Shell Finite Cell Method: A high order fictitious domain approach for thin-walled structures

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. ...

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The Finite Cell Method: A Higher Order Fictitious Domain Approach for Wave Propagation Analysis in Heterogeneous Structures

Lamb-Wave Based Structural Health Monitoring in Polymer Composites - Research Topics in Aerospace ◽

10.1007/978-3-319-49715-0_9 ◽

2017 ◽

pp. 217-239 ◽

Cited By ~ 1

Author(s):

S. Duczek ◽

U. Gabbert

Keyword(s):

Wave Propagation ◽

Higher Order ◽

Fictitious Domain ◽

Finite Cell Method ◽

Cell Method ◽

Propagation Analysis ◽

Heterogeneous Structures ◽

Finite Cell

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Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method

Computational Mechanics ◽

10.1007/s00466-017-1464-6 ◽

2017 ◽

Vol 61 (4) ◽

pp. 385-407 ◽

Cited By ~ 6

Author(s):

Tino Bog ◽

Nils Zander ◽

Stefan Kollmannsberger ◽

Ernst Rank

Keyword(s):

High Order ◽

Finite Cell Method ◽

Frictionless Contact ◽

Cell Method ◽

Embedded Interfaces ◽

Finite Cell

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The Isogeometric Shape Optimization Method Based on Finite Cell Method

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.621.655 ◽

2014 ◽

Vol 621 ◽

pp. 655-662

Author(s):

Gang He ◽

Zheng Yu Pan ◽

Zhi Hui Zou ◽

Deng Lin Zhu

Keyword(s):

Shape Optimization ◽

Optimization Design ◽

Boundary Representation ◽

Fictitious Domain ◽

Computational Domain ◽

Finite Cell Method ◽

Cell Method ◽

High Efficient ◽

Complex Boundary ◽

Finite Cell

Isogeometric analysis (IGA) method uses the same mathematical model in geometric design and engineering analysis, and is the most potential method to realize high accuracy and integrated optimization design. Finite Cell Method (FCM) introduces high order finite element method into fictitious domain method, and it has great advantages of complex boundary representation and high efficient convergence. In order to break through IGA’s limit on geomerty’s topology, IGA and FCM are combined together in this research. Function Heasivide and Dirac are used to approximate the computational domain and its first order derivative, then the stiffness matrix on the fictitious domain are calculated and the displacement in the shape with complex boundary is solved by IGA method. One order and two order implicit curves are used to the outer boundary representation of elastic optimization problem, and their coefficients are taken as design variable. The sensitivity formulas are deduced. MMA method is used to implement the IGA shape optimization based on FCM. The examples show that our method is efficient and the result is satisfied.

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A high-order enrichment strategy for the finite cell method

PAMM ◽

10.1002/pamm.201510094 ◽

2015 ◽

Vol 15 (1) ◽

pp. 207-208 ◽

Cited By ~ 1

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

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

Advanced Modeling and Simulation in Engineering Sciences ◽

10.1186/s40323-020-00182-1 ◽

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.

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