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Marcel König - Partitioned Solution Strategies for Strongly-Coupled Fluid-Structure Interaction Problems in Maritime Applications

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Marcel König

Partitioned Solution Strategies for Strongly-Coupled Fluid-Structure Interaction Problems in Maritime Applications

Series: Mechanik/Bruchmechanik

Volume 351 2018

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Titelei/Inhaltsverzeichnis S. I-XVI

„… -, vector-, or tensor-valued quantity u Generic discrete quantity U Dilatational part of the strain energy …” „… In this thesis, the following notation for the distinction of scalars, vectors, tensors, and matrices …” „… second-order tensors T defined as linear maps between vector spaces are typeset in bold italic font. Bold …”

Structural Problems S. 25-41

„… second-order identity tensor by I and recalling the definition of the deformation gradient F in Equation (3.2 …” „… be decomposed into an orthogonal rotation tensor R and a symmetric stretch tensor U or V …” „… , respectively, such that F = RU = V R . (3.11) The right stretch tensor U and the left stretch tensor V are …”

Fluid Problems S. 5-24

„… this equation is still retained if φ is a vector- or tensor-valued quantity. Equation (2.27) represents …” „… , (2.44) where σ denotes the stress tensor and b represents the volume force per unit mass. Recalling …” „… ) + ρbi dΩ , (2.55) or, again in tensor notation, ∫ Ωt ρ ⎛ ⎝ ∂v ∂t ∣∣∣∣∣ χ + ṽ · gradv ⎞ ⎠ dΩ = ∫ Ωt divσ …”

Software Library comana S. 98-157

„… array and tensor types. Eigen makes heavy use of expression templates and generates expression trees at …” „… integration points. In the getIntegrationPoints method, the integration points are initialized as the tensor …”

doi.org/10.51202/9783186351180

Stella Graßhof - Expressive Personalized 3D Face Models from 3D Face Scans

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Stella Graßhof

Expressive Personalized 3D Face Models from 3D Face Scans

Series: Informatik/ Kommunikation

Volume 868 2020

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Experiments S. 146-173

„… versions approximate the original data tensor, using the same cropping factors, i.e. dimension one for the …” „… level. Given the original 3D face shapes as data tensor T4,0 ∈ R3N×P ×L×E , and T 4,apathy representing …” „… the tensor which consists of the mean apathetic face, while T 4,neutral contains the mean neutral face …”

Fundamentals S. 15-39

„… defined as a tensor product based on applying the traditional SVD on the individual tensor-unfoldings, as …” „… the core tensor accordingly, see Fig. 2.2 for illustration. As the presented tensor-factorization is …” „… . 2.3 Factorization 25 Fourth-Order Cumulant Tensor The previously introduced fourth-order cumulants are …”

Face Models S. 114-145

„… , followed by the proposed tensor-based face model in different variants. An analysis of the proposed model …” „… ) is commonly used in published face tensor-models on both image and 3D data [18, 47, 30, 66] and is an …” „… position change. This process results in a fine detailed 3D face reconstruction. 5.3 Proposed Tensor Face …”

Summary and Conclusions S. 174-178

„… aligned and the resulting balanced data can be sorted into a data tensor, which is used in the following …” „… . In Chapter 5 four tensor face models, build from three different databases were presented, along with …” „… usages. Afterwards in order to investigate effects of the parameterizations of the tensor models, they …”

Titelei/Inhaltsverzeichnis S. I-XIV

„… – correspondence estimation – expression intensity – tensor – factorization – statistical models – expression …” „… – Korrespondenzschätzung – Intensität von Gesichtsausdrücken – Tensor – statistische Modelle – Transfer von Ge …” „… Tensor Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.1 Notation …”

Index S. 199-204

„… Animation Parameters, see FAP FACS, 5 FAP, 5 ffp, 42 flattening of tensor, 28 fooling, 143 Gaussian …” „… , 68 Singular Value Decomposition, see SVD SVD, 22, 30 tensor, 27, 116 time alignment, 100 transfer …” „… , 149 expression, 150 person, 150 uncanny valley, 2 unfolding of tensor, 29 whitening, 22 Wolfe …”

Introduction S. 1-14

„… from 2D input the proposed tensor-based face models outperform state-of-the-art approaches. 1.5 Thesis …” „… factorization approach of a higher-dimensional data structure, i.e. data tensor, of processed 3D face scans. The …” „… synchrony of facial motion. Chapter 5: Face Models • The factorization of 3D face tensors reveals structures …”

Appendix S. 179-188

„… information [75]. Columns five to seven show results of the proposed tensor models build from three different …” „… , whereas all tensor models rely on a subset of the shown 2D landmarks only. The presented examples confirm …”

Literature S. 189-198

„… Ensembles: TensorFaces. In: European Conference on Computer Vision (ECCV). 2350. 2002, pp. 447–460 …” „… : 10.1002/0471221317. [45] J. F. Cardoso. Eigen-structure of the fourth-order cumulant tensor with application to the …”

From 3D Face Scans to Aligned Faces S. 59-113

„… points, because otherwise they cannot be ordered into a matrix or tensor. 6. The points between each pair …” „… sequence s can be ordered into a data tensor Fs ∈ R3×N×Ts , s = 1, . . . , S. If the number of frames T …” „… statistical model [66, 30, 70, 71]. To reach this goal, the dimensionality of each of the 3D data tensors Fs …”

doi.org/10.51202/9783186868107

Lars Radtke - A partitioned solution approach for fluid-structure interaction problems in the arterial system

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Lars Radtke

A partitioned solution approach for fluid-structure interaction problems in the arterial system

Series: Mechanik/Bruchmechanik

Volume 353 2020

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Appendix S. 257-268

„… tensors A and B, and fourth-order tensorsA and B, the following operations are defined according to the …” „… Appendix A.1 Tensor algebra For an in-depth treatment of tensor algebra as well as tensor analyisis …” „… literature. A.1.1 Contractions and scalar products Considering first-order tensors a and b, second-oder …”

Mechanical modeling of the arterial system S. 23-68

„… spatial flux tensor Γ(x) and source vector β, one obtains∫ Ω(x) ∂ω ∂t ∣∣∣∣ x + div ( ω ⊗ v − Γ(x) ) − β …” „… form, respectively. From (3.41), the transformation rule for the flux tensor Γ(X) = J Γ(x)F−T (3.43 …” „… momentum, the Cauchy stress tensor σ can be identified as the spatial flux of linear momentum and sources …”

Titelei/Inhaltsverzeichnis S. I-X

„… . . . . . . . . . . . . . . . . . . . . . . . . 251 7 Summary and Outlook 253 Appendix 257 A.1 Tensor algebra …” „… order tensors . . . . . . . 257 A.1.3 Special fourth order tensors . . . . . . . . . . . . . . 258 A.2 …” „… Continuum mechanics . . . . . . . . . . . . . . . . . . . . . 258 A.2.1 Neo-Hookean elasticity tensor …”

Numerical methods S. 69-152

„… polynomial tensor-product basis of degree pg = 4 is considered. This gives 25 degrees of freedom for each …” „… = DdE∆d denotes the directional derivative of the Green- Lagrange strain tensor. Note that for the dynamic …” „… (4.30), CV denotes the Voigt representation of the elasticity tensor C = ∂S/∂E (see Section A.3.4 for …”

Numerical investigations S. 153-219

„… well. Therein, the trunk and the tensor product space were considered, while this study is augmented by …” „… ) is used instead of the tensor product space (TPS), the same error can be achieved with less degrees …” „… tensors, a corresponding addition is obtained as explained in Section 3.2.2. As can be seen from Figure …”

Bibliography S. 269-288

„… , 2010, pp. 143–178. [48] R. de Boer. Vektor- und Tensorrechnung für Ingenieure. Berlin and Heidelberg …” „… . Weller, G. Tabor, H. Jasak, and C. Fureby. “A Tensorial Approach to Computational Continuum Mechanics …”

doi.org/10.51202/9783186353184

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Bauingenieur

Browse Volumes: Bauingenieur

Bauingenieur Volume 94 (2019) Issue 12 ISSN Online: 0005-6650

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Mehran Motevalli, Jörg Uhlemann, Natalie Stranghöner, Daniel Balzani A new nonlinear polyconvex orthotropic material model for the robust simulation of technical fabrics in civil engineering applications at large strains – Validation with large-scale experiment/Ein neues polykonvexes orthotropes Materialmodell zur robusten Simulation von Textilmembranen im Bauingenieur- wesen unter Berücksichtigung großer Deformationen – Validierung anhand eines Großbauteilversuchs S. 488-497

„… simulation of tensile membrane structures. The notion of anisotropic metric tensors is employed in the …” „… interactions, one may directly use multiplicative mixed invariant terms of the right Cauchy-Green tensor and …” „… the classical structural tensors [13], [14]. However, these non-polyconvex formulations may lead to …”

doi.org/10.37544/0005-6650-2019-12

Mathias Würkner - Numerische Homogenisierung von Faserverbundwerkstoffen mit periodischer Mikrostruktur

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Mathias Würkner

Numerische Homogenisierung von Faserverbundwerkstoffen mit periodischer Mikrostruktur

Series: Mechanik/Bruchmechanik

Volume 346 2017

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Modellierung von Werkstoffen S. 9-20

„… Proportionalitätsfaktoren Cijkl sind Komponenten eines Tensors C vierter Stufe, die infolge der Homogenität des betrachteten …” „… Körpers invariant bezüglich x und somit konstant sind. Dieser Tensor wird Elastizitätstensor genannt …” „… durch diese Koeffizienten definierte Tensor vierter Stufe wird Nachgiebigkeitstensor genannt. Aus der …”

Titelei/Inhaltsverzeichnis S. I-XVI

„… Verschiebung E Vektor der elektrischen Feldstärke e Tensor der piezoelektrischen Kostanten (3. Stufe) κ Tensor …” „… bezüglich φ ẽ Matrixschreibweise des Tensors der piezoelektrischen Konstanten φ̂ vorgeschriebenes …” „… piezoelektrischen Tensors in Ω f emkij , i, j, k = 1, 2, 3 Koeffizienten des piezoelektrischen Tensors in Ω m κfij …”

Homogenisierungsverfahren S. 21-52

„… Koeffizienten materialbeschreibender Tensoren, wie zum Beispiel den Elastizitätstensor C und den Tensor der …” „… ) wobei die Komponenten ε0ij eines Tensors ε 0 vorgegeben sind. Die erste Bedingung aus Gl. (3-21) kann …” „… ) werden sechs Probleme mit speziellen vorgegebenen symmetrischen Tensoren ε0 betrachtet. Diese Tensoren …”

Einleitung S. 1-8

„… von materialbeschreibenden Tensoren eingegangen. Das dritte Kapitel widmet sich der …”

Berechnung effektiver Materialeigenschaften S. 65-112

„… Materialeigenschaften mation auf globale Koordinaten verändert sich die Darstellung des Tensors zu Gl. (2-43). Das …” „… Koordinatensystem ergibt sich ein Elastizitätstensor, dessen Darstellung in M-V-Notation der des Tensors bezüglich …” „… Transformation in ein geeignetes lokales Koordinatensystem kann der Tensor in M-V-Notation die Darstellung aus Gl …”

doi.org/10.51202/9783186346186

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