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. ...

The Finite Cell Method: High Order Simulation of Complex Structures without Meshing

2009 ◽  
pp. 87-92 ◽  
Author(s):  
Ernst Rank ◽  
Alexander Düster ◽  
Dominik Schillinger ◽  
Zhengxiong Yang
Keyword(s):  
High Order ◽  
Complex Structures ◽  
Finite Cell Method ◽  
Cell Method ◽  
Finite Cell

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.

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.

A high-order enrichment strategy for the finite cell method

PAMM ◽  
2015 ◽  
Vol 15 (1) ◽  
pp. 207-208 ◽  
Author(s):  
Meysam Joulaian ◽  
Nils Zander ◽  
Tino Bog ◽  
Stefan Kollmannsberger ◽  
Ernst Rank ◽  
...  
Keyword(s):  
High Order ◽  
Finite Cell Method ◽  
Cell Method ◽  
Enrichment Strategy ◽  
Finite Cell

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
Sign in / Sign up

Export Citation Format

Share Document