A comparison of parallel implementation of explicit DG and central difference method

Ekevid, Torbjörn; Wiberg, Nils‐Erik

doi:10.1002/cnm.515

Cited by 4 publications

(6 citation statements)

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“…There are many suitable explicit-integration algorithms used in structural wave propagation problems. [24][25][26][27][28][29] In this work we only apply the commonly used centered difference method. There are several possible re-formulations, cited for instance in Reference 26, and Algorithm 1 describes a variant particularly efficient with a diagonal damping matrix, which is what we assume in the examples below.…”

Section: Explicit Dynamics Of Linear Wave Propagation In Shell Struct...mentioning

confidence: 99%

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Explicit dynamics of shells with a flat‐facet triangular finite element

Krysl

2022

Numerical Meth Engineering

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The use of a flat‐facet finite element with three nodes and six degrees of freedom per node for modeling of linear wave‐propagation events is discussed. The triangular shell finite element was presented in a preceding publication. The main novelty of the current approach is the treatment of the drilling rotations that decouples the drilling degree of freedoms on the global level, and hence makes it possible to eliminate negative effects of these degrees of freedom on the explicit time‐stepping algorithms employed to compute the dynamic response, such as deterioration in accuracy or artificially reduced time step. The element is shown to be robust for wave propagation simulations, and its performance is illustrated with examples including guided‐wave scenarios.

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Section: Explicit Dynamics Of Linear Wave Propagation In Shell Struct...mentioning

confidence: 99%

“…There are many suitable explicit‐integration algorithms used in structural wave propagation problems 24‐29 . In this work we only apply the commonly used centered difference method.…”

Section: Explicit Dynamics Of Linear Wave Propagation In Shell Struct...mentioning

confidence: 99%

Explicit dynamics of shells with a flat‐facet triangular finite element

Krysl

2022

Numerical Meth Engineering

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“…The development of parallel computers and improvements in computer hardware has been of significant importance [29]. A dynamic event has a key characteristic that the incident pulse duration is very small in the order of microseconds that makes the frequency content of pulse very high (in the order of kHz).…”

Section: Introductionmentioning

confidence: 99%

“…This makes the system size enormously large. But in an explicit analysis, storage of large matrices is avoided with the added advantage of not requiring to solve linear algebraic equations [29]. Explicit methods are also conditionally stable, and so the time step size must be below a critical value that is dependent on the size of the smallest finite element [30].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Finite Element Analysis for Nonhomogeneous Materials Using Parallel Explicit Algorithm

Anandakumar¹,

Kim²

2020

Computational Models in Engineering

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This chapter addresses the behavior of functionally graded solids under dynamic impact loading within the framework of linear elasticity using parallel explicit algorithm. Numerical examples are presented that verify the dynamic explicit finite element code and demonstrate the dynamic response of graded materials. A threepoint bending beam made of epoxy and glass phases under low-velocity impact is studied. Bending stress history for beam with higher values of material properties at the loading edge is consistently higher than that of the homogeneous beam and the beam with lower values of material properties at the loading edge. Larger bending stresses for the former beam may indicate earlier crack initiation times, which were proven by experiments performed by other researchers. Wave propagation in a 3D bar is also investigated. Poisson's ratio and thickness effects are observed in the dynamic behavior of the bar. Finite element modeling and simulation discussed herein can be a critical tool to help understand physics behind the dynamic events.

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“…En adición, este método es fiable para los problemas que involucren impacto-contacto. Para aprovechar al máximo una formulación explícita se lleva a cabo una diagonalización de la matriz de masa del sistema, que se conserva durante todo el cálculo, de tal manera que la solución se puede obtener sin resolver ningún sistema de ecuaciones [124], a no ser que cambie la topología de la malla, por ejemplo, cuando se refina o se inserta una fractura en la misma, por lo que hay que recalcular dicha matriz nuevamente.…”

Section: Los Principales Métodos Integración Temporal Se Dividen En D...unclassified

Modelado de multifractura discreta en materiales quasi-frágiles

Lafontaine

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The stated goal of this work is to develop a numerical explicit finite element method able to effectively address the strain localization process, discrete fracture and fragmentation process in quasi-brittle materials, involving highly nonlinear processes, such as, contact, non-linear geometric and material behavior. The description of the quasi-brittle material is based in the concepts of classical fracture mechanics plasticity theory and more specifically in the plastic damage model and its fundamental variable, the plastic damage variable, using traditional Mohr-Coulomb and Rankine models. Three types of algorithms were needed to reach our goal. A search contact algorithm, a combined penalty and Lagrange multipliers algorithm and adaptive local refinement algorithm. The search algorithms is necessary to determine the pairs of potential contacts with a reasonable computational cost; the second for establishing and compute the normal contact forces and the third one to allow not only a local refinement but also draw geometric modeling of discrete fracture. Moreover, given the inability of the irreducible linear elements formulation to capture collapse mechanisms, ultimate loads and strain localization processes, we opted to develop an explicit mixed finite element displacements and strain formulation in solid mechanics stabilized with variational sub-scales method, particularly using Orthogonal Sub-scales Method (OSS). This stabilized formulation avoids the LBB condition ( inf-sup condition) and allow to use elements with independent and equal interpolation order for displacements and strain fields. This formulation is one of the main original contribution of this work. Our methodology, called MEX-FEM, and developed to address problems in small and large deformations, not only it comes to enhance the traditional explicit time integration scheme, but also can get an improved stresses and strains field in a finite element mesh and also a better description of the strain localization virtually free of mesh-bias dependence without using tracking algorithms and accurate solutions in nearly incompressible problems.These numerical tools developed were integrated as a whole for our main goal: the discrete modeling fracture and fragmentation of quasi-brittle materials using finite element method. El objetivo planteado en este trabajo es el desarrollo de una metodología numérica explícita de elementos finitos capaz de abordar de manera efectiva la simulación de procesos de localización, fractura discreta y fragmentación en materiales quasi-frágiles, envolviendo procesos altamente no lineales, como la no linealidad geométrica, la no linealidad del material y el contacto. La descripción del material quasi-frágil se basa en los conceptos de la mecánica de fractura clásica de la teoría de plasticidad y más específicamente en el modelo de daño plástico y su variable fundamental, la variable de daño plástico, empleando los modelos tradicionales de discontinuidad de Mohr-Coulomb y Rankine. Tres tipos de algoritmos fueron necesarias para trazar nuestro objetivo. Un algoritmo de búsqueda de contactos, un algoritmo combinado penalización y multiplicadores de Lagrange y un algoritmo de refinamiento local adaptable. La algoritmia de búsqueda es necesaria para determinar los pares de contactos potenciales con un coste computacional razonable; la segunda para establecer la condición de contacto y la tercera para permitir, no sólo un refinamiento local sino también trazar el modelado geométrico de la fractura discreta. Por otra parte, dada la incapacidad de los elementos lineales de la formulación irreducible para capturar mecanismos de colapso, cargas últimas y procesos de localización de deformaciones se optó por desarrollar la primera formulación mixta explícita de elementos finitos en desplazamientos y deformaciones dentro de la mecánica de sólidos estabilizada mediante el método de sub-escalas variacionales, particularmente en las sub-escalas ortogonales. Esta formulación estabilizada elude la condición LBB y permite obtener elementos con independiente e de igual orden de interpolación en el campo de los desplazamientos y deformaciones. Esta formulación constituye la principal aportación original de este trabajo. Nuestra metodología, bautizada como MEX-FEM, y desarrollada para abordar problemas en pequeñas y grandes deformaciones,no solamente viene a mejorar el esquema explicito tradicional de integración temporal de la ecuación de movimiento, sino que obtiene un mejor campo de tensiones y deformaciones en una malla de elementos finitos, una mejor descripción de los procesos de localización de deformaciones virtualmente libre de la dependencia de la malla y sin necesidad de emplear algoritmos de rastreo y una mejor solución a problemas cercanamente incompresibles. Todas estas herramientas numéricas desarrolladas fueron integradas en su conjunto para realizar nuestra principal meta: el modelado discreto la fractura y fragmentación de los materiales quasi-frágiles empleando el método de los elementos finitos.

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A comparison of parallel implementation of explicit DG and central difference method

Cited by 4 publications

References 9 publications

Explicit dynamics of shells with a flat‐facet triangular finite element

Explicit dynamics of shells with a flat‐facet triangular finite element

Three-Dimensional Finite Element Analysis for Nonhomogeneous Materials Using Parallel Explicit Algorithm

Modelado de multifractura discreta en materiales quasi-frágiles

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