scholarly journals General consistency of strong discontinuity kinematics in Embedded Finite Element Method (E-FEM) formulations

2021 ◽  
Author(s):  
Alejandro Ortega Laborin ◽  
Yann MALECOT ◽  
Emmanuel ROUBIN ◽  
Laurent DAUDEVILLE
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strong Discontinuity ◽  
Element Formulation ◽  
The Novel ◽  
Local Fracture ◽  
Multiple Dimensions ◽  
Kinematic Models ◽  
Algebraic Constraints ◽  
Element Method

This paper discusses the consistency of the theoretical basis behind the kinematic models of strong discontinuity methods for local fracture simulations using the Embedded Finite Element Method (E-FEM). A brief review is made on the elemental enhancement functions from the current E-FEM literature and how previous works managed to model mode I (normal) and mode II (parallel) fracture kinematics in multiple dimensions. Further analysis is made on how these approaches also introduce unintended mesh dependencies and basic kinematic inconsistencies of the fracture model with respect to its hosting element. Notable work from a few authors discussing some of these issues and their contributions to resolve them is reviewed as well. Based on this analysis, a new proposal of strong discontinuity enhancement functions is introduced to ensure a broader kinematic coherence within the element and to avoid the observed theoretical faults. This is done by making a more extensive use of the flexibility granted by the Hu-Washizu variational principle and by introducing new algebraic constraints that will ensure more correct fracture kinematics without compromising the acknowledged simplicity of the whole E-FEM framework. Element-level simulations are done to compare the outputs within a group of selected formulation approaches, including the novel proposal. Simulations show that the new element formulation grants a wider level of basic kinematic coherence between the local fracture outputs and element kinematics themselves, demonstrating an increase in robustness that might drive the usefulness and competitiveness of E-FEM techniques for fracture simulations to a higher level.

scholarly journals General Consistency of Strong Discontinuity Kinematics in Embedded Finite Element Method (E-FEM) Formulations

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5640
Author(s):  
Alejandro Ortega Ortega Laborin ◽  
Emmanuel Roubin ◽  
Yann Malecot ◽  
Laurent Daudeville
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strong Discontinuity ◽  
Element Formulation ◽  
The Novel ◽  
Local Fracture ◽  
Element Level ◽  
Depth Study ◽  
Definition Of ◽  
Element Method

This paper performs an in-depth study of the theoretical basis behind the strong discontinuity methods to improve local fracture simulations using the Embedded Finite Element Method (E-FEM). The process starts from a review of the elemental enhancement functions found in current E-FEM literature, providing the reader a solid context of E-FEM fundamentals. A set of theoretical pathologies is then discussed, which prevent current frameworks from attaining full kinematic consistency and introduce unintended mesh dependencies. Based on this analysis, a new proposal of strong discontinuity enhancement functions is presented considering generalised fracture kinematics in a full tridimensional setting and a more robust definition of internal auxiliary functions. Element-level simulations are performed to compare the outputs within a group of selected E-FEM approaches, including the novel proposal. Simulations show that the new element formulation grants a wider level of basic kinematic coherence between the local fracture outputs and element kinematics, demonstrating an increase in robustness that might drive the usefulness of E-FEM techniques for fracture simulations to a higher level.

scholarly journals An interface-enriched generalized finite element method for level set-based topology optimization

2020 ◽  
Vol 63 (1) ◽  
pp. 1-20
Author(s):  
S. J. van den Boom ◽  
J. Zhang ◽  
F. van Keulen ◽  
A. M. Aragón
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Level Set ◽  
Element Formulation ◽  
Generalized Finite Element Method ◽  
Level Set Function ◽  
Analytical Sensitivities ◽  
Generalized Finite Element ◽  
Element Method

AbstractDuring design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems.

A New Stabilized Finite Element Formulation for Solving Radiative Transfer Equation

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
L. Zhang ◽  
J. M. Zhao ◽  
L. H. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Second Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Stabilized Finite Element ◽  
Element Method

A new stabilized finite element formulation for solving radiative transfer equation is presented. It owns the salient feature of least-squares finite element method (LSFEM), i.e., free of the tuning parameter that appears in the streamline upwind/Petrov–Galerkin (SUPG) finite element method. The new finite element formulation is based on a second-order form of the radiative transfer equation. The second-order term will provide essential diffusion as the artificial diffusion introduced in traditional stabilized schemes to ensure stability. The performance of the new method was evaluated using challenging test cases featuring strong medium inhomogeneity and large gradient of radiative intensity field. It is demonstrated to be computationally efficient and capable of solving radiative heat transfer in strongly inhomogeneous media with even better accuracy than the LSFEM, and hence a promising alternative finite element formulation for solving complex radiative transfer problems.

scholarly journals Modelling of triaxial fracture processes in heterogeneous quasi-brittle materials using the Embedded Finite Element Method (E-FEM)

2021 ◽  
Author(s):  
Alejandro Ortega Laborin ◽  
Yann MALECOT ◽  
Emmanuel ROUBIN ◽  
Laurent DAUDEVILLE
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spherical Inclusion ◽  
Brittle Materials ◽  
Three Dimensions ◽  
Strong Discontinuity ◽  
Homogeneous Material ◽  
Fem Model ◽  
Fracture Processes ◽  
Element Method

This paper studies the use of the Embedded Finite Element Method (E-FEM) for the numerical modelling of triaxial fracture processes in non-homogeneous quasi-brittle materials. The E-FEM framework used in this study combines two kinematics enhancements: a weak discontinuity allowing the model to account for material heterogeneities and a strong discontinuity allowing the model to represent local fractures. The strong discontinuity features enriched fracture kinematics that allow the modelling of all typical fracture modes in three dimensions. A brief review is done of past work using similar enriched finite element frameworks to approach this problem. The work continues by establishing the theoretical basis of each kind of discontinuity formulation and their superposition through the Hu-Washizu variational principle. Afterwards, two groups of simulations have been done for discussing the performance of this combined E-FEM model: homogeneous simulations and simple heterogeneous simulations. Simple homogeneous material simulations aim to test the capabilities of the strong discontinuity model featuring full 3-D kinematics. Simple heterogeneous simulations show numerical applications of the model to the problem of a single spherical inclusion embedded into a homogeneous matrix. Comparisons will be made with another E-FEM model considering a single local fracture mode approach to discuss the differences on the representation of fracture physics under all explored conditions. A concluding statement is made on the benefits and complications identified for the E-FEM framework in this kind of applications.

Structural-Acoustic Design at High Frequency Using the Energy Finite Element Method

1995 ◽  
Author(s):  
Robert J. Bernhard ◽  
John E. Huff
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Frequency ◽  
Energy Flow ◽  
Flow Analysis ◽  
Element Formulation ◽  
Joint Models ◽  
Energy Flow Analysis ◽  
Element Method

Abstract Energy flow analysis methods, particularly as implemented using the finite element method, are useful as design techniques for high frequency structural-acoustic applications. In this paper, the derivation of energy flow analysis techniques are summarized. Particular attention is given to the specification of joint models for situations where there is a discontinuity in either geometric properties or material properties. The finite element formulation of this approach is also summarized. A case study is included to illustrate the utility of the method as a design technique.

scholarly journals Mathematical Optimization Problems for Particle Finite Element Analysis Applied to 2D Landslide Modeling

2019 ◽  
Author(s):  
Liang Wang ◽  
Xue Zhang ◽  
Filippo Zaniboni ◽  
Eugenio Oñate ◽  
Stefano Tinti
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Element Formulation ◽  
Numerical Implementation ◽  
Element Analysis ◽  
Landslide Modeling ◽  
Element Method

AbstractNotwithstanding its complexity in terms of numerical implementation and limitations in coping with problems involving extreme deformation, the finite element method (FEM) offers the advantage of solving complicated mathematical problems with diverse boundary conditions. Recently, a version of the particle finite element method (PFEM) was proposed for analyzing large-deformation problems. In this version of the PFEM, the finite element formulation, which was recast as a standard optimization problem and resolved efficiently using advanced optimization engines, was adopted for incremental analysis whilst the idea of particle approaches was employed to tackle mesh issues resulting from the large deformations. In this paper, the numerical implementation of this version of PFEM is detailed, revealing some key numerical aspects that are distinct from the conventional FEM, such as the solution strategy, imposition of displacement boundary conditions, and treatment of contacts. Additionally, the correctness and robustness of this version of PFEM in conducting failure and post-failure analyses of landslides are demonstrated via a stability analysis of a typical slope and a case study on the 2008 Tangjiashan landslide, China. Comparative studies between the results of the PFEM simulations and available data are performed qualitatively as well as quantitatively.

F-Bar Aided Edge-Based Smoothed Finite Element Method with 4-Node Tetrahedral Elements for Static Large Deformation Elastoplastic Problems

2019 ◽  
Vol 16 (05) ◽  
pp. 1840010 ◽  
Author(s):  
Yuki Onishi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Element Formulation ◽  
Tetrahedral Elements ◽  
Smoothed Finite Element Method ◽  
New Type ◽  
Displacement Based ◽  
Edge Based ◽  
Element Method

A new type of smoothed finite element method (S-FEM), F-barES-FEM-T4, is demonstrated in static large deformation elastoplastic cases. F-barES-FEM-T4 combines the edge-based S-FEM (ES-FEM) and the node-based S-FEM (NS-FEM) for 4-node tetrahedral (T4) elements with the aid of the F-bar method in order to resolve the major issues of Selective ES/NS-FEM-T4. As well as most of the other S-FEMs, F-barES-FEM-T4 inherits pure displacement-based formulation and thus has no increase in DOF. Moreover, the cyclic smoothing procedure introduced in F-barES-FEM-T4 is effective to adjust the smoothing level so that pressure checkerboarding (oscillation) is suppressed reasonably. Some examples of static large deformation analyses for elastoplastic materials proof the excellent performance of F-barES-FEM-T4 in contrast to the conventional hybrid T4 element formulation.

scholarly journals MIXED FINITE ELEMENT FORMULATION OF THE BIHARMONIC EQUATION

2005 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
A. D. GARNADI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimate ◽  
Biharmonic Equation ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Element Formulation ◽  
Abstract Setting ◽  
First Time ◽  
Element Method

<p>We will provide an abstract setting for mixed finite element method for biharmonic equation. The abstract setting casts mixed finite element method for first biharmonic equation and sec- ond biharmonic equation into a single framework altogether. We provide error estimates for both type biharmonic equation, and for the first time an error estimate for the second biharmonic equation.</p>

A Finite Element Formulation for Atrial Tissue Monolayer

2008 ◽  
Vol 47 (02) ◽  
pp. 131-139 ◽  
Author(s):  
H. E. Richter ◽  
G. Plank ◽  
B. Pfeifer ◽  
B. Tilg ◽  
C. N. Nowak ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Finite Thickness ◽  
Element Formulation ◽  
Anisotropic Conductivity ◽  
Volumetric Models ◽  
Volumetric Model ◽  
Activation Times ◽  
Element Method

Summary Objectives: Using computer models for the study of complex atrial arrhythmias such as atrial fibrillation is computationally demanding as long observation periods in the order of tens of seconds are required. A well established approach for reducing computational workload is to approximate the thin atrial walls by curved monolayers. On the other hand, the finite element method (FEM) is a well established approach to solve the underlying partial differential equations. Methods: A generalized 2D finite element method (FEM) is presented which computes the corresponding stiffness and coupling matrix for arbitrarily shaped monolayers (ML). Compared to standard 2D FEM, only one additional coordinate transformation is required. This allows the use of existing FEM software with minor modifications. The algorithm was tested to simulate wave propagation in benchmark geometries and in a model of atrial anatomy. Results: The ML model was able to simulate electric activation in curved tissue with anisotropic conductivity. Simulations in branching tissue yielded slightly different patterns when compared to a volumetric model with finite thickness. In the model of atrial anatomy the computed activation times for five different pacing protocols displayed a correlation of 0.88 compared to clinical data. Conclusions: The presented method provides a useful and easily implemented approach to model wave propagation in MLs with a few restrictions to volumetric models.

scholarly journals Temperature Variation at Solid-Fluid Interface of Thin Film Lubricated Contact Problems

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 922
Author(s):  
Szabolcs Szávai ◽  
Sándor Kovács
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Pressure Dependence ◽  
Hydrodynamic Pressure ◽  
Contact Problems ◽  
Element Formulation ◽  
Temperature And Pressure ◽  
Non Linear System ◽  
Element Method

Many calculating methods have been already developed for solving contact problems of parts such as gears, cams, and followers under fluid film lubrication conditions considering the temperature and pressure dependence. Similarly, the determination of the elasto-hydrodynamic pressure distribution the processes taking place in the lubricant and the contacting bodies, as well as in their environment, have to be dealt with simultaneously for the determination of the temperature field. A system of equation for the modelling of thermo-elastohydrodynamic lubrication between two contacting bodies containing hydrodynamic, thermodynamic, and strength problems is a highly non-linear system which becomes even more so if the temperature and pressure dependence of the material properties are considered. To solve this system, scientists started to use the finite element formulation in the 1960s and it was found to be a promising and reliable method. Earlier, the lubrication analysts used only the h-version finite element method (h-FEM) till 1991, when the first usage of the p-version finite element method (p-FEM) was published in the literature. In order to reduce the problem, in case of point or line contact, the contact bodies can be handled as semi-infinite ones. Following this simplification that had been successfully applied for the gap size determination, a substructure model was defined using analytical solution of the moving heat source. Instead of an iterative way between the solid and fluid problem, in this paper we present an efficient solution when thermal model for lubricant and surfaces were coupled and solved by a direct numerical method in one step.

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