Relevant bibliographies by topics / Cylindrical discretization

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Cylindrical discretization'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Cylindrical discretization"

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Hanawa, Tomoyuki, and Yosuke Matsumoto. "Relaxing Numerical Difficulties Arising from Discretization in the Cylindrical Coordinates." Journal of Physics: Conference Series 1623 (September 2020): 012014. http://dx.doi.org/10.1088/1742-6596/1623/1/012014.

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Chin, Char-Ming, and A. H. Nayfeh. "Bifurcation and Chaos in Externally Excited Circular Cylindrical Shells." Journal of Applied Mechanics 63, no. 3 (September 1, 1996): 565–74. http://dx.doi.org/10.1115/1.2823335.

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The nonlinear response of an infinitely long cylindrical shell to a primary excitation of one of its two orthogonal flexural modes is investigated. The method of multiple scales is used to derive four ordinary differential equations describing the amplitudes and phases of the two orthogonal modes by (a) attacking a two-mode discretization of the governing partial differential equations and (b) directly attacking the partial differential equations. The two-mode discretization results in erroneous solutions because it does not account for the effects of the quadratic nonlinearities. The resulting two sets of modulation equations are used to study the equilibrium and dynamic solutions and their stability and hence show the different bifurcations. The response could be a single-mode solution or a two-mode solution. The equilibrium solutions of the two orthogonal third flexural modes undergo a Hopf bifurcation. A combination of a shooting technique and Floquet theory is used to calculate limit cycles and their stability. The numerical results indicate the existence of a sequence of period-doubling bifurcations that culminates in chaos, multiple attractors, explosive bifurcations, and crises.
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Hanawa, Tomoyuki, and Yosuke Matsumoto. "A Proper Discretization of Hydrodynamic Equations in Cylindrical Coordinates for Astrophysical Simulations." Astrophysical Journal 907, no. 1 (January 27, 2021): 43. http://dx.doi.org/10.3847/1538-4357/abd2b2.

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Trotsenko, Ya P. "Numerical simulation of the flow of viscous incompressible fluid through cylindrical cavities." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2019): 218–21. http://dx.doi.org/10.17721/1812-5409.2019/1.51.

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The flow of viscous incompressible fluid in a cylindrical duct with two serial diaphragms is studied by the numerical solution of the unsteady Navier–Stokes equations. The discretization procedure is based on the finite volume method using the TVD scheme for the discretization of the convective terms and second order accurate in both space and time difference schemes. The resulting system of non-linear algebraic equations is solved by the PISO algorithm. It is shown that the fluid flow in the region between the diaphragms is nonstationary and is characterized by the presence of an unstable shear layer under certain parameters. A series of ring vortices is formed in the shear layer that causes quasi-periodic self-sustained oscillations of the velocity and pressure fields in the orifice of the second diaphragm. There can be four self-sustained oscillation modes depending on the length of the cavity formed by the diaphragms. With the increase in the distance between the diaphragms, the frequency of oscillations decreases within the same self-oscillation mode and rises sharply with the switch to the next mode.
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Yuan, Xuebo, Guochang Lin, and Youshan Wang. "Design of elliptic cylindrical thermal cloak with layered structure." International Journal of Modern Physics B 31, no. 01 (January 10, 2017): 1650244. http://dx.doi.org/10.1142/s0217979216502441.

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Thermal cloak has potential applications in thermal protection and sensing. Based on the theories of spatial transformation and effective medium, layered structure of elliptic cylindrical thermal cloak was designed. According to theoretical analysis and numerical simulation, the layered structure has typical characteristics of perfect thermal cloak. The external temperature field remains unchanged, while the internal temperature gradient decreases obviously. Meanwhile, the cloaking effect is stable in any direction. The cloaking effect can be improved by increasing the number of discretization layers or reducing the cloak thickness. The elliptic cylindrical cloak can be considered as cylindrical cloak when the focal distance is close to zero. This study has provided an effective way for realizing thermal cloak with more complex shapes.
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Wen, Yutong, Ding She, Lei Shi, and Jing Zhao. "COMPARISONS AMONG THREE COUPLING FORMS OF CYLINDRICAL NODAL EXPANSION METHODS." EPJ Web of Conferences 247 (2021): 10009. http://dx.doi.org/10.1051/epjconf/202124710009.

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Nodal expansion method (NEM) is a typical nodal method in solving neutron diffusion equation in coarse mesh spatial discretization. NEM has been extended to cylindrical geometry in previous studies. Cylindrical NEM can be realized by different forms, where the variables in the nodal coupling equations are classified as net current, flux or partial current at the nodal surface, respectively. The three types of coupling forms of NEM have been implemented in PANGU code for the high temperature gas-cooled reactor (HTGR) physics analysis. This paper derives the three types of coupling forms of NEM, and analyzes their performance in solving the HTGR model containing void region.
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Sysoev, Yu S., V. Sh Magdeev, and L. V. Kravchuk. "Choice of discretization frequency of the profiles of large cylindrical power engineering products." Measurement Techniques 40, no. 3 (March 1997): 237–45. http://dx.doi.org/10.1007/bf02504083.

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Chen, Wei, and Song Ping Wu. "Perfectly Matched Layer as an Absorbing Boundary Condition for Computational Aero-Acoustic." Advanced Materials Research 726-731 (August 2013): 3153–58. http://dx.doi.org/10.4028/www.scientific.net/amr.726-731.3153.

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Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the Perfectly Matched Layer (PML) for external boundaries in CAA. To achieve low dissipation and dispersion errors, Dispersion-Relation-Preserving (DRP) Schemes are used for spatial discretization of the acoustic equations. The classical fourth-order Runge-Kutta time scheme is applied to the acoustic equations for time discretization. Four cases are given to illustrate the 2D PML equations for the linearized/nonlinear Euler equations in Cartesian coordinates and Cylindrical coordinates. The results show that the PML is effective as absorbing boundary condition. Those are basis for PML in actual computations of acoustic problems.
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Jenkins, C. H., and J. W. Leonard. "Dynamic Wrinkling of Viscoelastic Membranes." Journal of Applied Mechanics 60, no. 3 (September 1, 1993): 575–82. http://dx.doi.org/10.1115/1.2900841.

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Problems associated with viscoelastic membrane structures have been documented, e.g., dynamic wrinkling and its effects on fatigue analysis and on snap loading. In the proposed analysis method, the constitutive equation is approximated by a finite difference equation and embedded within a nonlinear finite element spatial discretization. Implicit temporal integration and a modified Newton-Raphson method are used within a time increment. The stress-strain hereditary relation is formally derived from thermodynamic considerations. Use of modified strain-energy and dissipation functions facilitates the description of wrinkling during the analysis. Applications are demonstrated on an inflated cylindrical cantilever and on a submerged cylindrical membrane excited by waves.
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Senjanović, Ivo, Ivan Ćatipović, Neven Alujević, Nikola Vladimir, and Damjan Čakmak. "Sophisticated finite strip for vibration analysis of a rotating cylindrical shell." MATEC Web of Conferences 148 (2018): 07001. http://dx.doi.org/10.1051/matecconf/201814807001.

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In this article a two-node finite strip with eight degrees of freedom for free vibration analysis of pre-stressed rotating cylindrical shells is formulated. The circumferential mode shape profiles are described exactly using trigonometric functions. The axial mode shape profiles are approximated by bar and beam shape functions for membrane and bending displacements, respectively. In this way a semi-analytical formulation is facilitated so that the discretization is required only in the axial direction. The developed finite strip is validated by comparisons with analytical results. An excellent agreement is observed both for stationary and rotating shells.
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Dissertations / Theses on the topic "Cylindrical discretization"

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Pustějovský, Michal. "Optimalizace teplotního pole s fázovou přeměnou." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232173.

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This thesis deals with modelling of continuous casting of steel. This process of steel manufacturing has achieved dominant position not only in the Czech Republic but also worldwide. The solved casted bar cross-section shape is circular, because it is rarely studied in academical works nowadays. First part of thesis focuses on creating numerical model of thermal field, using finite difference method with cylindrical coordinates. This model is then employed in optimization part, which represents control problem of abrupt step change of casting speed. The main goal is to find out, whether the computation of numerical model and optimization both can be parallelized using spatial decomposition. To achieve that, Progressive Hedging Algorithm from the field of stochastic optimization has been used.
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Book chapters on the topic "Cylindrical discretization"

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Lee, Jungki. "Volume Integral Equation Method (VIEM)." In Advances in Computers and Information in Engineering Research, Volume 2, 79–138. ASME, 2021. http://dx.doi.org/10.1115/1.862025_ch4.

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A number of analytical techniques are available for the stress analysis of inclusion problems when the geometries of inclusions are simple (e.g., cylindrical, spherical or ellipsoidal) and when they are well separated [9, 41, 52]. However, these approaches cannot be applied to more general problems where the inclusions are anisotropic and arbitrary in shape, particularly when their concentration is high. Thus, stress analysis of heterogeneous solids or analysis of elastic wave scattering problems in heterogeneous solids often requires the use of numerical techniques based on either the finite element method (FEM) or the boundary integral equation method (BIEM). However, these methods become problematic when dealing with elastostatic problems or elastic wave scattering problems in unbounded media containing anisotropic and/or heterogeneous inclusions of arbitrary shapes. It has been demonstrated that the volume integral equation method (VIEM) can overcome such difficulties in solving a large class of inclusion problems [6,10,20,21,28–30]. One advantage of the VIEM over the BIEM is that it does not require the use of Green’s functions for anisotropic inclusions. Since the elastodynamic Green’s functions for anisotropic media are extremely difficult to calculate, the VIEM offers a clear advantage over the BIEM. In addition, the VIEM is not sensitive to the geometry or concentration of the inclusions. Moreover, in contrast to the finite element method, where the full domain needs to be discretized, the VIEM requires discretization of the inclusions only.
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Sankararaman, Shankar, You Ling, and Sankaran Mahadevan. "Fatigue Crack Growth Analysis and Damage Prognosis in Structures." In Emerging Design Solutions in Structural Health Monitoring Systems, 207–33. IGI Global, 2015. http://dx.doi.org/10.4018/978-1-4666-8490-4.ch010.

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This chapter describes a computational methodology for fatigue crack growth analysis and damage prognosis in structures. This methodology is applicable to a variety structural components and systems with complicated geometry and subjected to variable amplitude multi-axial loading. Finite element analysis is used to address complicated geometry and calculate the stress intensity factors. Multi-modal stress intensity factors due to multi-axial loading conditions are combined to calculate an equivalent stress intensity factor using a characteristic plane approach. Crack growth under variable amplitude loading is modeled using a modified Paris law that includes retardation effects. During cycle-by-cycle integration of the crack growth law, a Gaussian process surrogate model is used to replace the expensive finite element analysis, thereby significantly improving computational effort. The effect of different types of uncertainty – physical variability, data uncertainty and modeling errors – on crack growth prediction is investigated. The various sources of uncertainty include, but not limited to, variability in loading conditions, material parameters, experimental data, model uncertainty, etc. Three different types of modeling errors – crack growth model error, discretization error and surrogate model error – are included in analysis. The different types of uncertainty are incorporated into the framework for calibration and crack growth prediction, and their combined effect on crack growth prediction is computed. Finally, damage prognosis is achieved by predicting the probability distribution of crack size as a function of number of load cycles, and this methodology is illustrated using a numerical example of surface cracking in a cylindrical component.
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Kobayashi, Shiro, Soo-Ik Oh, and Taylan Altan. "Axisymmetric Isothermal Forging." In Metal Forming and the Finite-Element Method. Oxford University Press, 1989. http://dx.doi.org/10.1093/oso/9780195044027.003.0012.

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According to Spies, the majority of forgings can be classified into three main groups. The first group consists of compact shapes that have approximately the same dimensions in all three directions. The second group consists of disk shapes that have two of the three dimensions (length and width) approximately equal and larger than the height. The third group consists of the long shapes that have one main dimension significantly larger than the two others. All axially symmetric forgings belong to the second group, which includes approximately 30% of all commonly used forgings. A basic axisymmetric forging process is compression of cylinders. It is a relatively simple operation and thus it is often used as a property test and as a preforming operation in hot and cold forging. The apparent simplicity, however, turns into a complex deformation when friction is present at the die–workpiece interface. With the finite-element method, this complex deformation mode can be examined in detail. In this chapter, compression of cylinders and related forming operations are discussed. Since friction at the tool–workpiece interface is an important factor in the analysis of metal-forming processes, this aspect is also given particular consideration. Further, applications of the FEM method for complex-shaped dies are shown in the examples of forging and cabbaging. Finite-element discretization with a quadrilateral element is similar to that given in Chap. 8. The cylindrical coordinate system (r, ϑ, z) is used instead of the rectangular coordinate system. The element is a ring element with a quadrilateral cross-section, as shown in Fig. 9.1. The ξ and η of the natural coordinate system vary from −1 to 1 within each element.
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Conference papers on the topic "Cylindrical discretization"

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Korotkov, A. N., S. N. Shabunin, and V. A. Chechetkin. "The cylindrical luneburg lens discretization influence on its radiation parameters." In 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON). IEEE, 2017. http://dx.doi.org/10.1109/sibircon.2017.8109914.

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Chen, Hailong, Yile Hu, and Benjamin W. Spencer. "Peridynamics Using Irregular Domain Discretization With MOOSE-Based Implementation." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71527.

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In this paper, reformulation of classical bond-based peridynamic thermomechanical model for irregular domain decomposition and its MOOSE-based implicit formulation are presented. First, the irregular grid based peridynamic thermomechanical model is formulated and model parameters are derived. Following this, an implicit formulation for the solution of static or quasi-static problems is presented. Some aspects of the MOOSE-based implementation are given. After that, the formulation is verified against benchmark solutions for thermomechanic problems. Crack initiation and propagation in circular (2D) and cylindrical (3D) nuclear fuels at high temperature are studied using irregular grids.
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Xu, Liang, and Liming Dai. "A Numerical Approach of Assessing Fluid Oscillatory Motions in 3D Partially Filled Horizontal Cylindrical Tanks." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81301.

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The longitudinal liquid dynamics in partially filled horizontal cylindrical tanks is studied on the basis of a fully 3D mathematical approach. Governing equations based on the potential flow theory for liquid in tanks are solved to obtain natural frequencies and transient liquid motion. The governing equations are transformed by continuous coordinate mappings to perform the discretization in the computational domain for overcoming the difficulties in dealing with the boundary conditions at the curved walls and the free surface. The natural frequencies of liquid sloshing in partially filled tanks are determined by solving the generalized eigenvalue problem of liquid under different fill levels and for different tank configurations. The efficiency of the method is presented by comparing with the frequency results reported in other publications.
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Liu, Tao, Wei Zhang, Yan Zheng, and Yufei Zhang. "Internal Resonance and Nonlinear Vibrations of Eccentric Rotating Composite Laminated Circular Cylindrical Shell." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97101.

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Abstract This paper is focused on the internal resonances and nonlinear vibrations of an eccentric rotating composite laminated circular cylindrical shell subjected to the lateral excitation and the parametric excitation. Based on Love thin shear deformation theory, the nonlinear partial differential equations of motion for the eccentric rotating composite laminated circular cylindrical shell are established by Hamilton’s principle, which are derived into a set of coupled nonlinear ordinary differential equations by the Galerkin discretization. The excitation conditions of the internal resonance is found through the Campbell diagram, and the effects of eccentricity ratio and geometric papameters on the internal resonance of the eccentric rotating system are studied. Then, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equations in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. Finally, we study the nonlinear vibrations of the eccentric rotating composite laminated circular cylindrical shell systems.
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Strozzi, Matteo, Francesco Pellicano, and Antonio Zippo. "Nonlinear Vibrations of Functionally Graded Cylindrical Shells: Effect of the Geometry." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70417.

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In this paper, the effect of the geometry on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. In the linear analysis, after spatial discretization, mass and stiff matrices are computed, natural frequencies and mode shapes of the shell are obtained. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions obtained by the linear analysis; specific modes are selected. The Lagrange equations reduce nonlinear partial differential equations to a set of ordinary differential equations. Numerical analyses are carried out in order to characterize the nonlinear response of the shell. A convergence analysis is carried out to determine the correct number of the modes to be used. The analysis is focused on determining the nonlinear character of the response as the geometry of the shell varies.
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Pellicano, F., M. Amabili, and M. P. Pai¨doussis. "Stability of Empty and Fluid-Filled Circular Cylindrical Shells Subjected to Dynamic Axial Loads." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32212.

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In the present study the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analyzed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell’s nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Both driven and companion modes are included allowing for travelling-wave response of the shell. Axisymmetric modes are included because they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position. The shell is simply supported and presents a finite length. Boundary conditions are considered in the model, which includes also the contribution of the external axial loads acting at the shell edges. The effect of a contained liquid is also considered. The linear dynamic stability and nonlinear response are analysed by using continuation techniques.
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Hiermaier, Stefan, and Martin Sauer. "Adaptive FE-Meshfree-Modelling for Impacts of Liquid Filled Vessels on Thin Walled Structures." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-55189.

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A principal approach to simulate the airplane impact and the collapse of World Trade Center North Tower has been shown by Quan and Birnbaum [4]. Using the general purpose hydrocode AUTODYN the impact damage, fire induced strength reduction and progressive collapse were investigated. Both for the fuel propagation after tank break up and the thermodynamic burn processes assumptions have been taken. It is the aim of this paper to focus on the numerical aspects of simulating the fluid propagation after vessel break up. The release of a fluid out of a broken vessel after impact is not easily represented in a numerical simulation as the fluid flow and its interaction with structures can not be modelled using Lagrangian type element formulations. These elements, typically applied for structural analyses, fail under massive deformation and usually need then to be taken out of the simulation. Typical fluid dynamic discretization methods, so called Eulerian grids, would have to cover the whole space potentially being reached by the fluid flow and are therefore inefficient in a large three dimensional simulation. As an alternative method a coupled discretization using Lagrange elements and Lagrange type meshfree methods is proposed here. Meshfree methods have been introduced to structural dynamics more then ten years ago specifically to simulate processes including large deformation [1]. Originally developed as pure meshfree code, the EMI SOPHIA [3] provides now a new form of adaptivity that allows for more efficiency and accuracy. This is achieved by the use of finite elements as long as deformation is capable for the elements. At definable strain or failure thresholds any element can be transformed into one or more meshfree particles. This way, mass and volume of the original elements are conserved. As the particles interact with each other as well as with the remaining elements, all physical processes can be modelled continuously. The purpose of this study was to contribute to numerical simulation of the airplane impacts into the World Trade Center. It includes impact simulations of cylindrical vessels filled with water against thin walled rectangular shaped bars. It shows that coupled discretizations and specifically an adaptive FE-meshfree discretization offer the flexibility needed to gain both accuracy and efficiency in the simulation.
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Kamath, Arun, Hans Bihs, and Øivind A. Arntsen. "Calculation of Wave Forces on Cylindrical Piles Using a 3D Numerical Wave Tank." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10337.

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Offshore constructions generally include a large number of vertical cylinders in the support structure. The calculation of wave forces on a vertical cylinder and hydrodynamic effects on it in the presence of neighbouring cylinders is of practical interest. In this paper, a 3D numerical model is used to calculate wave forces on bottom fixed cylindrical piles. Two cases are considered in this study: a single cylinder and a pair of tandem cylinders. A scenario with multiple cylindrical structures in close proximity introduces complex wave-structure interactions and would be of great interest to observe this in detail in a three-dimensional simulation. The wave force exerted on a cylindrical pile is numerically calculated by integrating the pressure and the wall shear stress around the surface of the cylinder. In the case of the single cylinder, the force calculated by the model is compared to the force predicted by the Morison formula and MacCamy-Fuchs theory. In the second case, the pair of cylinders is aligned in the direction of the incoming waves. The numerically calculated inline wave force on each cylinder is compared to the analytical solution for this setup and a good agreement is seen. The Reynolds-Averaged Navier-Stokes equations are used as the governing equations for the fluid flow in the numerical model. The convective terms are discretized using a 5th-order conservative finite difference WENO scheme. A 3rd-order accurate TVD Range-Kutta scheme is used for time discretization. Chorin’s projection method is used to discretize the pressure. The Poisson equation for pressure is solved using a preconditioned BiCGStab algorithm. The level set method is used to obtain a sharp representation of the free water surface. Turbulence in the flow is simulated using the k-ω model. The numerical model is adapted to parallel processing using the MPI library to improve the computing performance of the code.
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Arts, Tony. "Effects of Tip Endwall Contouring on the Three Dimensional Flow Field in an Annular Turbine Nozzle Guide Vane: Part 2 — Numerical Investigation." In ASME 1985 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1985. http://dx.doi.org/10.1115/85-gt-108.

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This paper describes the numerical investigation of the three dimensional flow through a low speed, low aspect ratio, high turning annular turbine nozzle guide vane with meridional tip endwall contouring. This rotational flow field has been simulated using a finite volume discretization and a time marching technique to solve the three dimensional, time dependent Euler equations expressed in a cylindrical coordinates system. The results are presented under the form of contour plots, spanwise pitch-averaged distributions and blade static pressure distributions. Detailed comparisons with the measurements described in part I of the paper are also provided.
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Schurzig, Daniel, Sebastian Tatzko, Lars Panning-von Scheidt, and Jörg Wallaschek. "Modeling Contact Dynamics of Vanes With Adjustable Upstream Flow Angles." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-68185.

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In this paper, a simulation method is proposed for a sub-category of compressor vanes showing nonlinear behavior due to an adjustable upstream flow angle. The proposed algorithm computes the forced response of a single vane based on the New-mark time stepping scheme after reducing the structural matrices using the Craig-Bampton method. The contacts are modeled by Coulomb friction and Newton impact constraints. Contact forces are determined using linear complementarity conditions with decoupled orthogonal friction force directions. Different discretization methods for the cylindrical contact partners are proposed. Finally, numerical results are shown in order to validate the proposed algorithms.
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