Journal articles: '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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Wu, Shi Hao, Ye Gao Qu, Xiu Chang Huang, and Hong Xing Hua. "Free Vibration Analysis on Combined Cylindrical-Spherical Shell." Applied Mechanics and Materials 226-228 (November 2012): 3–8. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.3.

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Based upon the Reissner-Naghdi-Berry’s shell theory, a domain decomposition method (DDM) is utilized to investigate the vibration characteristics of the combined cylindrical-spherical shell with different boundary conditions. The combined shell was first apart from prescribed-displacement boundary and then divided into some cylindrical and spherical shell subdomains, respectively. The boundary equations were introduced into the energy functional of the combined shell as well as the constraint equations derived from interface continuity conditions between two adjacent shell subdomains. Fourier series and Chebyshev orthogonal polynomials were employed as the admissible displacement functions for each shell subdomain in the circumferential direction and axial direction in order to obtain the discretization equations of motion of the combined shell. Exact free vibration solutions of the combined shell has been performed via the DDM and were compared with those obtained by the finite element software ANSYS to confirm the reliability and accuracy.

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SCHUBERT, FRANK, BERND KOEHLER, and ALEXANDER PEIFFER. "TIME DOMAIN MODELING OF AXISYMMETRIC WAVE PROPAGATION IN ISOTROPIC ELASTIC MEDIA WITH CEFIT — CYLINDRICAL ELASTODYNAMIC FINITE INTEGRATION TECHNIQUE." Journal of Computational Acoustics 09, no. 03 (September 2001): 1127–46. http://dx.doi.org/10.1142/s0218396x0100098x.

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The Elastodynamic Finite Integration Technique (EFIT), originally developed by Fellinger et al.,1–3 represents a stable and efficient numerical code to model elastic wave propagation in linearly-elastic isotropic and anisotropic, homogeneous and heterogeneous as well as dissipative and nondissipative media. In previous works, the FIT discretization of the basic equations of linear elasticity, Hooke's law and Cauchy's equation of motion, was exclusively carried out in Cartesian coordinates. For problems in cylindrical geometries it is more suitable to use cylindrical coordinates. By that, axisymmetric problems can be treated in a two-dimensional staggered grid in the r,z-plane. The paper presents an EFIT version for axisymmetric problems in cylindrical coordinates called Cylindrical EFIT (CEFIT). After demonstrating the accuracy of the numerical code by a comparison between simulation results and analytical solutions, different examples of application are given. These examples include modeling of sound fields of ultrasonic transducers, thermoelastic laser sources, geophysical borehole probes, impact-echo measurements in layered media, and load simulations of the European Spallation Source (ESS) mercury target.

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Hornung, Peter, Martin Rumpf, and Stefan Simon. "On material optimisation for nonlinearly elastic plates and shells." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 82. http://dx.doi.org/10.1051/cocv/2020053.

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This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are investigated and a compliance cost functional is taken into account. Under symmetry assumptions on the material distribution and the load it is shown that cylindrical solutions are stationary points. Furthermore, it is demonstrated that the optimal design of cylindrically deforming, clamped rectangular plates is non trivial, i.e. with a material distribution which is not just depending on one axial direction on the plate. Analytical results are complemented with numerical optimization results using a suitable finite element discretization and a phase field description of the material phases. Finally, using numerical methods an outlook on the optimal design of non isometrically deforming plates and shells is given.

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Fan, Zhenhong, and Ru-Shan Chen. "COMBINING PSEUDOSPECTRAL DISCRETIZATION WITH METHOD OF LINES IN FULL-WAVE ANALYSIS OF CYLINDRICAL MICROSTRIP." Progress In Electromagnetics Research Letters 5 (2008): 109–21. http://dx.doi.org/10.2528/pierl08101801.

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Erdélyi, R., M. Goossens, and S. Poedts. "Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: I. The Code and Test Cases." International Astronomical Union Colloquium 144 (1994): 503–5. http://dx.doi.org/10.1017/s0252921100025926.

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AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.

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Barocas, V. H., and R. T. Tranquillo. "A Finite Element Solution for the Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Effect of Contact Guidance on Isometric Cell Traction Measurement." Journal of Biomechanical Engineering 119, no. 3 (August 1, 1997): 261–68. http://dx.doi.org/10.1115/1.2796090.

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We present a method for solving the governing equations from our anisotropic biphasic theory of tissue-equivalent mechanics (Barocas and Tranquillo, 1997) for axisymmetric problems. A mixed finite element method is used for discretization of the spatial derivatives, and the DASPK subroutine (Brown et al., 1994) is used to solve the resulting differential-algebraic equation system. The preconditioned GMRES algorithm, using a preconditioner based on an extension of Dembo’s (1994) adaptation of the Uzawa algorithm for viscous flows, provides an efficient and scaleable solution method, with the finite element method discretization being first-order accurate in space. In the cylindrical isometric cell traction assay, the chosen test problem, a cylindrical tissue equivalent is adherent at either end to fixed circular platens. As the cells exert traction on the collagen fibrils, the force required to maintain constant sample length, or load, is measured. However, radial compaction occurs during the course of the assay, so that the cell and network concentrations increase and collagen fibrils become aligned along the axis of the cylinder, leading to cell alignment along the axis. Our simulations predict that cell contact guidance leads to an increase in the load measured in the assay, but this effect is diminished by the tendency of contact guidance to inhibit radial compaction of the sample, which in turn reduces concentrations and hence the measured load.

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Guo, Pei Quan, Fen Liu, and Xiao Li Lai. "Cutting Force Prediction of Disc Cam Contour Milling." Materials Science Forum 800-801 (July 2014): 285–89. http://dx.doi.org/10.4028/www.scientific.net/msf.800-801.285.

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Cutting force equation was established for milling with flat end cutter as feeding in straight-line path by means of discretization method. The model of milling force was conducted based on the manufacturing character of cylindrical surface. The milling force is continual change in manufacturing process, it’s not only influenced by milling parameter, but also related with the shape of cam’s contour. Milling force can result in vibration as machining. Milling force prediction is very useful for manufacturing accuracy control.

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Alvarez, Jorge, Mikel Zatarain, David Barrenetxea, Naiara Ortega, and Ivan Gallego. "Semi-discretization for stability analysis of in-feed cylindrical grinding with continuous workpiece speed variation." International Journal of Advanced Manufacturing Technology 69, no. 1-4 (April 25, 2013): 113–20. http://dx.doi.org/10.1007/s00170-013-4993-y.

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Maatar, M., and P. Velex. "An Analytical Expression for the Time-Varying Contact Length in Perfect Cylindrical Gears: Some Possible Applications in Gear Dynamics." Journal of Mechanical Design 118, no. 4 (December 1, 1996): 586–89. http://dx.doi.org/10.1115/1.2826933.

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This paper presents an analytical expression of the time-varying contact length between perfect involute spur and helical gears. It is shown that contact lengths can be expressed as Fourier series whose numerical expansions correlate very well with the results of numerical time-step simulations based on contact length discretization. Finally, some possible examples of application in gear dynamics are suggested.

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Gaspar, Francisco J., Francisco J. Lisbona, and Petr N. Vabishchevich. "A Numerical Model for the Radial Flow Through Porous and Deformable Shells." Computational Methods in Applied Mathematics 4, no. 1 (2004): 34–47. http://dx.doi.org/10.2478/cmam-2004-0003.

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AbstractEnergy estimates and convergence analysis of finite difference methods for Biot's consolidation model are presented for several types of radial ow. The model is written by a system of partial differential equations which depend on an integer parameter (n = 0; 1; 2) corresponding to the one-dimensional ow through a deformable slab and the radial ow through an elastic cylindrical or spherical shell respectively. The finite difference discretization is performed on staggered grids using separated points for the approximation of pressure and displacements. Numerical results are given to illustrate the obtained theoretical results.

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Li, Xue-Qin, Guang-Chen Bai, Lu-Kai Song, and Wei Zhang. "Nonlinear Vibration Analysis for Stiffened Cylindrical Shells Subjected to Electromagnetic Environment." Shock and Vibration 2021 (July 19, 2021): 1–26. http://dx.doi.org/10.1155/2021/9983459.

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The nonlinear vibration behaviors of stiffened cylindrical shells under electromagnetic excitations, transverse excitations, and in-plane excitations are studied for the first time in this paper. Given the first-order shear deformation theory and Hamilton principle, the nonlinear partial differential governing equations of motion are derived with considering the von Karman geometric nonlinearity. By employing the Galerkin discretization procedure, the partial differential equations are diverted to a set of coupled nonlinear ordinary differential equations of motion. Based on the case of 1 : 2 internal resonance and principal resonance-1/2 subharmonic parametric resonance, the multiscale method of perturbation analysis is employed to precisely acquire the four-dimensional nonlinear averaged equations. From the resonant response analysis and nonlinear dynamic simulation, we discovered that the unstable regions of stiffened cylindrical shells can be narrowed by decreasing the external excitation or increasing the magnetic intensity, and their working frequency range can be expanded by reducing the in-plane excitation. Moreover, the different nonlinear dynamic responses of the stiffened cylindrical shell are acquired by controlling stiffener number, stiffener size, and aspect ratio. The presented approach in this paper can provide an eﬃcient analytical framework for nonlinear dynamics theories of stiffened cylindrical shells and will shed light on complex structure design in vibration test engineering.

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Cheng, Juan, and Chi-Wang Shu. "Improvement on Spherical Symmetry in Two-Dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes." Communications in Computational Physics 11, no. 4 (April 2012): 1144–68. http://dx.doi.org/10.4208/cicp.030710.131210s.

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AbstractIn, Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations of compressible gas dynamics in cylindrical coordinates. These schemes use a node-based discretization of the numerical fluxes. The control volume version has several distinguished properties, including the conservation of mass, momentum and total energy and compatibility with the geometric conservation law (GCL). However it also has a limitation in that it cannot preserve spherical symmetry for one-dimensional spherical flow. An alternative is also given to use the first order area-weighted approach which can ensure spherical symmetry, at the price of sacrificing conservation of momentum. In this paper, we apply the methodology proposed in our recent work to the first order control volume scheme of Maire in to obtain the spherical symmetry property. The modified scheme can preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid, and meanwhile it maintains its original good properties such as conservation and GCL. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of symmetry, non-oscillation and robustness properties.

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Ghadimi, Parviz, and Arsham Reisinezhad. "Numerical simulation of flood waves and calculation of exerted forces on the cylindrical piers in contraction channels with different cross section profiles." Journal of Hydroinformatics 14, no. 2 (June 21, 2011): 366–85. http://dx.doi.org/10.2166/hydro.2011.062.

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A numerical model based on two-dimensional shallow water equations is presented. The depth-averaged velocity components with free-surface elevation have been used as independent variables in the model. The finite element technique is applied to discretize the spatial derivatives. Triangular elements with quadratic and linear interpolating functions are employed for two horizontal velocity components and the free-surface elevation, respectively. The standard Galerkin method is applied for discretization of the governing equations. Time discretization is performed using an implicit scheme. The resulting linear system of equations is solved by the GMRES method. The model is validated using three test cases and the results are compared with an analytical solution, the result of numerical work and experimental data, respectively. Favorable agreement was achieved in all three cases. Subsequently, the developed model is applied to simulate free-surface elevation through a channel contraction. The effects of width of the narrow section as well as the profile of the cross section of the channel on the wave forces exerted on a circular cylinder were studied. This was done in a channel with a quartic narrow section. Plots of time histories of the drag coefficient on the cylinder were produced, demonstrating the effects of the mentioned parameters.

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Mao, Yong Jian, Yu Long Li, and Han Jun Huang. "A Simplified Method for Distribution Design of Explosive Rods to Simulate Cosine-Distributed Impulse on Cylindrical/Conical Shell." Advanced Materials Research 108-111 (May 2010): 1039–42. http://dx.doi.org/10.4028/www.scientific.net/amr.108-111.1039.

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The cosine-distributed impulsive loads induced by intense soft X-ray radiation are often simulated by explosive rods in laboratory tests. The conventional design method of rods distribution needs a complicated process, by trials or optimization, to ensure the rod number as an integer. This paper proposes a simplified method based on the principle of load discretization and impulse equivalence. It has higher efficiency and more convenience, and can automatically let the rod number be an integer. This study provides an effective design tool for rod-explosive simulation tests of aerospace structures under intense soft X-ray radiation.

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Benmoussa, Amine, Lakhdar Rahmani, and Mebrouk Rebhi. "Numerical Study of Fluid Behavior Induced by Anchor Impeller in a Stirred Vessel." Applied Mechanics and Materials 789-790 (September 2015): 257–62. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.257.

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In the present paper, we have described in-depth numerical study of the basic fluid mechanics problem of yield stress fluid flow with regularization model of Berovier and Engelman in a cylindrical vessel not chicaned equipped with an anchor stirrer by using computational fluid dynamics (CFD) based on the finite volumes method discretization of Navier - Stokes equations formulated in variables (U.V.P). We study the effect of inertia and the yield stress influence by the variation of Hedström number on the flow; we have analyzed also the influence of rheological parameters on the hydrodynamic flow behavior, such as the velocity components and the power consumption.

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Shen, Y., G. P. Neitzel, D. F. Jankowski, and H. D. Mittelmann. "Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process." Journal of Fluid Mechanics 217 (August 1990): 639–60. http://dx.doi.org/10.1017/s002211209000088x.

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Energy stability theory has been applied to a basic state of thermocapillary convection occurring in a cylindrical half-zone of finite length to determine conditions under which the flow will be stable. Because of the finite length of the zone, the basic state must be determined numerically. Instead of obtaining stability criteria by solving the related Euler–Lagrange equations, the variational problem is attacked directly by discretization of the integrals in the energy identity using finite differences. Results of the analysis are values of the Marangoni number, MaE, below which axisymmetric disturbances to the basic state will decay, for various values of the other parameters governing the problem.

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Crooijmans, M. T. M., H. J. H. Brouwers, D. H. van Campen, and A. de Kraker. "Limit Cycle Predictions of a Nonlinear Journal-Bearing System." Journal of Engineering for Industry 112, no. 2 (May 1, 1990): 168–71. http://dx.doi.org/10.1115/1.2899561.

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An analysis is presented of the self-excited vibrations of a journal carried in a cylindrical fluid film bearing. Using linear stability theory, the values of the system parameters at the point of loss of stability are determined. These values agree well with those of previous investigators. Solutions of the nonlinear system equations are obtained by time discretization and by an arc-continuation method for solving the obtained nonlinear algebraic equations. In this way periodic solutions of the nonlinear equations of motion are calculated as a function of the system parameters. The behavior of the journal can be explained by the results of these calculations.

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Mahanta, B. B., P. Reddy, Anjan Dutta, and Debabrata Chakraborty. "Reliable Computation of Contact Force in FRP Composite Laminates under Transverse Impact." Shock and Vibration 11, no. 2 (2004): 129–42. http://dx.doi.org/10.1155/2004/824581.

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A simple and computationally efficient adaptive finite element analysis strategy has been adopted for accurate and reliable evaluation of contact force under transverse impact. Contact of a spherical and cylindrical impactor on FRP composite laminates are considered. Adaptive mesh refinement enables the finite element mesh to be obtained iteratively and automatically for the solution to have the desired level of accuracy. The refined meshes influence the calculated contact force and contact period appreciably. Influences of impactor velocity, mass of impactor, mass of the plate on discretization error as well as on contact force history have also been studied and are found to be sensitive.

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Hadi, Abbas, Hamid Reza Ovesy, Saeed Shakhesi, and Jamshid Fazilati. "Large Amplitude Dynamic Analysis of FGM Cylindrical Shells on Nonlinear Elastic Foundation Under Thermomechanical Loads." International Journal of Applied Mechanics 09, no. 07 (October 2017): 1750105. http://dx.doi.org/10.1142/s1758825117501058.

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Nonlinear dynamic characteristics of functionally graded material (FGM) cylindrical shells surrounded by nonlinear elastic foundation under axial static and lateral dynamic loads in thermal environment are investigated in the current paper. The main emphasis is on the simulation of the elastic foundation model and thermal loads. Nonlinear tri-parametric elastic foundation including linear and nonlinear parameters is used to model the reaction of the elastic foundation on the cylindrical shell. Different thermal loading scenarios are applied to the system to study the effects of thermal environment, including uniform, linear and nonlinear temperature distribution across the shell thickness. Governing equations are derived based on the Donnell’s thin shell theory. Material properties of the FGM are assumed to be variable through the shell thickness according to a power law function. Discretization of the obtained governing equations is performed using the Galerkin’s method. An averaging method and the Runge–Kutta method are applied to obtain the frequency–amplitude relation and time–deflection relation, respectively. Comprehensive numerical results are given for investigating the effects of thermo-mechanical loads, material and geometrical properties and nonlinear elastic foundation parameters on nonlinear dynamic characteristics of the functionally graded cylindrical shells (FGCSs). Present formulations are validated by comparing the results with the published data for some specific cases.

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Hasrati, Emad, Reza Ansari, and Jalal Torabi. "Nonlinear Forced Vibration Analysis of FG-CNTRC Cylindrical Shells Under Thermal Loading Using a Numerical Strategy." International Journal of Applied Mechanics 09, no. 08 (December 2017): 1750108. http://dx.doi.org/10.1142/s1758825117501083.

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Employing an efficient numerical strategy, the nonlinear forced vibration analysis of composite cylindrical shells reinforced with single-walled carbon nanotubes (CNTs) is carried out. It is assumed that the distribution of CNTs along the thickness direction of the shell is uniform or functionally graded and the temperature dependency of the material properties is accounted. The governing equations are presented based on the first-order shear deformation theory along with von-Karman nonlinear strain-displacement relations. The vectorized form of energy functional is derived and directly discretized using numerical differential and integral operators. By the use of variational differential quadrature (VDQ) method, discretized nonlinear governing equations are obtained. Then, the time periodic differential operators are applied to perform the discretization procedure in time domain. Finally, the pseudo-arc length continuation method is employed to solve the nonlinear governing equations and trace the frequency response curve of the nanocomposite cylindrical shell. A comparison study is first presented to verify the efficiency and validity of the proposed numerical method. Comprehensive numerical results are then given to investigate the effects of the involved factors on the nonlinear forced vibration characteristics of the structure. The results show that the changes of fundamental vibrational mode shape have considerable effects on the frequency response curves of composite cylindrical shells reinforced with CNTs.

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Wang, Dongdong, Chao Song, and Huikai Peng. "A Circumferentially Enhanced Hermite Reproducing Kernel Meshfree Method for Buckling Analysis of Kirchhoff–Love Cylindrical Shells." International Journal of Structural Stability and Dynamics 15, no. 06 (June 17, 2015): 1450090. http://dx.doi.org/10.1142/s0219455414500904.

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A circumferentially enhanced Hermite reproducing kernel (HRK) meshfree method is developed for the buckling analysis of Kirchhoff–Love cylindrical shells. In this method, in order to accurately represent the circumferential periodicity of cylindrical shells, the shell mid-surface is first discretized by a set of physical nodes in the two-dimensional parametric space, thereafter another set of dummy nodes are added by a straightforward periodic translation of the physical nodes. Subsequently the meshfree shape functions are constructed using both the physical nodes and the dummy nodes through a periodically linked relationship. The resulting meshfree shape functions exhibit the desired circumferential periodicity. The meshfree shape functions are formulated in the HRK framework which can be degenerated to the standard reproducing kernel (RK) shape functions just by removing the rotational terms. Meanwhile, the cylindrical shell buckling equations are rationally derived from the consistent linearization of the internal virtual work. During the meshfree discretization, the in-plane shell displacements are represented by the conventional RK shape functions, while the out-of-plane shell deflection is approximated by the Hermite meshfree shape functions with both directional and rotational degrees of freedom. The numerical integration of the material as well as the geometric stiffness matrices are carried out by the strain smoothing sub-domain stabilized conforming integration (SSCI) method. Numerical examples show that the proposed approach yields very favorable results for the buckling analysis of cylindrical shells.

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Yu, Guojun, Bo Yu, Yu Zhao, Qianqian Shao, and Jianyu Xie. "The Discretization Method for Convention-diffusion Equations in Two-dimensional Cylindrical Coordinate Systems based on Unstructured Grids." Procedia Computer Science 18 (2013): 2117–26. http://dx.doi.org/10.1016/j.procs.2013.05.382.

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Oud, G. T., D. R. van der Heul, C. Vuik, and R. A. W. M. Henkes. "A fully conservative mimetic discretization of the Navier–Stokes equations in cylindrical coordinates with associated singularity treatment." Journal of Computational Physics 325 (November 2016): 314–37. http://dx.doi.org/10.1016/j.jcp.2016.08.038.

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Yu, Guojun, Bo Yu, Yu Zhao, Jingfa Li, Qianqian Shao, and Jianyu Xie. "An unstructured grids-based discretization method for convection–diffusion equations in the two-dimensional cylindrical coordinate systems." International Journal of Heat and Mass Transfer 67 (December 2013): 581–92. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.08.059.

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Chiorescu, Dan, Gheorghe Nagîț, Oana Dodun, and Ștefan Mihalache. "The Influence of Dimensional-Type Mathematical Model for Cylindrical Deep Drawing on the Distribution of Extreme Unitary Stresses." Applied Mechanics and Materials 657 (October 2014): 168–72. http://dx.doi.org/10.4028/www.scientific.net/amm.657.168.

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The The 3D modelling, compared to the 2D-symmetrical rotation (axial) modelling, is much more complex and one of the reasons for this, with a view to plastic anisotropy, is that 3D modelling adopts normal anisotropy while 2D modelling adopts symmetrical rotational anisotropy. When the finite element method is used for numerical solving, the number of nodes in the discretization network is much larger in the 3D modelling and even when using last generation PCs the processing time is much longer. For this reason, for expedite calculations, as those needed to establish, in a first approximation, the optimal parameters of a deep drawing process I analysed in this paper the possibility to use the 2D-symmetrical rotation (axial) modelling. In a first phase, we intend to create a representative set of deep drawing problems and then to solve them through numerical simulations using Ansys package, using both the 3D modelling, in cartesian coordinates, and the 2D-symmetrical rotation (axial) modelling, in cylindrical coordinates. Runnings shall be carried out for various refinement levels of discretization network in finite elements. The calculation times shall be compared for these two modellings and following the comparative analysis of the results we can deduce the errors entered in the 2D modelling. These errors shall be assessed by analysing and comparing the extreme unitary stresses as follows: normal stress by the Ox and Oy axes , in the 3D modelling, and in the 2D modelling by the Ox / Oy axis; shear stresses by the XZ and YZ planes, in the 3D modelling and in the 2D modelling by the XZ plane.

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NIENHÜSER, CH, and H. C. KUHLMANN. "Stability of thermocapillary flows in non-cylindrical liquid bridges." Journal of Fluid Mechanics 458 (May 10, 2002): 35–73. http://dx.doi.org/10.1017/s0022112001007650.

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The thermocapillary flow in liquid bridges is investigated numerically. In the limit of large mean surface tension the free-surface shape is independent of the flow and temperature fields and depends only on the volume of liquid and the hydrostatic pressure difference. When gravity acts parallel to the axis of the liquid bridge the shape is axisymmetric. A differential heating of the bounding circular disks then causes a steady two-dimensional thermocapillary flow which is calculated by a finite-difference method on body-fitted coordinates. The linear-stability problem for the basic flow is solved using azimuthal normal modes computed with the same discretization method. The dependence of the critical Reynolds number on the volume fraction, gravity level, Prandtl number, and aspect ratio is explained by analysing the energy budgets of the neutral modes. For small Prandtl numbers (Pr = 0.02) the critical Reynolds number exhibits a smooth minimum near volume fractions which approximately correspond to the volume of a cylindrical bridge. When the Prandtl number is large (Pr = 4) the intersection of two neutral curves results in a sharp peak of the critical Reynolds number. Since the instabilities for low and high Prandtl numbers are markedly different, the influence of gravity leads to a distinctly different behaviour. While the hydrostatic shape of the bridge is the most important effect of gravity on the critical point for low-Prandtl-number flows, buoyancy is the dominating factor for the stability of the flow in a gravity field when the Prandtl number is high.

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Alvarez, Jorge, Mikel Zatarain, David Barrenetxea, Jose Ignacio Marquinez, and Borja Izquierdo. "Implicit Subspace Iteration to Improve the Stability Analysis in Grinding Processes." Applied Sciences 10, no. 22 (November 19, 2020): 8203. http://dx.doi.org/10.3390/app10228203.

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An alternative method is devised for calculating dynamic stability maps in cylindrical and centerless infeed grinding processes. The method is based on the application of the Floquet theorem by repeated time integrations. Without the need of building the transition matrix, this is the most efficient calculation in terms of computation effort compared to previously presented time-domain stability analysis methods (semi-discretization or time-domain simulations). In the analyzed cases, subspace iteration has been up to 130 times faster. One of the advantages of these time-domain methods to the detriment of frequency domain ones is that they can analyze the stability of regenerative chatter with the application of variable workpiece speed, a well-known technique to avoid chatter vibrations in grinding processes so the optimal combination of amplitude and frequency can be selected. Subspace iteration methods also deal with this analysis, providing an efficient solution between 27 and 47 times faster than the abovementioned methods. Validation of this method has been carried out by comparing its accuracy with previous published methods such as semi-discretization, frequency and time-domain simulations, obtaining good correlation in the results of the dynamic stability maps and the instability reduction ratio maps due to the application of variable speed.

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Bogey, Christophe, Nicolas de Cacqueray, and Christophe Bailly. "Finite differences for coarse azimuthal discretization and for reduction of effective resolution near origin of cylindrical flow equations." Journal of Computational Physics 230, no. 4 (February 2011): 1134–46. http://dx.doi.org/10.1016/j.jcp.2010.10.031.

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Pilgun, G., and M. Amabili. "Non-linear vibrations of shallow circular cylindrical panels with complex geometry. Meshless discretization with the R-functions method." International Journal of Non-Linear Mechanics 47, no. 3 (April 2012): 137–52. http://dx.doi.org/10.1016/j.ijnonlinmec.2011.11.011.

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Sharma, Nayhel, and Rakesh Kumar. "The simulation of single wraparound fin on a semi-cylindrical missile body." Aircraft Engineering and Aerospace Technology 92, no. 3 (January 13, 2020): 418–27. http://dx.doi.org/10.1108/aeat-04-2019-0083.

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Purpose The purpose of this paper is to establish a freestream computational fluid dynamics (CFD) model of a three-dimensional non-spinning semi-cylindrical missile model with a single wrap around fin in Mach 2.70-3.00M range and 0° angle of attack, and ultimately establishing itself for future research study. Design/methodology/approach In this study, the behaviour of flow around the fin was investigated using a κ-ϵ turbulence model of second-order of discretization. This was done using a highly structured mesh. Additionally, an inviscid CFD simulation involving the same boundary conditions have also been carried out for comparison. Findings The obtained values of aerodynamic coefficients and pressure contours visualizations are compared against their experimental and computational counterparts. A typical missile aerodynamic characteristic trend can be seen in the current CFD. Practical implications The predicted values of the aerodynamic coefficients of this single fin model have also been compared to those of the full missile body comprising of four fins from the previous research studies, and a similar aerodynamic trend can be seen. Originality/value This study explores the possibility of the use of turbulence modelling in a single fin model of a missile and provides a basic computational model for further understanding the flow behaviour near the fin.

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Poedts, Stefaan, Wolfgang Kerner, and Marcel Goossens. "Alfvén-wave heating in resistive MHD." Journal of Plasma Physics 42, no. 1 (August 1989): 27–58. http://dx.doi.org/10.1017/s0022377800014173.

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Resonant absorption of Alfvén waves in tokamak plasmas is studied numerically using the linearized equations of resistive magnetohydrodynamics. A numerical code based on a finite-element discretization is used for determining the stationary state of a cylindrical plasma column that is excited by an external periodic driver. The energy dissipation rate in the stationary state is calculated and the dependence of the plasma heating on electrical resistivity, the equilibrium profiles, and the wavenumbers and frequency of the external driver is investigated. Resonant absorption is extremely efficient when the plasma is excited with a frequency near that of a so-called ‘collective mode’. The heating of a plasma by driving it at the frequencies of discrete Alfvén waves is also investigated.

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JIA, FEI, YAN-PING CAO, YAN ZHAO, and XI-QIAO FENG. "BUCKLING AND SURFACE WRINKLING OF AN ELASTIC GRADED CYLINDER WITH ELASTIC MODULUS ARBITRARILY VARYING ALONG RADIAL DIRECTION." International Journal of Applied Mechanics 06, no. 01 (February 2014): 1450003. http://dx.doi.org/10.1142/s1758825114500033.

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This paper investigates the buckling and surface wrinkling phenomena of an elastic graded cylinder under axial compression. We develop a semi-analytical finite element model based on elastic stability theory and the work of Lee et al. [Journal of Mechanics and Physics of Solids56 (2008) 858–868], which enables us to determine the critical compressive strain and corresponding wrinkling wavelength of a soft cylindrical structure with the shear modulus arbitrarily varying along the radial direction. A number of examples of practical interest have been explored to validate the proposed method, including: (i) surface wrinkling a soft cylinder with a hard outer surface, (ii) surface wrinkling of a soft cylindrical tube with a hard inner surface layer, (iii) buckling of a soft cylinder with an embedded hard layer, (iv) surface wrinkling of a soft cylinder covered by a bilayer, and (v) surface wrinkling of an elastic graded soft cylinder covered by a hard layer. The results demonstrate that the proposed method is valid for all these situations. In comparison to conventional finite element method, the discretization and meshing in the present method are much easier and the degrees of freedom involved are much smaller.

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Rahmani, L., O. Seghier, A. Benmoussa, and B. Draoui. "CFD study of the thermal transfer of a non-Newtonian fluid within a tank mechanically stirred by an anchor-shaped impeller." EPJ Web of Conferences 180 (2018): 02089. http://dx.doi.org/10.1051/epjconf/201818002089.

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The most of operations of chemical, biochemical or petrochemical industries are carried out in tanks or in reactors which are mechanically-controlled. The optimum mode of operation of these devices requires a finalized knowledge of the thermo-hydrodynamic behavior induced by the agitator. In the present work, the characterization of the incompressible hydrodynamic and thermal fields of a non-Newtonian fluid (Bingham) in a flat, non-baffled cylindrical vessel fitted with anchor agitator was undertaken by numerical simulation, using the CFD code Fluent (6.3.26) based on the finite volume discretization method of the energy equation and the Navier-Stokes equations which are formulated in (U.V.P) variables. We have summarized this simulated system by comparing of the consumed power and the Nusselt number for this type of mobile (Anchor agitator).

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Yuan, Xuebo, Guochang Lin, and Youshan Wang. "Design of layered structure for thermal cloak with complex shape." Modern Physics Letters B 30, no. 20 (July 30, 2016): 1650256. http://dx.doi.org/10.1142/s0217984916502560.

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Thermal cloaks have potential applications in thermal protection and sensing, and those cloaks with complex shapes are much more efficient in application. Layered discretization is a valid way to realize thermal cloaks designed through spatial transformation which are usually nonhomogeneous and anisotropic. However, previous studies are limited to two-dimensional cylindrical ones. Based on the theories of spatial transformation and effective medium, a four-step design method for layered structure of thermal cloak with complex shape is proposed. It is expected to realize the designed layered structure by utilizing the existing regular materials. According to the numerical simulations, the thermal cloaking performances of layered structures are good and close to that of the perfect thermal cloaks. This study has provided an effective way for realizing thermal cloak with complex shape.

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Amabili, Marco. "Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1993 (June 28, 2013): 20120474. http://dx.doi.org/10.1098/rsta.2012.0474.

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Reduced-order models are essential to study nonlinear vibrations of structures and structural components. The natural mode discretization is based on a two-step analysis. In the first step, the natural modes of the structure are obtained. Because this is a linear analysis, the structure can be discretized with a very large number of degrees of freedom. Then, in the second step, a small number of these natural modes are used to discretize the nonlinear vibration problem with a huge reduction in the number of degrees of freedom. This study finds a recipe to select the natural modes that must be retained to study nonlinear vibrations of an angle-ply laminated circular cylindrical shell that the author has previously studied by using admissible functions defined on the whole structure, so that an accuracy analysis is performed. The higher-order shear deformation theory developed by Amabili and Reddy is used to model the shell.

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Aralova, Albina. "On Certain Problems of Identification of Thermal Density of the Temperature State of the Hollow Cylinder Shell." Cybernetics and Computer Technologies, no. 1 (March 31, 2020): 32–40. http://dx.doi.org/10.34229/2707-451x.20.1.4.

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Introduction. In conditions of the active use of composite materials, as when accomplishing the tasks of extending the service life of existing structures, problems on recovering unknown parameters of their components under the known data on their surface arise. In [1-4], to solve the problems of identification ofparameters of a wide range, it is proposed to construct explicit expressions of the gradients of residual functionals by means of the corresponding conjugate problems obtained from the theory of optimal control of the states of multicomponent distributed systems, which is the development of the corresponding researches of Zh. Lyons. In [5-7], this technology is extended to the problem of thermoelastic deformation of multicomponent bodies. In this article some problems of optimal control of the temperature state of a cylindrical body with a cavity are considered. The purpose of the paper is to show the algorithm for identifying the parameters of a cylindrical hollow shell, based on the theory of optimal control and using the gradient methods of Alifanov. Results. Based on the theory of optimal control, the temperature control of a cylindrical shell is studied. To solve the problem of identifying the parameters of a hollow cylindrical shell, namely, finding the heat flux powers on its surfaces, based on [1,2,5-7], a direct and conjugate problem and gradients of non-viscous functionals are constructed. Discretization by the finite element method using piecewise quadratic functions is carried out and accuracy estimates for it are presented. The initial problem in the model examples presented is solved using gradient methods, where at each step of determining the (n + 1) the approximation of the solution, the direct and adjoint problems are solved using finite element method with the help piecewise quadratic functions by minimizing the corresponding energy functional. A number of model examples solved.

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Sysoev, Yu S., V. Sh Magdeev, and V. V. Manevich. "Discretization of the profiles of large cylindrical products in analysis of shape deviations with allowance for evaluations of the curvature." Measurement Techniques 40, no. 1 (January 1997): 63–70. http://dx.doi.org/10.1007/bf02505168.

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Gigante, Giacomo, and Christian Vergara. "On the Choice of Interface Parameters in Robin–Robin Loosely Coupled Schemes for Fluid–Structure Interaction." Fluids 6, no. 6 (June 8, 2021): 213. http://dx.doi.org/10.3390/fluids6060213.

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We consider two loosely coupled schemes for the solution of the fluid–structure interaction problem in the presence of large added mass effect. In particular, we introduce the Robin–Robin and Robin–Neumann explicit schemes where suitable interface conditions of Robin type are used. For the estimate of interface Robin parameters which guarantee stability of the numerical solution, we propose a new strategy based on the optimization of the reduction factor of the corresponding strongly coupled (implicit) scheme, by means of the optimized Schwarz method. To check the suitability of our proposals, we show numerical results both in an ideal cylindrical domain and in a real human carotid. Our results showed the effectiveness of our proposal for the calibration of interface parameters, which leads to stable results and shows how the explicit solution tends to the implicit one for decreasing values of the time discretization parameter.

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Panning, Lars, Walter Sextro, and Karl Popp. "Spatial Dynamics of Tuned and Mistuned Bladed Disks with Cylindrical and Wedge-Shaped Friction Dampers." International Journal of Rotating Machinery 9, no. 3 (2003): 219–28. http://dx.doi.org/10.1155/s1023621x03000198.

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One of the main tasks in the design of turbomachines like turbines, compressors, and fans is to increase the reliability and efficiency of the arrangement. Failures due to blade cracks are still a problem and have to be minimized with respect to costs and safety aspects. To reduce the maximum stresses, the blades can be coupled via friction damping devices such as underplatform dampers that are pressed onto the blade platforms by centrifugal forces. In this work, a method will be presented to optimize two different types of underplatform dampers in bladed disk applications with respect to a maximum damping effect.In practice, underplatform dampers with various geometric properties—cylindrical and wedge-shaped—are commonly used and lead to different contact conditions. A discretization of the contact areas between the blade platforms and the dampers is applied to be able to investigate nearly arbitrary contact geometries and spatial blade vibrations. The functionality of the two mentioned damper types has been studied in detail under different working conditions of the assembly. The advantages and disadvantages of both damper types are pointed out and strategies are presented to improve the damper design. In this context, the influence of mistuning effects is discussed in terms of statistical mistuning of the blades' natural frequencies due to manufacturing tolerances as well as systematical mistuning due to a deliberate slight variation of the blade masses or geometries.

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Geranmayeh, Amir, Wolfgang Ackermann, and Thomas Weiland. "Space-FFT-accelerated marching-on-in-degree methods for finite periodic structures." International Journal of Microwave and Wireless Technologies 1, no. 4 (June 19, 2009): 331–37. http://dx.doi.org/10.1017/s1759078709990328.

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A fast, yet unconditionally stable, solution of time-domain electric field integral equations (TD EFIE) pertinent to the scattering analysis of uniformly meshed and/or periodic conducting structures is introduced. A one-dimensional discrete fast Fourier transform (FFT)-based algorithm is proffered to expedite the calculation of the recursive spatial convolution products of the Toeplitz–block–Toeplitz retarded interaction matrices in a new marching-without-time-variable scheme. Additional saving owing to the system periodicity is concatenated with the Toeplitz properties due to the uniform discretization in multi-level sense. The total computational cost and storage requirements of the proposed method scale as O(Nt2Nslog Ns) and O(Nt Ns), respectively, as opposed to O(Nt2Ns2) and O(NtNs2) for classical marching-on-in-order methods, where Nt and Ns are the number of temporal and spatial unknowns, respectively. Simulation results for arrays of plate-like and cylindrical scatterers demonstrate the accuracy and efficiency of the technique.

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Journal articles on the topic 'Cylindrical discretization'

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