VDI Verlag eLibrary

The hierarchical finite cell method for problems in structural mechanics

Meysam Joulaian

Series: Mechanik/Bruchmechanik

Volume 348 2017

Results in this title

Numerical integration algorithms for the FCM S. 27-71

„… 27 Chapter 3 Numerical integration algorithms for the FCM In this chapter, our aim is to study the …” „… numerical integration algorithms for the FCM. As the mesh does not necessarily conform geometrically to the …” „… interface within the cell. In view of the numerical integration, the underlying integrals of unbroken cells …”

Bibliography S. 140-154

„… propagation and nonstandard reduced integration. SIAM Journal on Numerical Analysis, 48:346–371, 2010. [20] S …” „… . [92] S. Hubrich, M. Joulaian, and A. Düster. Numerical integration in the finite cell method based on …” „… , 199(49–52):3237–3249, 2010. [127] S. E. Mousavi and N. Sukumar. Numerical integration of polynomials and discontinuous …”

Titelei/Inhaltsverzeichnis S. I-X

„… introduce and study different numerical integration schemes, such as the adaptive integration method and …” „… boundary conditions . . . . . . . . . . . . . . . . . . 15 2.4.3 Numerical integration of cut cells …” „… integration algorithms for the FCM 27 3.1 Numerical integration of unbroken cells …”

Summary and Outlook S. 133-135

„… work was to improve this method from the viewpoint of numerical integration and the local enrichment …” „… follows. • Numerical integration of the FCM: We discussed different numerical integration schemes in the …” „… FCMwith the moment fitting method only requires slightly more effort in terms of numerical integration in …”

Introduction S. 1-4

„… challenges – which are, for instance, the numerical integration of elements that are cut by the boundary [14 …” „… performing a simulation with the FCM. In Chapter 3, we will then focus on the issue of numerical integration …” „… propose a novel integration approach based on the moment fitting method [127, 129, 167]. Several numerical …”

The spectral cell method S. 111-132

„… mass matrix, we apply the GLL quadrature rule of order ng = p + 1 for the numerical integration of …” „… is resolved during the numerical integration of the cells, so we apply the adaptive quadtree …” „… 111 Chapter 5 The spectral cell method An intricate field of the numerical analysis is the dynamic …”

Finite cell method for problems in solid mechanics S. 5-26

„… ⎤ ⎥⎦ . (2.24) One of the advantages of a simple mapping is that it allows an exact numerical integration of the …” „… captured during the numerical integration of the (discretized) weak form. To obtain an efficient …” „… the scope of the numerical integration, we need to find out whether an integration point happens to be …”

Local enrichment of the FCM S. 72-110

„… accurately. In this particular case, it is possible to perform the numerical integration exactly up to …” „… geometrical mesh and the discretization mesh, special care has to be taken during the numerical integration …” „… . That is, the numerical integration has to be carried out on the finer mesh – usually the geometrical …”

Polynomial integrands S. 138

„… investigate the accuracy of the discussed numerical integration algorithms. These polynomials are based on the …”

doi.org/10.51202/9783186348180

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The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

Simeon Hubrich

Series: Mechanik/Bruchmechanik

Volume 355 2021

Results in this title

Bibliography S. 154-169

„… with Applications, 75:3298–3316, 2018. [31] S. Hubrich and A. Düster. Adaptive numerical integration of …” „… Mathematics and Mechanics, 18:e201800089, 2018. [32] S. Hubrich and A. Düster. Numerical integration for …” „… . Düster. Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme …”

The finite cell method S. 23-35

„… well as the derivation of the discrete equation system. Sec. 3.3 focuses on the numerical integration …” „… Numerical integration When it comes to computing the local cell quantities, special care has to be taken …” „… during the numerical integration process. Thereby, we have to distinguish between cut and noncut finite …”

Introduction S. 1-5

„… bottleneck of the FCM is related to the numerical integration of finite cells. Integrals of cells that are …” „… subcells and, thus, in a large number of integration points. This in turn renders the numerical calculation …” „… numerical integration of finite cells. Within the context of the FCM, it is common to employ adaptive …”

Titelei/Inhaltsverzeichnis S. I-VII

„… – Numerical integration – Moment fitting quadratures – Basis function removal – Remeshing – Data transfer …” „… schemes are introduced that allow to reduce the effort of the numerical integration process significantly …” „… Discretization of the weak forms . . . . . . . . . . . . . . . . . . . . 27 3.3 Numerical integration …”

Summary and outlook S. 150-153

„… aspects are briefly summarized. • In the first topic this thesis, we discussed the numerical integration …” „… large number of quadrature points, thus leading to computationally expensive numerical integration …” „… processes. To perform the numerical integration more efficiently, we proposed novel quadrature methods based …”

Moment fitting quadratures S. 36-78

„… numerical integration process. This is due to the fact that the computational mesh is decoupled from the …” „… scope of this chapter, we focus on the numerical integration process of the finite cell method. As …” „… are discussed in the following. A rather simple commonly applied numerical integration approach is …”

Basis function removal for the FCM S. 79-123

„… to numerical integration, we employ the moment fitting method given in Sec. 4.2.1. For the …” „… fitting – presented in Sec. 4.2 – in order to reduce the error induced by the numerical integration. For …” „… reduced significantly, thus, reducing the effort of the numerical integration process. In this thesis, we …”

A remeshing strategy for the FCM S. 124-149

„… mesh builds the basis for the numerical integration of the cut cells. Here, it is used to check whether …” „… . Moreover, for the numerical integration, we employ the adaptive Gaussian scheme utilizing an octree based …” „… apply α = 10−q with q = 5 and an order of p = 2 for the ansatz. Furthermore, the numerical integration …”

Basic elements of continuum mechanics S. 6-22

„… } . (2.82) Now, applying integration by parts formula of the first term in Eq. (2.81) and making use of the …” „… approximate solution. Due to its nonlinear character numerical algorithms have to be utilized to solve the …”

doi.org/10.51202/9783186355188

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Improving the robustness of the finite cell method for problems with large deformations

Wadhah Garhuom

Series: Mechanik/Bruchmechanik

Volume 359 2024

Results in this title

Bibliography S. 135-152

„… . Kudela, S. Kollmannsberger, E. Rank, A. A Schröder,and A. Düster. Numerical integration of …” „… Bibliography[78] S. Hubrich and A. Düster. Adaptive numerical integration of broken finite cellsbased on …” „… 201800089, 2018.[79] S. Hubrich and A. Düster. Numerical integration for nonlinear problems of thefinite …”

Introduction S. 1-5

„… conventional Gaussian quadrature schemes. Tocarry out the numerical integration in the cut cells, it is …” „… spatial discretiza-tion of the weak form is performed. Finally, the numerical integration based on …” „… 1 Introduction1.1 MotivationThe finite element method (FEM) is a numerical approach used to solve …”

Titelei/Inhaltsverzeichnis S. I-VIII

„… . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Numerical integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.1 Gaussian …” „… wird entwickelt, um die Integration von gebrochenen Zellen zu verbessern und die Newton-Raphson-Methode …” „… the FCM robustness for large deformation analysis. Different numerical examples showcase the …”

The finite cell method S. 17-26

„… .3.3 Numerical integrationThe integrals introduced in Sections 3.2.2 and 3.2.3 for the cell stiffness …” „… there-fore numerical integration schemes are utilized. A well-known integration method in thecontext of …” „… respect to a reference cellΩc□ by utilizing the mapping functions. Afterwards, the numerical integration …”

Remeshing strategy for large deformations in the FCM S. 89-129

„… .(6.10)Second, the geometry is used during the numerical integration to perform inside-outsidetesting to …” „… strain problems in solid mechanics are still adifficult challenge using numerical techniques such as the …” „… at the integration pointsof the new mesh – which can be thought of as some kind of history data …”

Summary and outlook S. 130-133

„… inthis work. For the integration of broken cells using the finite cell method, we developed a …” „… non-negative moment fitting quadrature rule, described in Chapter 4. Here, each integra-tion point is created …” „… integration pointsgreater than the number of moments should be distributed in the physical domain.This choice …”

Non-negative moment fitting quadrature for cut finite elements and cells S. 27-58

„… . Therefore, special integration schemes are requiredto perform the numerical integration in the cut cells.One …” „… moment fitting quadrature for cut finite elements and cellsFigure 4.1: Numerical integration of a broken …” „… distribute the points without any refinements (kNNMF = 0).Figure 4.3: Numerical integration of a broken cell …”

doi.org/10.51202/9783186359186

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Partitioned solution strategies for electro-thermo-mechanical problems applied to the field-assisted sintering technology

Patrick Erbts

Series: Mechanik/Bruchmechanik

Volume 345 2016

Results in this title

Numerical methods S. 45-78

„… reference is made to [19, 43]. 3.2.4 Numerical integration So far, the computation of the integrals arising …” „… 45 CHAPTER3 Numerical methods The third chapter is concerned with numerical methods to find an …” „… numerical solution procedures for the governing equations of the mechanical, thermal, electrical and …”

Bibliography S. 186-204

„… / simulia/portfolio/abaqus/overview/, 2012. [2] A. Aitken. On Bernoulli’s numerical solution of algebraic equations. Proceedings of …” „… Numerical Methods in Engineering, 35:737–766, 1992. [4] F. Armero and J.C. Simo. A priori stability …” „… , 122(1-2):1–21, 2000. Numerical Analysis in the 20th Century Vol. II: Interpolation and Extrapolation. [18] C …”

Conclusions and outlook S. 171-173

„… for several numerical computations. Apart from academic examples serving to test the partitioned …” „… , different numerical models for the radiative transfer are discussed. For the special case of vacuum …” „… , the three different numerical radiation models are investigated and compared to the standard, but the …”

Titelei/Inhaltsverzeichnis S. I-XVI

„… – Numerical thermal radiation – Convergence acceleration – Fluid-structure interaction – Coupled problems …” „… (CFD) solvers. The numerical results are compared to experiments. Moreover, an in-depth study of …” „… . . . . . . . . . . . . . . . . 39 2.3.4 Coupling to other fields . . . . . . . . . . . . . . . . . . . . . 41 3 Numerical methods 45 …”

Solution of coupled problems S. 79-144

„… coupling algorithm is generally embedded in a time integration procedure, as shown in Figure 4.1. This …” „… applying an implicit time integration procedure [3]. 4.1. Coupling algorithms: an introduction 81 tn Solve …” „… Newton-Raphson procedure might become extremely large and also unsymmetrical. For some cases, the numerical …”

Governing equations S. 8-44

„… the numerical solution process. More specifically, this part does not fulfil the material 2.1. Basic …” „… continuum mechanics 13 objectivity requirement, which is why it is not suitable for further numerical …” „… often neglected or only treated approximately in numerical analysis. With increasing temperature …”

doi.org/10.51202/9783186345189

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Softwareagenten-basierte Berechnung interdisziplinärer gekoppelter Simulation

Matthias Jüttner

Series: Rechnerunterstützte Verfahren

Volume 469 2017

Results in this title

Literaturverzeichnis S. 98-110

„… , J. Hoeflinger, L. Kale und M. Bhandarkar, „A New Approach to Software Integration Frameworks for …” „… Stuttgart, Institut für Theorie der Elektrotechnik, 2015. [64] M. Nikraz, „Agent-Based Integration of …” „… ] M. Kaltenbacher, Numerical Simulation of Mechatronic Sensors and Actuators. Springer, 2015, Bd. 3 …”

doi.org/10.51202/9783186469205

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Experimental testing and numerical simulation of granules as crash absorber for double hull structures

Christian Woitzik

Series: Mechanik/Bruchmechanik

Volume 356 2021

Results in this title

Numerical investigation S. 88-112

„… 6 Numerical investigation After obtaining the experimental results, the modelling of the collision …” „… Section 2.1. A brief overview over some of the numerical results for Experiment 1 to 4 is presented in …” „… [72]. An explicit time integration method is applied – which is a common choice for crash and impact …”

Introduction S. 1-5

„… granules will be carried out, followed by a numerical study to describe the mechanical behaviour. In the …” „… commercial FEM tools that are used as standard tools in industry. The numerical methods and material models …” „… sufficiently evaluated with numerical methods in a fairly easy manner. Thus, new designs, such as X-Core …”

Constitutive equations and numerical implementation S. 6-23

„… 2 Constitutive equations and numerical implementation This chapter serves to summarize the …” „… element method. The governing equations and the numerical implementation are shown in the next section …” „… Constitutive equations and numerical implementation referred to as plastic flow. Here, plastic strains arise …”

Bibliography S. 119-136

„… numerical simulation to analyze ship collision, in: International Conference on Collision and Grounding of …” „… [24] J. Amdahl, D. Kavlie, Experimental and numerical simulation of double hull stranding, in: DNV-MIT …” „… . Ringsberg, E. Johnson, M. Hoseini, A. Ulfvarson, Experimental and numerical investigation of bulb impact …”

Determination of bulk particle properties S. 40-63

„… conducted. This approach is called direct identification [137]. On the other hand, a numerical optimization …” „… identification. Due to the approach of a direct parameter identification, followed by a numerical correction …” „… Simulations Figure 4.1: Schematic view of experimental and numerical relations between the different tests and …”

doi.org/10.51202/9783186356185

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

Marcel König

Series: Mechanik/Bruchmechanik

Volume 351 2018

Results in this title

Bibliography S. 252-266

„… numerical dissipation for time integration algorithms in structural dynamics”. In: Earthquake Engineering …” „… flow around aircraft”. In: Proceedings of the 3rd International Workshop on Numerical Modelling in …” „… Aerospace Sciences. Bucharest, Romania, 2015. [2] A. Aitken. “On Bernoulli’s numerical solution of algebraic …”

Fluid Problems S. 5-24

„… ) Apparently, the numerical integration of the surface and the volume integrals require the evaluation of the …” „… different numerical methods for their solution. First of all, we derive the Navier-Stokes equations in a …” „… , especially with a view to maritime applications, are of notable interest to engineers. For the numerical …”

Conclusions and Outlook S. 241-251

„… that the proposed solution procedure is very well suited for the numerical treatment of …” „… discretization schemes for their numerical treatment. Following this, we presented a generic partitioned …” „… allows to use different numerical schemes for the discretization of space and time in each of the …”

Introduction S. 1-4

„… numerical treatment. Following that, we outline the integration of the subproblems into the partitioned …” „… be prohibitively expensive or impossible. Numerical simulations have therefore evolved as an …” „… computational processing power, numerical simulations of even very complex phenomena have become feasible and …”

Benchmark Problems S. 158-217

„… 6 Benchmark Problems In this chapter, we present several numerical examples in order to verify and …” „… benchmark definition, the time step size is changed to Δt = 0.1 s, and the structural time integration …” „… three-dimensional cavity at time t = 24.7 s. radius ρ∞ = 0.9 to reduce numerical damping as compared to the …”

Structural Problems S. 25-41

„… finite element method (FEM) for the efficient numerical analysis of the problem. If the body undergoes …” „… numerical methods for their solution in Section 3.2. 3.1 Deformable Body Equations To study the dynamic …” „… amenable to a numerical analysis, we transform the strong form of the equilibrium equations into a weak …”

Advanced Applications S. 218-240

„… particular interest. Substantiated by the results obtained in these numerical studies, it is demonstrated …” „… wind energy offshore. For the numerical studies conducted in this work, a constant density ρa = 1.2 …” „… summarizes the mass properties of the individual components of the floating OWT. For the numerical analysis …”

Titelei/Inhaltsverzeichnis S. I-XVI

„… Discretization and Numerical Solution . . . . . . . . . . . . . . . . 14 2.2 Potential Flow Equations …” „… Discretization and Numerical Solution . . . . . . . . . . . . . . . . 23 3 Structural Problems 25 3.1 Deformable …” „… . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.4.4 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.5 …”

Software Library comana S. 98-157

„… Points_ }; static constexpr std::size_t localSpaceDimension { 2 }; using IntegrationPoint …” „… = Comana::IntegrationPoint; using IntegrationPoints = Array<IntegrationPoint, numberOfIntegrationPoints>; static const …” „… IntegrationPoints & getIntegrationPoints() noexcept; }; An IntegrationPoint combines the coordinates of the sampling …”

Coupled Problems S. 42-97

„… formulated in a manner that allows for a seamless integration into the generic partitioned solution procedure …” „… interpolation schemes are chosen for all the numerical examples presented in Chapter 6 and 7. The interpolation …” „… procedure will certainly result in an unacceptably high numerical effort. It is therefore advisable to …”

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Plastics in Automotive Engineering 2017

VDI Wissensforum GmbH (ed.)

Series: VDI-Berichte

Volume 4348 2017

Results in this title

P. Hörmann, K. Bornemann, F. Flueggen, H. Herten, V. Hohm, T. Ströhlein Lightweight design at Volkswagen S. 203-214

„… , numerical validation and final experimental testing for the development of a so-called FRP door sill tube …” „… context of a validated numerical design. These requirements differ significantly from those of the …” „… testing in a drop-tower rig and a real car crash. The FRP material was characterized for numerical …”

A. Liebsch, R. Kupfer, M. Gude, P. Müller, N. Andricevic Hollow profiles, organo-sheets and LFRT node structures: hybrid components made of fiber-reinforced plastics for automotive serial production S. 215-226

„… . Additional functionalization with injection-molding compound allows the integration of highly complex rib …” „… . Experimental and numerical investigations into overmolding hollow profiles The deepening and expansion of the …” „… , the 'Dresden rocket' The numerical mold-filling simulations were carried out with AUTODESK MOLDFLOW …”

doi.org/10.51202/9783182443483

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Pinch-based Methods for Absorption and Extraction Process and Solvent Screening

Christian Redepenning

Series: Verfahrenstechnik

Volume 955 2018

Results in this title

Software S. 137-142

„… the shortcut methods. This shortcoming prior to this thesis probably prevented the robust integration …” „… , expandability, as well as numerical efficiency. New interfaces, new prototypes, and new frontends added as part …” „… communication with the numerical routines module and continuation algorithm module. The numerical routines …”

Bibliography S. 173-198

„… ). Numerical continuation, and computation of normal forms. In B. Hasselblatt, & A. B. Katok (Eds.), Handbook …” „… ., Grossmann, I. E., & Miller, D. C. (2015). Simultaneous process optimization and heat integration based on …” „… ., & El-Halwagi, M. (2002). Property integration— a new approach for simultaneous solution of process and …”

Recommendations for further research S. 143-156

„… concepts. General-purpose numerical algorithms can provide such a general solution concept. Local …” „… investigation of the performance of such a concept which is based on general-purpose numerical algorithms. The …” „… correlations. The integration of transport limitations increases the complexity of the separation model which …”

Introduction S. 1-20

„… exploit all potentials to be competitive, including sophisticated methods of heat integration …” „… integration (level 5). Between the low and the high level, each additional level shows more and more details …” „… : separation devices Level 5: heat-integration Figure 1.3.: Hierarchical framework of Douglas (1985 …”

Pinch-based solvent screening for absorption and extraction processes S. 90-136

„… recovery column. The evaluation of additional units, heat integration, or optimization of the operating …” „… for heat integration, rectification, absorption, and extraction perfectly complement. All interactions …” „… absorption-rectification process. Several thousands of solvents are screened and heat integration as well as optimization …”

Pinch-based shortcut method for the design of isothermal extraction columns S. 59-89

„… refers to the existence of the pinch point. Consequently, integration of accurate pinch modeling has the …” „… basic shortcut model with an appropriate numerical solver can be attempted directly. If no solution is …”

doi.org/10.51202/9783186955036

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International Conference on Gears 2023

VDI Wissensforum GmbH (ed.)

Series: VDI-Berichte

Volume 2422 2023

Results in this title

W. Ramdane, C. Changenet, S. S. Ouali, C. Chevrel-Fraux, P. Casanova Thermal model of a planetary gear set using an isothermal approach S. 451-466

„… or forced convection are taken into account. Then numerical integration is used to estimate …” „… used. This approach assumes that all gearbox’s components have the same temperature. A numerical model …” „… thedetermination of oil temperature during transient regime. Finally, a comparison between numerical and …”

I. Criscuolo, F. Carneiro, G. Guimarães, R. Rego, J. Mascheroni Indirect Selective Laser Sintering: Modeling and analysis of surface densification by shot peening S. 1681-1698

„… explanation to the densification phenomena were based on a numerical approach of the shot peening process. The …” „… and the explanations of the densification phenomena with SP were based on a numerical approach …” „… . The selected element, C3D8R, is a general-purpose linear brick element, with reduced integration (1 …”

A. Beinstingel, F. Haringer, W. Sigmund, M. Heider, B. Pinnekamp, S. Marburg Investigation of Sound and Vibration Behavior of Cylindrical Gears S. 599-618

„… terms of lubrication theory [21]. The numerical solution of the associated Reynold’s equation is carried …” „… suggested by Gumbel [23]. The gear mesh algorithm is established as a nonlinear hybrid analytical-numerical …” „… pair of teeth. The numerical representation is based on the Isogeometric Analysis (IGA) [31] and hence …”

C. Karampatzakis, A. Mihailidis, A. Mantzaflaris, C. Provatidis Contact simulation of tooth flanks using Isogeometric Analysis S. 413-428

„… VDI-Berichte Nr. 2422, 2023 427 [16] Irons, B. M.: Engineering applications of numerical integration in …” „… and enforced at the integration (Gauss) points of the master-worker interface. Not all integration …” „… denotes the integration point belonging to the set of integration points of the worker side (1) within …”

B. Guilbert, D. Dureisseix, P. Velex Hybrid models for the simulation of displacements and stresses in lightweight gears S. 315-328

„… numerical viewpoint, it is found that numerical convergence on gear body stresses at high speeds requires …” „… function is shown in Figure 4-a. The axial dynamic displacement amplitudes obtained by numerical time-step …” „… integration and the recombination of displacements in (2) at the corresponding mesh frequency are represented …”

J. Langhart, S. Ebrahimi, T. Kelichhaus A comparison of time and frequency domain approaches for NVH S. 583-598

„… order differential equations, which are then solved by integration methods using numerical time …” „… with numerical methods. Those methods calculate the response of VDI-Berichte Nr. 2422, 2023 583the …” „… results into 14,000 single integration time step. The CPU time to solve this problem was 15 hours on a …”

S. Sepp, A. Wenig, M. Otto, K. Stahl Acoustical behavior of periodic flank modifications under dynamic operating conditions S. 341-356

„… vector The solution of the general differential equation is solved by a numerical time step integration …” „… separately for each load and speed step by calculating the dynamic conditions in the system using nu-merical …” „… time-step integration. The damping was assumed to be 5 %, which corresponds to typical values found in gear …”

J. D. M. Marafona, J. H. O. Seabra, P. M. T. Marques, R. C. Martins Effect of overlap ratio on gear dynamic behavior and noise level S. 1239-1256

„… the results presented in this work consist on a preliminary numerical analysis of the effect of the …” „… integration algorithm ( = 0.5 and 𝛼 = 0.25); time discretization is the same as for the time-varying mesh …” „… . Considering the numerical simulations performed, it can be concluded that:• Stiffness: increasing the overlap …”

J.-A. Meis Parametric system simulation of load sharing in planetary gearboxes S. 269-280

„… product development. The two main reasons for this are the necessary data and the numerical effort of …” „… in each journal bearing (gained by integration of the pressure distribution) can also be an indicator …”

doi.org/10.51202/9783181024225

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Kupplungen und Kupplungssysteme in Antrieben 2021

VDI Wissensforum GmbH (ed.)

Series: VDI-Berichte

Volume 2382 2021

Results in this title

R. Leister, J. Kriegseis, B. Frohnapfel, D. Gatti, A. F. Najafi Analytical modeling and dimensionless characteristics of open wet clutches in consideration of gravity S. 129-144

„… present work. In general, the flow system can be addressed with analytical, numerical or experimental …” „… flow as yet was mostly obtained via numerical analysis such as [17,19]. Different groove designs were …” „… technique of numerical analysis inherently is in need of appropriate fluid flow models and the …”

D. Groetsch, K. Voelkel, H. Pflaum, K. Stahl Echtzeit-Temperaturberechnung und Temperaturprädiktion nasslaufender Lamellenkupplungen S. 115-128

„… statistical evaluation. The development of the model in Matlab/Simulink enables the integration of the model …” „… /j.icheatmasstransfer.2015.12.026. [11] Le Li, Li, H., and Wang, L., “Numerical analysis of dynamic characteristics of …” „… , doi:10.1016/j.applthermaleng.2018.03.016. [16] Yu, L., Ma, B., Li, H., Liu, J. et al., “Numerical …”

doi.org/10.51202/9783181023822

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Partitioned Fluid-Structure Interaction Simulation of Maritime Applications

Jorrid Lund

Series: Mechanik/Bruchmechanik

Volume 360 2024

Results in this title

Bibliography S. 124-138

„… ] J. Chung, G. Hulbert, A time integration algorithm for structural dynamics withimproved numerical …” „… . Bulirsch, Introduction to numerical analysis, Springer, 2002. doi:10.1007/978-0-387-21738-3.[39] J. Bonet …” „… dynamics, International Journal for Numerical Methods in Engi-neering 45 (1999) 569–599. doi:10.1002/(sici …”

Structural mechanics S. 5-20

„… fractions.Gaussian quadrature is one of the most common numerical integration techniques, notonly in the FEM. The …” „… certain order can beintegrated exactly. Details about numerical integration using Gaussian quadrature can …” „… common numerical integration techniques, notonly in the FEM. The integration with Gaussian quadrature is …”

Ship propeller S. 81-117

„… 7 Submersible mixerThe numerical simulations allow for a visualization of the strain at every …” „… implicit time integration method.This meshing approach leads to degenerated elements on the leading and …” „… experimental results of Savio et al. [117].8.1.2 Numerical errors due to rotational movementA problem in the …”

Fluid mechanics S. 21-34

„… theNavier-Stokes equationsOne of the most common approaches for the numerical solution of the …” „… the solution of theNavier-Stokes equationsOne of the most common approaches for the numerical solution …” „… biggest challenges in the numerical solution of the Navier-Stokes equations isthe velocity-pressure …”

Fluid-structure interaction S. 35-48

„… integration points on the surface of the structural mesh xs. InEqs. (4.6) and (4.7), the interpolation is only …” „… Gaussian integration points on the surface of the structural mesh xs. InEqs. (4.6) and (4.7), the …” „… integration points, a different procedure must be applied.Similar to the previously described approach, the …”

Submersible mixer S. 71-80

„… measurement butalso numerical simulation with the unsteady vortex lattice method (UVLM). The UVLMmethod is …” „… results are obtained with numerical methods and both methods are basedon the potential theory. In addition …” „… [20] in the experimental tests. Lass did not only perform experimental measurement butalso numerical …”

Floating windturbine S. 49-61

„… structural setupfor the simulation were developed in the workgroup “Numerical Structural Analysis …” „… such that numerical damping is apparent in the simulation. Numericaldamping is used to reduce …” „… that numerical damping is apparent in the simulation. Numericaldamping is used to reduce high-frequency …”

doi.org/10.51202/9783186360182

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Reactor network synthesis with guaranteed robust performance

Xiao Zhao

Series: Verfahrenstechnik

Volume 952 2017

Results in this title

Bibliography S. 158-176

„… Numerical Method of Lines: Integration of Partial Differential Equations. Academic Press, 1991. [152] S …” „… numerical methods for optimizing matrix stability. Linear Algebra and its Applications, 351-352:117–145 …” „… : A MATLAB package for numerical bifurcation analysis of ODEs. ACM TOMS, 29:141–164, 2003. [34] M …”

Introduction S. 1-16

„… AR methods is their integration with other synthesis methods for complete process design [133]. These …” „… method with numerical optimization. Superstructure approach. The superstructure approach for reactor …” „… the reactors is postulated first. Based on the usage of numerical optimization tools, an optimal …”

Solution methods S. 60-106

„… numerical solvers in literature or even the open domain that can solve problems with all these features. In …” „… barrier term, which requires that si,j > 0 during all numerical iterations. In the above formulation, both …” „… application of the SQP method, solving a sequence of subproblems leads to inferior numerical performance …”

Titelei/Inhaltsverzeichnis S. I-XIV

„… , Integration of process and control system design, Superstructure approach, Eigenvalue constraints …” „… the symbols for reviewing different numerical optimization methods shown in Chapter 5 are not …”

doi.org/10.51202/9783186952035

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International Conference on Gears 2022

VDI Wissensforum GmbH (ed.)

Series: VDI-Berichte

Volume 2389 2022

Results in this title

A. Beinstingel, M. Heider, B. Pinnekamp, S. Marburg Gear mesh excitation and non-uniform rational B-splines S. 91-102

„… appropriate alternative for numerical modeling speeding up computation time by still maintaining the …” „… numerical technique to compute the excitation behavior of the changing contact conditions during power …” „… stresses occurring during power transmission. Accordingly, the numerical approach of [5] is first tested …”

B. Guilbert, P. Velex Influence of thin rimmed/-webbed gears on transmission dynamic behaviour – Approximate dynamic factor formula S. 523-532

„… figure 3.b. The dynamic factor has been calculated by numerical time integration of the hybrid model …” „… solved by a time-step Newmark’s integration scheme combined with a unilateral contact algorithm verifying …” „… and numerical results in this example with a solid gear. 4. Analysis of the thin –rimmed/-webbed …”

P. Mahendra Rao, S. Foletti, L. Bonaiti, C. Gorla, S. Beretta, F. Concli Mode III threshold under rolling contact fatigue and development of a test gearbox for planet gears S. 499-510

„… mixed approach based on both, numerical simulations and experimental tests is needed. The main goal of …” „… exercise has helped us quantify its effect and extent in our case. Hence, the above numerical results are …” „… . The design solution is envisaged in such a way so that the integration of the test gearbox with the …”

L. Ryali, D. Talbot Dynamic load distribution of planetary gear sets subject to both internal and external excitations S. 389-408

„… . [19] is a three-dimensional multibody body dynamic elastic contact solver that uses a numerical …” „… integration scheme in conjunction with a modified simplex algorithm to simultaneously solve for the load …” „… integration of the flexible shaft formulation and external excitations into the baseline dynamic model. P1P2P3 …”

S. A. Bohme, J. Keski-Rahkonen, T. Komssi A standardizable approach to tooth flank fracture S. 371-388

„… integration ofits planar stresses to a gear-specific set of analytical equations. Both, the lack of model …” „… visualize the proposed analytical equations against an accurate,2D plane strain, numerical stress prediction …” „… . 2389, 2022 375Draftand deviate only in the surface-near region, where the numerical model considers the …”

D. Sackmann, T. Husemann, B. Karpuschewski The effect of a multi-stage grinding process on the barkhausen noise signal S. 695-706

„… was the RMS-value of the Barkhausen noise (BN). For integration of the microstructures influence, a …” „… .; Tiitto, K.: Evaluation of Surface and Subsurface Stresses with Barkhausen Noise: A Numerical Approach. 3 …”

S. Matkovič, M. Kalin Effect of tribological properties on tooth root fatigue failure of polymer gears S. 1257-1268

„… were quadrilateral 4-node bilinear plane stress with reduced integration and hourglass control, named …” „… document [1] K. Mao, A numerical method for polymer composite gear flash temperature prediction, Wear. 262 …”

H.-J. Dennig, L. Zumofen, A. Kirchheim, S. Winterberg, D. Stierli Increasing the safety against scuffing of additive manufactured gear wheels by internal cooling channels S. 1345-1364

„… toolmaking, the integration of internal channel structures enables new opportunities for optimisation [5, 6 …” „… test gears for the FZG scuffing test Dimension Symbol Numerical Value Unit Centre distance a 91.5 mm …”

doi.org/10.51202/9783181023891

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PIAE EUROPE

VDI Wissensforum GmbH (ed.)

2020

Results in this title

A. Wüst, T. Metzner Development of an energy-absorbing structural element made of polyamide integrated in the plastic front-end carrier of the new Mercedes S-Class S. 1-4

„… . Fig. 1: Crash situation The integration of additional large-area crash levels with no hard …” „… the FE software LS-Dyna® with Ultrasim®, a software tool developed by BASF for numerical mapping of …” „… thermoplastic materials all in a single numerical approach. These include variables such as VDI-Berichte Nr …”

doi.org/10.51202/9783181023693

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Results (369)