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

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. ...

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
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