Finite Cell Method: High-Order Structural Dynamics for Complex Geometries

2015 ◽  
Vol 15 (07) ◽  
pp. 1540018 ◽  
Author(s):  
M. Elhaddad ◽  
N. Zander ◽  
S. Kollmannsberger ◽  
A. Shadavakhsh ◽  
V. Nübel ◽  
...  
Keyword(s):  
Transient Analysis ◽  
Mathematical Formulation ◽  
Time Integration ◽  
Implicit Time ◽  
Weak Formulation ◽  
Finite Cell Method ◽  
Cell Method ◽  
Integration Schemes ◽  
Linear Elastodynamics ◽  
Finite Cell

In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A 1D benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using state-of-the-art commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate computational effort.

The hierarchical finite cell method for problems in structural mechanics

2017 ◽  
Author(s):  
Meysam Joulaian
Keyword(s):  
Integration Method ◽  
Partition Of Unity ◽  
Heterogeneous Material ◽  
High Order ◽  
Partition Of Unity Method ◽  
Finite Cell Method ◽  
Cell Method ◽  
Integration Schemes ◽  
The Moment ◽  
Finite Cell

The finite cell method (FCM) is a combination of the fictitious domain approach and high-order finite elements. This thesis is concerned with the study of the numerical challenges of this method, and it investigates possible approaches to overcome them. Herein, we will introduce and study different numerical integration schemes, such as the adaptive integration method and the moment fitting approach. To improve the convergence behavior of the FCM for problems with heterogeneous material, we will also propose two high-order enrichment strategies based on the hp-d approach and the partition of unity method. Moreover, the application of the FCM will be extended to the simulation of wave propagation problems, employing spectral elements and a novel mass lumping technique. ...

PERFORMANCE OF DIFFERENT INTEGRATION SCHEMES IN FACING DISCONTINUITIES IN THE FINITE CELL METHOD

2013 ◽  
Vol 10 (03) ◽  
pp. 1350002 ◽  
Author(s):  
ALIREZA ABEDIAN ◽  
JAMSHID PARVIZIAN ◽  
ALEXANDER DÜSTER ◽  
HASSAN KHADEMYZADEH ◽  
ERNST RANK
Keyword(s):  
Order Approximation ◽  
Gauss Quadrature ◽  
The Finite Element Method ◽  
Approximation Space ◽  
High Order Approximation ◽  
Finite Cell Method ◽  
Precise Integration ◽  
Cell Method ◽  
Integration Schemes ◽  
Finite Cell

In many extended versions of the finite element method (FEM) the mesh does not conform to the physical domain. Therefore, discontinuity of variables is expected when some elements are cut by the boundary. Thus, the integrands are not continuous over the whole integration domain. Apparently, none of the well developed integration schemes such as Gauss quadrature can be used readily. This paper investigates several modifications of the Gauss quadrature to capture the discontinuity within an element and to perform a more precise integration. The extended method used here is the finite cell method (FCM), an extension of a high-order approximation space with the aim of simple meshing. Several examples are included to evaluate different modifications.

scholarly journals Finite cell method for functionally graded materials based on V-models and homogenized microstructures

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Benjamin Wassermann ◽  
Nina Korshunova ◽  
Stefan Kollmannsberger ◽  
Ernst Rank ◽  
Gershon Elber
Keyword(s):  
Functionally Graded Materials ◽  
Large Scale ◽  
Functionally Graded ◽  
Material Behavior ◽  
Modeling Framework ◽  
Finite Cell Method ◽  
Geometric Framework ◽  
Graded Materials ◽  
Cell Method ◽  
Finite Cell

AbstractThis paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modeling framework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These types of objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, in particular when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The first one, multi-material FGM is described using the inherent property of V-rep models to assign different properties throughout the interior of a domain. The second, single-material FGM—which is heterogeneously micro-structured—characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach.

scholarly journals Hierarchical multigrid approaches for the finite cell method on uniform and multi-level hp-refined grids

2021 ◽  
Vol 386 ◽  
pp. 114075
Author(s):  
J. Jomo ◽  
O. Oztoprak ◽  
F. de Prenter ◽  
N. Zander ◽  
S. Kollmannsberger ◽  
...  
Keyword(s):  
Finite Cell Method ◽  
Cell Method ◽  
Multi Level ◽  
Finite Cell

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

scholarly journals A Semi-Implicit Version of the MPAS-Atmosphere Dynamical Core

2015 ◽  
Vol 143 (9) ◽  
pp. 3838-3855 ◽  
Author(s):  
Steven Sandbach ◽  
John Thuburn ◽  
Danail Vassilev ◽  
Michael G. Duda
Keyword(s):  
Time Integration ◽  
Standard Test ◽  
Newton Iteration ◽  
Atmospheric Modeling ◽  
Implicit Time ◽  
Integration Scheme ◽  
Baroclinic Wave ◽  
Time Step ◽  
Integration Schemes ◽  
Helmholtz Problem

Abstract An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge–Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank–Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%–20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.

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