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 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.

A Robust Discontinuous Galerkin High-Order Finite Element Method for Elasticity Problems with Interfaces

2019 ◽  
Vol 17 (09) ◽  
pp. 1950076 ◽  
Author(s):  
Jianfei Zhang ◽  
Xiaowei Deng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Discontinuous Galerkin ◽  
Element Formulation ◽  
Element Level ◽  
Elasticity Problems ◽  
Dg Method ◽  
Variational Form ◽  
Stabilization Parameter ◽  
Element Method

A robust discontinuous Galerkin (DG) finite element method is proposed for elasticity problems with interfaces, where the continuity across the interfaces is weakly enforced by using Nitsche’s method. We employ a weighting for the interfacial consistency terms arising in the Nitsche variational form and present a detailed finite element formulation of this DG method. The stabilization parameter is evaluated by solving element level generalized eigenvalue problem for higher-order elements. Consequently, we give the choice of the weighting parameter that results in an estimate for the stabilization parameter such that the method remains well behaved in the pathological cases. The accuracy and robustness of the proposed method are then demonstrated through several numerical examples.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

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.

Definition of the Temperature and Heat Flux in Micromilling of Hardened Steel Using the Finite Element Method

2014 ◽  
Vol 39 (10) ◽  
pp. 7229-7239 ◽  
Author(s):  
Sergio Luiz Moni Ribeiro Filho ◽  
Marcelo Oliveira Gomes ◽  
Carlos Henrique Lauro ◽  
Lincoln Cardoso Brandão
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Finite Element ◽  
Hardened Steel ◽  
The Finite Element Method ◽  
Definition Of ◽  
Element Method

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.

scholarly journals INFORMATIZATION OF CONSTRUCTION MANAGEMENT AS A BASIS FOR PREVENTING MAN-MADE ACCIDENTS

2021 ◽  
Vol 4 (4) ◽  
pp. 11-31
Author(s):  
S. Koryagina
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Calculation Results ◽  
Definition Of ◽  
Deep Pits ◽  
Geotechnical Problems ◽  
Seismic Impacts ◽  
Base Structure ◽  
Element Method

the article presents the principles and algorithms of the finite element method in solving geotechnical prob-lems taking into account seismic impacts for determining the stress-strain state of structures and slope stabil-ity, implemented in the Midas GTS NX software package. GTS NX allows you to perform calculations of various types of geotechnical problems and solve complex geotechnical problems in a single software envi-ronment. GTS NX covers the entire range of engineering and geotechnical projects, including calculations of the "base-structure" system, deep pits with various mounting options, tunnels of complex shape, consolida-tion and filtration calculations, as well as calculations for dynamic actions and stability calculations. At the same time, all types of calculations in GTS NX can be performed both in 2D and in 3D. The author does not claim to be the author of the finite element method, but he cannot do without pointing out the basic equa-tions, as this affects the definition of the boundaries of use, the formulation of algorithms for constructing calculation schemes and the analysis of calculation results.

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.

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