermoforming. Simulations with this model showed that moisture content mostly affects the pressure required to push the sheet into the mould while moisture variation during thermoforming has little effect on the final thickness distribution of the product. Considerable discrepancies were found in the thickness distribution between the predictions from the model and the experimental measurements. Further attempts were made to take account of the elasto-plastic behaviour of the material and a more complex three-dimensional FE model was developed using ANSYS/LS-DYNA. Based on the findings in the simpler modelling work, no attempt was made to incorporate the moisture content effect on material behaviour but the material parameters for the elasto-plastic constitutive equation were obtained from high speed tensile tests so that moisture variation during thermoforming could be minimised and neglected. The predictions from this model have led to significant improvements in prediction of the thickness distribution which has become much closer to the experimental measurements in comparison with the hyperelastic model. This work provides some important insights into thermoforming of thermoplastic starch materials: a) Deformation behaviour of such materials depends strongly on the moisture content and the temperature, both of which affect behaviour during thermoforming processes, including the preheating stage; b) moisture variation during the thermoforming process has a significant effect on the pressure required for the deformation. This also leads to variation of moisture content distribution in the final product, which in turn affects the material properties such as ductility or impact strength at different positions in the thermoformed structure; c) thermoforming of thermoplastic starch materials can be simulated more accurately by an elasto-plastic model and the LS-DYNA algorithm in comparison with a hyperelastic membrane model. This work has provided useful information on thermoforming of thermoplastic starch materials with particular reference to the design of thermoforming tools and to the careful control of processing conditions including preheating. It has also laid a solid foundation for future work on how the moisture variation impacts on the formation of defects such as incomplete forming due to material hardening and fracture due to loss of ductility.
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Ferro, Newton Carlos Pereira. "Uma combinação MEC/MEF para análise de interação solo-estrutura." Universidade de São Paulo, 1999. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-08122017-102331/.

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No presente trabalho, uma combinação do método dos elementos de contorno (MEC) com o método dos elementos finitos (MEF) é apresentada para a análise da interação entre estacas e o solo, considerado como um meio infinito tridimensional e homogêneo. O meio contínuo tridimensional de domínio infinito é modelado pelo MEC, enquanto as estacas consideradas como elementos reticulares são tratadas pelo MEF. As equações das estacas oriundas do método dos elementos finitos são combinadas com as do meio contínuo obtidas a partir do método dos elementos de contorno, resultando em um sistema completo de equações, que convenientemente tratadas, proporcionam a formulação de coeficientes de rigidez do conjunto solo-estacas. Finalmente, uma formulação para a análise do comportamento não-linear do solo na interface com a estaca é desenvolvida, tornando o modelo mais abrangente.
In the present work a combination of the Boundary Element Method (BEM) and the Finite Element Method (FEM) is used for pile-soil interaction analyses, considering the soil as a homogeneous, three-dimensional and infinite medium. The three-dimensional infinite continuous medium is modeled by the BEM, and the piles are, considered as beam elements, modeled by the FEM. This combination also is used for studying the interaction of plates sitting on a continuous medium. The pile equations generated from the FEM are combined with the medium equations generated from the BEM, resulting a complete equation system. Manipulating properly this equation system, a set of stiffness coefficients for the system soil-pile is obtained. Finally, to make the model more comprehensive, it presented a formulation to take into account the soil nonlinear behavior at the pile interface.
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Janhunen, Tony, and Martin Mikus. "Dynamisk analys och utmattningskontroll med hjälp av fältmätningar och FEM : Fallstudie över SL:s Bro norr om Söderströmsbron." Thesis, KTH, Structural Design and Bridges, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-12228.

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Följande examensarbete omfattar en fallstudie av Bro norr om Söderströmsbron, en tunnelbanebro i stål med fyra spår. Den byggdes 1956 som en del av förbindelsen mellan station Gamla stan och station Slussen i Stockholm. I fallstudien, som är ett samarbete mellan KTH och SL, ingår att bedöma brons dynamiska egenskaper, tillstånd avseende utmattning samt att skapa en finita elementmodell av bron. Vidare begränsas fallstudien till brokonstruktionen för det spår som går närmast slussen mellan Mälaren och Saltsjön, och som i dagsläget utgör gröna tunnelbanelinjen mot Farsta strand, Hagsätra och Skarpnäck.

Under 2005 trafikerades det aktuella spåret under högtrafik av 30 tåg i timmen och under lågtrafik av 15 tåg i timmen. När tåg passerar visar bron stora förskjutningar och glapp mellan sliprar och underliggande stålkonstruktion. Dessa förskjutningar skapar spänningar i stålet och avgörande för brons tillstånd avseende utmattning är antalet skadliga spänningsvidder vid kritiska snitt som inträffat sedan brons färdig­ställande.

Dagens spänningsvidder mäts med hjälp av töjningsgivare placerade i fältmitt. Mätningen har utförts av KTH, avdelningen för Brobyggnad i samband med examens­arbetet. Av intresse är utmattningsrisk för svetsad anslutning mellan lång- och tvär­balkar. Utmattningsrisken beräknas dels med typiserade spänningskollektiv enligt BSK 07, dels med verkliga spänningskollektiv enligt Palmgren-Miners delskade­hypotes. Enligt båda metoderna konstateras utmattningshållfastheten vara uttömd, med reservation för förbandsklasser och partialkoefficienter. Kollektivparametern κ enligt BSK 07, vilken vid dimensionering beaktar spänningskollektivets form, uppskattas vara närmare 2/3 än SL:s nuvarande värde 5/6.

Ur responsen från givarna konstateras att den dynamiska förstoringsfaktorn vid 60 km/h varierar mellan 0.63 och 1.43, vilket visar att brons respons har ett stort dynamiskt innehåll.

En finita elementmodell skapas i Abaqus med hjälp av Matlab, med syftet att komplettera resultat från mätningar. I modellen studeras töjning, vertikal förskjutning och acceleration, dynamisk förstoringsfaktor och egenmoder. Den statiska responsen för modell och bro konstateras vara snarlik.


This thesis includes a case study of the Bro norr om Söderströmsbron, a steel subway bridge with four rail tracks. The bridge was built in 1956 as a part of the connection between the two subway stations Gamla stan and Slussen in Stockholm. The case study, which is a collaboration between KTH and SL, includes an evaluation of the dynamic properties of the bridge, in which condition it is regarding fatigue and the creation of a finite element model of the bridge. The case study is limited to the construction carrying the rail track closest to the lock between Mälaren and Saltsjön, and now represents the green subway line towards Farsta strand, Hagsätra and Skarpnäck.

In 2005, the train frequency during rush hour was 30 trains per hour and during low traffic 15 trains per hour. When a train crosses, the bridge shows large displacements and gaps between the sleepers and the underlying steel structure. The displacements cause stresses in the steel and crucial to the bridge fatigue state is the number of damaging stress ranges that have occurred since the opening of the bridge.

The current stress variations are measured using strain gauges positioned in the mid-span. Measurements were carried out by KTH, division of Structural Design & Bridges, during this thesis. Of key interest is a welded edge between the main- and crossbeams. The risk of fatigue is calculated using standardised stress ranges according to BSK 07 and Palmgren-Miners cumulative damage theory. According to both methods, the fatigue life of the bridge is exceeded, with reservations to the detail category and partial coefficients. The stress collective parameter κ according to BSK 07, which in design accounts for the distribution of the stress collective, is estimated closer to 2/3 than SL’s present value of 5/6.

According to the strain gauges, the dynamic amplification factor at 60 km/h varies between 0.63 and 1.43, indicating that the bridge’s response has a large dynamic content.

A finite element model is created in Abaqus using Matlab, with the purpose of complementing results from the measurements. In the model, the strain, vertical displacements and acceleration, dynamic amplification and natural modes are studied. The static response of the model and bridge were found to be similar.


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Books on the topic "Finite element methods (FEMs)"

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Whiteley, Jonathan. Finite Element Methods. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49971-0.

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Schwarz, H. R. Finite element methods. London: Academic, 1988.

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Schwarz, Hans Rudolf. Finite element methods. London: Academic Press, 1988.

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Papadopoulos, Vissarion, and Dimitris G. Giovanis. Stochastic Finite Element Methods. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-64528-5.

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Fix, George J. Singular finite element methods. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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Fix, George J. Singular finite element methods. Hampton, Va: ICASE, 1987.

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Wriggers, P. Nonlinear finite element methods. Berlin: Springer, 2008.

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T, Leung A. Y., ed. Finite element methods in dynamics. Beijing: Science Press, 1991.

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Sabonnadière, Jean-Claude, and Jean-Louis Coulomb. Finite Element Methods in CAD. Boston, MA: Springer US, 1987. http://dx.doi.org/10.1007/978-1-4615-9879-4.

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Roters, Franz, Philip Eisenlohr, Thomas R. Bieler, and Dierk Raabe. Crystal Plasticity Finite Element Methods. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA, 2010. http://dx.doi.org/10.1002/9783527631483.

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Book chapters on the topic "Finite element methods (FEMs)"

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Kaveh, A. "Optimal Force Method for FEMs: Low Order Elements." In Computational Structural Analysis and Finite Element Methods, 215–80. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02964-1_6.

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Kaveh, A. "Optimal Force Method for FEMS: Higher Order Elements." In Computational Structural Analysis and Finite Element Methods, 281–339. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02964-1_7.

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Beuchler, Sven. "Inexact Additive Schwarz Solvers for hp-FEM Discretizations in Three Dimensions." In Advanced Finite Element Methods and Applications, 91–108. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30316-6_4.

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Schneider, René. "A Review of Anisotropic Refinement Methods for Triangular Meshes in FEM." In Advanced Finite Element Methods and Applications, 133–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30316-6_6.

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Cuvelier, C., A. Segal, and A. A. van Steenhoven. "Error Analysis of the FEM." In Finite Element Methods and Navier-Stokes Equations, 396–406. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-010-9333-0_13.

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Pechstein, Clemens, and Clemens Hofreither. "A Rigorous Error Analysis of Coupled FEM-BEM Problems with Arbitrary Many Subdomains." In Advanced Finite Element Methods and Applications, 109–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30316-6_5.

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Fröhlich, Peter. "Finite Elemente Methode." In FEM-Anwendungspraxis, 12–23. Wiesbaden: Vieweg+Teubner Verlag, 2005. http://dx.doi.org/10.1007/978-3-663-10053-9_2.

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Fröhlich, Peter. "Die Finite Elemente Methode." In FEM-Leitfaden, 13–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79383-7_2.

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Klein, Bernd. "Grundgleichungen der nichtlinearen Finite-Element-Methode." In FEM, 247–65. Wiesbaden: Vieweg+Teubner, 2010. http://dx.doi.org/10.1007/978-3-8348-9388-8_10.

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Klein, Bernd. "Grundgleichungen der linearen Finite-Element- Methode." In FEM, 16–33. Wiesbaden: Vieweg+Teubner, 2010. http://dx.doi.org/10.1007/978-3-8348-9388-8_3.

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Conference papers on the topic "Finite element methods (FEMs)"

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Liu, G. R. "On Smoothed Finite Element Methods." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62239.

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The paper presents an overview of the smoothed finite element methods (S-FEM) which are formulated by combining the existing standard FEM with the strain smoothing techniques used in the meshfree methods. The S-FEM family includes five models: CS-FEM, NS-FEM, ES-FEM, FS-FEM and α-FEM (a combination of NS-FEM and FEM). It was originally formulated for problems of linear elastic solid mechanics and found to have five major properties: (1) S-FEM models are always “softer” than the standard FEM, offering possibilities to overcome the so-called overly-stiff phenomenon encountered in the standard the FEM models; (2) S-FEM models give more freedom and convenience in constructing shape functions for special purposes or enrichments (e.g, various degree of singular field near the crack-tip, highly oscillating fields, etc.); (3) S-FEM models allow the use of distorted elements and general n-sided polygonal elements; (4) NS-FEM offers a simpler tool to estimate the bounds of solutions for many types of problems; (5) the αFEM can offer solutions of very high accuracy. With these properties, the S-FEM has rapidly attracted interests of many. Studies have been published on theoretical aspects of S-FEMs or modified S-FEMs or the related numerical methods. In addition, the applications of the S-FEM have been also extended to many different areas such as analyses of plate and shell structures, analyses of structures using new materials (piezo, composite, FGM), limit and shakedown analyses, geometrical nonlinear and material nonlinear analyses, acoustic analyses, analyses of singular problems (crack, fracture), and analyses of fluid-structure interaction problems.
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Kaszynski, Alexander A., Joseph A. Beck, and Jeffrey M. Brown. "Automated Finite Element Model Mesh Updating Scheme Applicable to Mistuning Analysis." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-26925.

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Advancement of optical geometric measurement hardware has enabled the construction of accurate 3D tessellated models for a wide range of turbomachinery components. These tessellated models can be reverse-engineered into computer-aided design (CAD) models and input into grid generation software for finite element analyses. However, generating a CAD model from scan data is a time consuming and cumbersome process requiring significant user-involvement for even a single model. While it is possible to generate finite element models (FEMs) directly from tessellated data, current direct-grid methods produce unstructured grids that can introduce fictitious, numerical mistuning in these models, obscuring geometric mistuning. Nonetheless, as-measured scan data captured in a structured grid is essential for accurate geometric mistuning analyses, provided the tessellated scan data can be rapidly and accurately transformed into a FEM. This paper outlines and demonstrates an approach for rapidly generating structured FEMs for a population of integrally bladed rotors (IBRs) without requiring the arduous task of generating a CAD model for each as-measured IBR. This is accomplished by morphing the structured mesh of a nominal model to the tessellated data set collected from an optical scanner. It is shown that the fidelity and structure of these FEMs can be utilized for accurate mistuning analyses.
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Geng, Jia, Xingwu Zhang, Xuefeng Chen, and Xiaofeng Xue. "High-Frequency Vibration Analysis of Thin Plate Based on B-Spline Wavelet on Interval Finite Element Method." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65487.

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For the dynamic analysis of thin plate bending problems, the Finite Element Methods (FEMs) are the most commonly used numerical techniques in engineering. However, due to the deficiency of low computing efficiency and accuracy, the FEMs can’t be directly used to effectively evaluate dynamic analysis of thin plate with high modal density within low-high frequency domain. In order to solve this problem, the Wavelet Finite Element Methods (WFEMs) has been introduced to solve the problem by improving the computing efficiency and accuracy in this paper. Due to the properties of multi-resolution, the WFEMs own excellently high computing efficiency and accuracy for structure analysis. Furthermore, for the destination of predicting dynamic response of thin plate within high frequency domain, this paper introduces the Multi-wavelet element method based on c1 type wavelet thin plate element and a new assembly procedure to significantly promote the calculating efficiency and accuracy which aim at breaking up the limitation of frequency domain when using the existing WFEMs and traditional FEMs. Besides, the numerical studies are applied to certify the validity of the method by predicting state response of thin plate within 0∼1000Hz based on a special numerical example with high modal density. According to the literature, the frequency domain between 0 to 1000Hz contains the low-high frequency domain aiming at the numerical example. The numerical results show excellent agreement with the reference solutions captured by FEM and analytical expressions respectively. Among these, it is noteworthy that the relative errors between the analytical solutions and numerical solution are less than 0.4% when the dynamic response involved with 1000 modes.
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Vavalle, Nicholas A., Daniel P. Moreno, Joel D. Stitzel, and F. Scott Gayzik. "Application of a Standard Quantitative Comparison Method to Assess a Full Body Finite Element Model in Frontal Impact." In ASME 2013 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/sbc2013-14787.

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Advanced human body finite element models (FEMs) are gaining popularity in the study of injury biomechanics [1, 2]. FEMs must be validated to ensure that model outputs correspond to experimentally-observed phenomena. During the validation process researchers often qualitatively compare the model response to a laboratory experiment. However, a more rigorous approach is to use quantitative methods. Often, these methods attempt to parse the error contributions of phase, magnitude, and a shape factor. The purpose of this study is to apply one such method for validation quantification, called the enhanced error assessment of response time histories (EEARTH), to a model that was recently developed. The EEARTH method is anticipated to be part of the forthcoming ISO standard (ISO/TC 22/SC 10/WG 4) on comparing model outcomes to experimental data. The subject of this study is the Global Human Body Models Consortium (GHBMC) 50 th percentile male seated model (M50). The mission statement of the consortium is to develop a set of biofidelic computational human body models to aid in the study injury biomechanics and safety system enhancement.
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Xin, Chen, Qin Ye, Yuan Xiguang, Zhang Ping, and Sun Jian. "Updating Finite Element Model of Combined Structures on the Basis of Dynamic Test Results." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dac-1061.

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Abstract According to the real situation, a new method of updating the finite element model (FEM) of a combined structure step by step is proposed in this paper. It is assumed that there are two types of error when establishing the FEMs. One of them results from the simplifications, in fact, it is severe for complicated structures, which usually assume many simplifications; the other is from the process of identifying structural joint parameters. For this reason, it is recommended that the FEM should be established in two stages. At the first stage, the local physical parameters relating with the simplifications are corrected by using the dynamic test data of the corresponding substructures. Then, the structural joint parameters that link the substructures are corrected by the dynamic test data of the combined structure as a whole. The updating formula is presented and proved, and its algorithm is also described. And the experimental results show that the efficiency and accuracy of the proposed method are quite satisfactory.
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Tu, Tse-Yi, Paul C. P. Chao, Yung-Pin Lee, and Yung-Hua Kao. "Optimal Design and Experimental Validation of a New No-Cuff Blood Pressure Sensor Based on a New Finite Element Model." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35552.

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A new multi-physics finite element model (FEM) on the vibration of the radial artery on the wrist is built by this study to predict vibration of wrist artery vessel vibration and then diastolic and systolic blood pressures. The FEM includes the sensor of gel capsule and strain-sensing electrodes, skin, bones and muscles. The vibrations of skin surface and the sensor module are successfully simulated by the established FEM. The resulted vibratory deformation of the sensor electrodes are further transformed to resistance variations to mimic realistic electronics of the front-end readout circuit via establishing a cross-discipline sub-FEM model. The established FEM can is particularly customized to varied ages, weights, heights, genders, and special cardiovascular diseases of users. The customization can be performed in a fashion of one-time calibration by medical staff and/or medical staff. With the customized FEM in high accuracy level, the diastolic and systolic pressures can be accurately predicted by the simulated output resistance variation. Based on simulation FEMs, the design of the pulse sensor is successfully optimized via the processes of Taguchi and numerical methods. The measurements are also conducted to a dozen of subjects. It shows that the designed novel blood pressure sensor is capable of sensing the blood pressure to require accuracy level of the error less than 10% as compared to commercial counterparts with a cumbersome cuff.
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Kaszynski, Alexander A., Joseph A. Beck, and Jeffrey M. Brown. "Harmonic Convergence Estimation Through Strain Energy Superconvergence." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-44140.

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Grid convergence in finite element analysis, despite a wide variety of tools available to date, remains an elusive and challenging task. Due to the complex and time consuming process of remeshing and solving the finite element model (FEM), convergence studies can be part of the most arduous portion of the modeling process and can even be impossible with FEMs unassociated with CAD. Existing a posteriori methods, such as relative error in the energy norm, provide a near arbitrary indication of the model convergence for eigenfrequencies. This paper proposes a new approach to evaluate the harmonic convergence of an existing model without conducting a convergence study. Strain energy superconvergence takes advantage of superconvergence points within a FEM and accurately recovers the strain energy within the model using polyharmonic splines, thus providing a more accurate estimate of the system’s eigenfrequencies without modification of the FEM. Accurate eigenfrequencies are critical for designing for airfoil resonance avoidance and mistuned rotor response prediction. Traditional error estimation strategies fail to capture harmonic convergence as effectively as SES, potentially leading to a less accurate airfoil resonance and rotor mistuning prediction.
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Dong, Tianyu, Shenfang Yuan, and Tianxiang Huang. "Beam Element-Based Inverse Finite Element Method for Shape Reconstruction of a Wing Structure." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-73502.

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Abstract Shape sensing technology is the basis for the control system of the adaptive deformation wing. There are various deformation reconstruction methods based on strain information. The inverse Finite Element Method (iFEM) is popular for the advantages of no need to know the structural material and load information. However, iFEM, which mainly uses shell elements, has problems when applied on purely bending beam structures such as large amount of calculation and the waste of more than half of the element’s degrees of freedom. To solve this problem, this paper proposes a beam element-based inverse finite element method. This paper firstly derives the theoretical process of the beam element-based inverse finite element method based on the classical beam bending theory and the least squares variational principle. Then, the proposed method is applied on the main load-bearing structure of the fishbone shape of an adaptive deformable wing. COMSOL is used to calculate the displacement and strain and the FEM strain can be used as the input of the beam element-based inverse finite element method to calculate the reconstruction displacement. At last, the effectiveness and accuracy of the proposed method are verified by comparing the error of reconstruction and simulation displacement.
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Ianculescu, Cristian, and Lonny L. Thompson. "Parallel Iterative Finite Element Solution Methods for Three-Dimensional Acoustic Scattering." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-55266.

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Efficient and scalable parallel solution methods are presented for three-dimensional acoustic scattering problems on unbounded domains. A separable boundary is applied at an arbitrary distance from the scatterer, to define a finite computational domain, and thus enable application of the Finite Element Method (FEM). A modified non-reflecting Dirichlet-to-Neumann (DtN) boundary condition is applied along the truncation boundary, in the form of local second-order differential operators, and a harmonic series. For elongated scatterers (e.g. a submarine or ship), suitable finite element formulations are derived and implemented on spheroidal coordinates, reducing the size of computational domain without affecting the accuracy of the numerical solution. The outer-product structure of the DtN boundary operator is exploited to efficiently handle non-locality in an iterative process. Computational performance of the DtN condition is analyzed and shown to be significantly more cost-effective when compared with local boundary conditions producing similar accuracy. The effective use of non-local DtN conditions in a 32-processor parallel distributed memory environment is demonstrated for a three-dimensional submarine scatterer. By exploiting the outer-product structure, it is shown that communication costs due to non-locality depend only on a small number of harmonics in the DtN operator, and thus have little impact on the scalability of the solution on multiple processors.
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Kwon, Y. W. "Coupling of Lattice Boltzmann and Finite Element Methods for Fluid-Structure Interaction Application." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93212.

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In order to analyze the Fluid-Structure Interaction (FSI) between a flow and a flexible structure, an algorithm was presented to couple the Lattice Boltzmann Method (LBM) and the Finite Element Method (FEM). The LBM was applied to the fluid dynamics while the FEM was applied to the structural dynamics. The two solution techniques were solved in a staggered manner, i.e. one solver after another. Continuity of the velocity and traction was applied at the interface boundaries between the fluid and structural domains. Furthermore, so as to make the fluid-structure interface boundary more flexible in terms of the computational modeling perspective, a technique was also developed for the LBM so that the interface boundary might not coincide with the fluid lattice mesh. Some example problems were presented to demonstrate the developed techniques.
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Reports on the topic "Finite element methods (FEMs)"

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Martín, A., L. Cirrottola, A. Froehly, R. Rossi, and C. Soriano. D2.2 First release of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.010.

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This document presents a description of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. As it is discussed in Section 1.3.2 of part B of the project proposal there are two parallel research lines aimed at developing scalable adaptive mesh refinement (AMR) algorithms and implementations. The first one is based on using octree-based mesh generation and adaptation for the whole simulation in combination with unfitted finite element methods (FEMs) and the use of algebraic constraints to deal with non-conformity of spaces. On the other hand the second strategy is based on the use of an initial octree mesh that, after make it conforming through the addition of templatebased tetrahedral refinements, is adapted anisotropically during the calculation. Regarding the first strategy the following items are included:
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Costa, Timothy, Stephen D. Bond, David John Littlewood, and Stan Gerald Moore. Peridynamic Multiscale Finite Element Methods. Office of Scientific and Technical Information (OSTI), December 2015. http://dx.doi.org/10.2172/1227915.

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Dolbow, John, Ziyu Zhang, Benjamin Spencer, and Wen Jiang. Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM). Office of Scientific and Technical Information (OSTI), September 2015. http://dx.doi.org/10.2172/1244633.

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Kirby, Robert M., and Robert Haimes. Visualization of High-Order Finite Element Methods. Fort Belvoir, VA: Defense Technical Information Center, August 2008. http://dx.doi.org/10.21236/ada500484.

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Holst, M. Research on parallel adaptive finite element methods. Office of Scientific and Technical Information (OSTI), November 2000. http://dx.doi.org/10.2172/15013124.

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Binev, Peter, Wolfgang Dahmen, and Ron DeVore. Adaptive Finite Element Methods with Convergence Rates. Fort Belvoir, VA: Defense Technical Information Center, January 2003. http://dx.doi.org/10.21236/ada640658.

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Kirby, Robert M., and Robert Haimes. Visualization of High-Order Finite Element Methods. Fort Belvoir, VA: Defense Technical Information Center, March 2013. http://dx.doi.org/10.21236/ada578239.

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Brannick, James. Finite Element Methods and Multigrid Methods for the Dirac Equation. Office of Scientific and Technical Information (OSTI), January 2017. http://dx.doi.org/10.2172/1341949.

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Garikipati, Krishna, and Jakob T. Ostien. Discontinuous Galerkin finite element methods for gradient plasticity. Office of Scientific and Technical Information (OSTI), October 2010. http://dx.doi.org/10.2172/1008112.

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Aronson, E. A. Modeling of magnetic devices with finite-element methods. Office of Scientific and Technical Information (OSTI), March 1989. http://dx.doi.org/10.2172/6363054.

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