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Journal articles on the topic 'Analytical and numerical'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

NUNES, R. P., and F. B. RIZZATO. "Analytical method for determining at equilibrium the envelope and emittance of initially mismatched beams." Journal of Plasma Physics 75, no. 6 (June 3, 2009): 829–39. http://dx.doi.org/10.1017/s0022377809990079.

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AbstractThis work presents a fully analytic way of determining relevant equilibrium quantities of a high-intensity charged particle beam submitted to magnetic focusing while inside a linear channel. Through the current approach, some intermediate steps of our original hybrid model which had to be solved numerically can now be eliminated, leading to the obtainment of a fully analytic expression. This expression relates the initial beam parameters with those at equilibrium, allowing beam macroscopic quantities such as envelope and emittance to be naturally and analytically determined. For validation, full self-consistent N-particle beam numerical simulations have been carried out and the results compared with the predictions supplied by the full analytical model. The agreement is shown to be good with the simulations and also with the original hybrid numerical-analytical version of the model.

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2

Ningsi, Gabariela Purnama, Fransiskus Nendi, and Lana Sugiarti. "An application of the finite difference method for solving the mass spring system equation." Jurnal Matematika, Statistika dan Komputasi 16, no. 3 (April 28, 2020): 404. http://dx.doi.org/10.20956/jmsk.v16i3.9574.

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The numerical method is one method that can be used to solve differential equations, both differential equations that are easy or difficult to solve analytically. The solution obtained from the calculation results is an approximate solution or a solution that approaches an analytic solution, not an analytic solution. That is, in solving differential equations numerically, there is always an error. In this paper, an analytical solution is described and described and the application of different methods in solving a damped mass spring system with a known limit value. The error between the analytic and numerical solutions obtained is very small.

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3

Rowlands, R. E. "OS03W0436 Commingling thermoelasticity with other experimental, analytical and numerical tools." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2003.2 (2003): _OS03W0436. http://dx.doi.org/10.1299/jsmeatem.2003.2._os03w0436.

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4

Wong, Leong Sing, and Shamini Somanathan. "Analytical and Numerical Modelling of One-Dimensional Consolidation of Stabilized Peat." Civil Engineering Journal 5, no. 2 (February 26, 2019): 398. http://dx.doi.org/10.28991/cej-2019-03091254.

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The objective of the paper is to compare and evaluate analytical and numerical solutions of one-dimensional consolidation of stabilized peat. The type of analytical method used to solve the problem is exact method by separation of variables and utilization of Fourier series. Plaxis 2D 8.2 Professional version software was used to find numerical solution to the problem by employing the finite element method. One-dimensional consolidation problem of stabilized peat was solved numerically and validated with the one solved analytically based on laboratory experimental results. From the results, it was discovered that the consolidation characteristics of stabilized peat evaluated numerically were found to have close approximation to those evaluated analytically. There is a novel value in developing an accurate numerical prediction for the vertical consolidation of stabilized peat considering the complexity of the soil treatment method. It must be noted that peat is highly problematic because it is produced from plant decomposition with extremely high organic matter.

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Коrniyenko, Yu V., and M. G. Suryaninov. "Development of CAD implementing the algorithm of boundary elements’ numerical analytical method." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 1 (March 31, 2015): 128–33. http://dx.doi.org/10.15276/opu.1.45.2015.21.

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6

Abbas, Inrahim A., and Mohamed I. A. Othman. "Analytical and Numerical Solution of 2D Problem for Transversely Isotropic Generalized Thermoelastic Medium with Green-Naghdi Model II." International Journal of Acoustics and Vibration 23, No 3, September 2018 (September 2018): 294–301. http://dx.doi.org/10.20855/ijav.2018.23.31053.

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In this paper, a comparison was made between the analytical and numerical solution of a two-dimensional problem for a transversely isotropic generalized thermoelastic medium. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi’s theory of type II. The problem has been solved analytically using the normal mode method with the eigenvalue approach and numerically using a finite element method. The accuracy of the finite element formulation was validated by comparing the analytical and numerical solutions for the field quantities.

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Maximov, Serguei, Felipe Gonzalez-Montañez, Rafael Escarela-Perez, Juan Carlos Olivares-Galvan, and Hector Ascencion-Mestiza. "Analytical Analysis of Magnetic Levitation Systems with Harmonic Voltage Input." Actuators 9, no. 3 (September 11, 2020): 82. http://dx.doi.org/10.3390/act9030082.

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In this paper, a new analytical method using Lagrange equations for the analysis of magnetic levitation (MagLev) systems is proposed, using Thomson’s jumping ring experiment. The method establishes the dependence of the primary and induced currents, and also the equilibrium height of the levitating object on the input voltage through the mutual inductance of the system. The mutual inductance is calculated in two ways: (i) by employing analytical formula; (ii) through an improved semi-empirical formula based on both measurements and analytical results. The obtained MagLev model was analyzed both analytically and numerically. Analytical solutions to the resulting equations were found for the case of a dynamic equilibrium. The numerical results obtained for the dynamical model under transient operation show a close correspondence with the experimental results. The good precision of the analytical and numerical results demonstrates that the developed method can be effectively implemented.

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8

Parker, A. P., and X. Huang. "Autofrettage and Reautofrettage of a Spherical Pressure Vessel." Journal of Pressure Vessel Technology 129, no. 1 (March 10, 2006): 83–88. http://dx.doi.org/10.1115/1.2389020.

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There is a numerical procedure for modeling autofrettage of thick-walled cylinders that incorporates the Bauschinger effect as a function of prior plastic strain and Von Mises’ yield criterion. In this paper the numerical procedure is extended to solve the analogous problem of a spherical, thick walled steel vessel. An equivalent new analytical solution for the case of a spherical vessel is also formulated. The analytical and numerical solutions are shown to be in close agreement. It is demonstrated numerically that a reautofrettage procedure, previously proposed for cylindrical vessels, may be extremely beneficial for spherical vessels. Additional commentary is provided on the limitations of certain analytic solutions.

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9

Ebner, H. "THE ANALYTICAL PLOTTER AND NUMERICAL PHOTOGRAMMETRY." Photogrammetric Record 10, no. 58 (August 26, 2006): 409–20. http://dx.doi.org/10.1111/j.1477-9730.1981.tb00140.x.

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10

Vanden, Kirk J., and Paul D. Orkwis. "Comparison of numerical and analytical Jacobians." AIAA Journal 34, no. 6 (June 1996): 1125–29. http://dx.doi.org/10.2514/3.13202.

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11

Golestani Dariani, A. A., and M. M. Ahmadi. "CPT Cone Factor: Numerical-Analytical Approach." International Journal of Geomechanics 19, no. 12 (December 2019): 04019132. http://dx.doi.org/10.1061/(asce)gm.1943-5622.0001521.

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12

Fathi, Nima, Seyed Sobhan Aleyasin, and Peter Vorobieff. "Numerical–analytical assessment on Manzanares prototype." Applied Thermal Engineering 102 (June 2016): 243–50. http://dx.doi.org/10.1016/j.applthermaleng.2016.03.133.

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13

Aktaş, Mehmet. "Buckling Behaviour of Carbon/Epoxy Laminated Composite Plates under Biaxial Loading." Advanced Composites Letters 18, no. 3 (May 2009): 096369350901800. http://dx.doi.org/10.1177/096369350901800303.

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In this numerical and analytical study; the length-to-thickness ratio (a/t), aspect ratio (a/b), Young modulus ratio ( E1/ E2), load ratio ( Nx/ Ny) and different boundary conditions effect on buckling behaviour of carbon/epoxy composite laminated plate were investigated. The composite plate was assumed four plies as [θ°]4. The fibre orientation, θ, was chosen as 0°, 15°, 30°, 45°, 60°, 75° and 90°. The Veres-Kollar approach [ 1 ] was used to calculate the buckling load, analytically. Also, ANSYS 10 commercial software was used for determination of buckling load, numerically. The plate has simple supported boundary condition at four edges during analytical and numerical study. Good agreements between analytical and numerical results were obtained. Results showed that the buckling load changes depend on the dimension and material properties of the plate, boundary conditions and loading cases.

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14

Wrzesień, Stanisław, Michał Frant, and Maciej Majcher. "Numerical analysis of axial fan characteristics." Mechanik 91, no. 7 (July 9, 2018): 606–8. http://dx.doi.org/10.17814/mechanik.2018.7.98.

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The paper presents an analysis and comparison of basic characteristics of axial fans, both analytically and numerically. Such characteristics are: the characteristics of the total pressure, power and total efficiency as a function of the volumetric flow rate. The presented results showed significant quantitative and qualitative differences in the characteristics obtained by two methods. The usefulness of numerical methods in relation to the results of the initial analytical project was confirmed.

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15

Chizhonkov, Eugene V., and Alexander A. Frolov. "Influence of electron temperature on breaking of plasma oscillations." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 2 (April 24, 2019): 71–84. http://dx.doi.org/10.1515/rnam-2019-0006.

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Abstract The influence of thermal motion of electrons on the processes of relativistic plasma oscillations is studied analytically and numerically. It is shown that if the temperature of electrons grows and exceeds a certain critical level, then the breaking effect vanishes due to transformation of plasma oscillations into travelling waves. Analytical conclusions are made in the framework of the theory of small perturbations based on Lagrangian variables. Numerical simulation of the transformation is performed using three different algorithms constructed on the basis of the method of finite differences in Eulerian variables. The analytical results are in good agreement with numerical experiments.

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16

GRECH, DARIUSZ K. "NUMERICAL REEXAMINATION OF SUPERSYMMETRIC AND NONSUPERSYMMETRIC SU(5)-LIKE GRAND UNIFIED MODELS." International Journal of Modern Physics A 04, no. 10 (June 1989): 2531–59. http://dx.doi.org/10.1142/s0217751x89000984.

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The significance of numerical analysis in both nonsupersymmetric and supersymmetric Grand Unified Theories is pointed out. The exact analytical and numerical analysis we present shows a need of larger corrections to the values of unifying parameters, i.e. sin 2 θw, Mx, τp than those often quoted in literature. When an unmodified nonsupersymmetric version of SU(5) is considered we show that numerical computation allows some of the models still to be experimentally admissible. The difference between analytical and numerical results for the supersymmetric SU(5) model is also stressed. In particular, corrections due to the mass threshold of additional generations or supersymmetric particles are calculated both analytically and numerically at the two-loop level. We found them far more important for the final values of sin 2 θw, Mx and τp than the effects of Higgs-Yukawa couplings between scalars and fermions.

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17

Farutin, A., H. Wu, W. F. Hu, S. Rafaï, P. Peyla, M. C. Lai, and C. Misbah. "Analytical study for swimmers in a channel." Journal of Fluid Mechanics 881 (October 24, 2019): 365–83. http://dx.doi.org/10.1017/jfm.2019.751.

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There is an overabundance of microswimmers in nature, including bacteria, algae, mammalian cells and so on. They use flagellum, cilia or global shape changes (amoeboid motion) to move forward. In the presence of confining channels, these swimmers exhibit often non-trivial behaviours, such as accumulation at the wall, navigation and so on, and their swimming speed may be strongly influenced by the geometric confinement. Several numerical studies have reported that the presence of walls either enhances or reduces the swimming speed depending on the nature of the swimmer, and also on the confinement. The purpose of this paper is to provide an analytical explanation of several previously obtained numerical results. We treat the case of amoeboid swimmers and the case of squirmers having either a tangential (the classical situation) or normal velocity prescribed at the swimmer surface (pumper). For amoeboid motion we consider a quasi-circular swimmer which allows us to tackle the problem analytically and to extract the equations of the motion of the swimmer, with several explicit analytical or semi-analytical solutions. It is found that the deformation of the amoeboid swimmer as well as a high enough order effect due to confinement are necessary in order to account for previous numerical results. The analytical theory accounts for several features obtained numerically also for non-deformable swimmers.

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18

Siakavellas, Nicolaos J. "The Importance of Analytic Solutions for Verification: Application to the Secondary Magnetic Flux of a Conductive Disk." International Journal of Electrical Engineering & Education 44, no. 4 (October 2007): 342–57. http://dx.doi.org/10.7227/ijeee.44.4.5.

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The method and value of analytical methods and the importance of analytic solutions for verification must be emphasised to both under- and post-graduate students. So, they must be able to: (i) derive by their own expressions for the quantities of interest, and (ii) test their numerical results by an independent method. Hence, they must be motivated to try to solve any problem analytically, before proceeding to a numerical solution. Towards this aim, a sample problem is proposed and an analytic expression is derived for the secondary magnetic flux induced in a conductive disk by a time-varying magnetic field. This expression, involving elliptic and improper integrals, is finally reduced into a single integral, depending on the current distribution on the disk. Next, an analytical solution for a simplified version of the problem is obtained, which may be used for verification of the numerical solution of the more complex and general problem.

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19

Giotis, Theofanis, and Dimitrios Pavlou. "Flexural dynamic response of monopile foundations under linear wave loads." Pipeline Science and Technology 4, no. 1 (March 31, 2020): 44–50. http://dx.doi.org/10.28999/2514-541x-2020-4-1-44-50.

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An analytical solution for the dynamic response of submerged slender circular cylindrical structures subjected to linear wave loads is presented. A double Laplace transform with respect to temporal and spatial variables is applied both to motion equation and boundary conditions. The dynamic deflection of the beam is obtained by inversion of the Laplace transform. The latter with respect to spatial variable is obtained analytically, while the one concerning the temporal variable is numerically calculated using Durbin numerical scheme. Results in the case of a representative example for a monopile foundation subjected to Airy waves are presented and discussed, and the analytical result is compared against numerical dynamic and static solutions.

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20

Du, Kaibing, Yongjian Li, Shuangfu Suo, and Yuming Wang. "Semi-Analytical Dynamic Analysis of Noncontacting Finger Seals." International Journal of Structural Stability and Dynamics 15, no. 04 (May 2015): 1450060. http://dx.doi.org/10.1142/s0219455414500606.

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Noncontacting finger seals represent a new noncontacting and compliant seal in gas turbine sealing technology. The compliance and noncontacting nature make this kind of seals fully adaptive to rotor excursions in the radial direction without damaging the seal performance. A new semi-analytical method is developed for characterizing the linearized dynamic performance of noncontacting finger seals. The linearized dynamic characteristics of the gas film are numerically computed using the step jump method and then approximated analytically in the equations of motion using a Prony series. By combining the gas film analytical dynamic characterization with the constitutive model for the dynamic properties of noncontacting finger seals, the dynamic equation of motion for the system is derived in analytical form. The results are presented of the gas film properties, natural transient response to initial conditions, steady-state response to rotor excursion, transmissibility ratios and dynamic stability analysis using the analytical model. It is demonstrated that the steady-state responses from the closed-form solutions agree well with those by the numerical simulation, and the analytical solutions can be used as the benchmark for calibrating the results from numerical analysis.

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21

Deghboudj, Samir, Wafia Boukhedena, and Hamid Satha. "Modal Analysis of Orthotropic Thin Rectangular Plate Based on Analytical and Finite Element Approaches." Revue des Composites et des Matériaux Avancés 30, no. 5-6 (December 30, 2020): 217–25. http://dx.doi.org/10.18280/rcma.305-604.

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The present work aims to carry out modal analysis of orthotropic thin rectangular plate to determine its natural frequencies and mode shapes by using analytical method based on Rayleigh-Ritz energy approach. To demonstrate the accuracy of this approach, the same plate is discritisated and analyzed using the finite element method. The natural and angular frequencies were computed and determined analytically and numerically by using ABAQUS finite element code. The convergency and accuracy of the numerical solution was examined. The effects of geometrical parameters and boundary conditions on vibrations are investigated. The results obtained showed a very good agreement between the analytical approach and the numerical simulations. Also, the paper presents simulations results of testing of the plate with passive vibration control.

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22

Lei, Hanlun, and Jian Li. "Dynamical structures of retrograde resonances: analytical and numerical studies." Monthly Notices of the Royal Astronomical Society 504, no. 1 (April 8, 2021): 1084–102. http://dx.doi.org/10.1093/mnras/stab960.

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ABSTRACT In this work, retrograde mean motion resonances (MMRs) are investigated by means of analytical and numerical approaches. Initially, we define a new resonant angle to describe the retrograde MMRs and then perform a series of canonical transformations to formulate the resonant model, in which the phase portrait, resonant centre, and resonant width can be analytically determined. To validate the analytical developments, the non-perturbative analysis is made by taking advantage of Poincaré surfaces of section. Some modifications are introduced in the production of Poincaré sections and, in particular, it becomes possible to make direct comparisons between the analytical and numerical results. It is found that there exists an excellent correspondence between the phase portraits and the associated Poincaré sections, and the analytical results agree well with the numerical results in terms of the resonant width and the location of resonant centre. Finally, the numerical approach is utilized to determine the resonant widths and resonant centres over the full range of eccentricity. In particular, seven known examples of retrograde asteroids including 2015 BZ509, 2008 SO218, 1999 LE31, 2000 DG8, 2014 AT28, 2016 LS, and 2016 JK24 are found inside the libration zones of retrograde MMRs with Jupiter. The results obtained in this work may be helpful for understanding the dynamical evolution for asteroids inside retrograde MMRs.

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23

Brunner, Hermann, and Peter Linz. "Analytical and Numerical Methods for Volterra Equations." Mathematics of Computation 48, no. 178 (April 1987): 841. http://dx.doi.org/10.2307/2007853.

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24

D'Alessandro, Felice, Giuseppe Roberto Tomasicchio, Fausta Musci, and Andrea Ricca. "DUNE EROSION PHYSICAL, ANALYTICAL AND NUMERICAL MODELLING." Coastal Engineering Proceedings 1, no. 33 (December 14, 2012): 32. http://dx.doi.org/10.9753/icce.v33.sediment.32.

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The present paper provides an overview of the large-scale physical model experiments performed at the Canal d’Investigaciò i Esperimentaciò Marìtima (CIEM), Laboratori d’Enginyeria Marìtima (LIM), Universitat Politècnica de Catalunya (UPC), Barcelona, within the EU-Hydralab III Integrated Infrastructure Initiative. The model tests have been carried out in a flume with a sandy dune exposed to a combination of water levels and wave conditions. Different regimes of wave attacks on the sandy/beach dune system have been investigated; in particular, the study provides a unique set of large-scale physical data concerning the storm waves induced dune overwash (Tomasicchio et al. 2011a; Tomasicchio et al.2011b). The effects of various “load parameters” on the dune erosion process generation, including dune recession rates in terms of the retreat of the dune face, Δx, and the eroded volume, ΔV, have been investigated and discussed. The laboratory data sets have been adopted to calibrate and verify the analytical model proposed by Larson et al. (2004) in order to calculate the values of ΔV at specific time intervals. Furthermore, the profile measurements have been used to calibrate and verify the numerical model C-SHORE (Kobayashi et al. 2007) predicting the beach-dune profile modifications over the near-shore region (Tomasicchio et al. 2011a; Tomasicchio et al.2011b).

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25

Mainini, Edoardo, Hideki Murakawa, Paolo Piovano, and Ulisse Stefanelli. "Carbon-nanotube geometries: Analytical and numerical results." Discrete & Continuous Dynamical Systems - S 10, no. 1 (2017): 141–60. http://dx.doi.org/10.3934/dcdss.2017008.

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26

Lindsay, K. A., J. R. Rosenberg, and G. Tucker. "Analytical and numerical construction of equivalent cables." Mathematical Biosciences 184, no. 2 (August 2003): 137–64. http://dx.doi.org/10.1016/s0025-5564(03)00059-2.

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27

Multamäki, Tuomas, and Iiro Vilja. "Analytical and numerical properties of Q-balls." Nuclear Physics B 574, no. 1-2 (May 2000): 130–52. http://dx.doi.org/10.1016/s0550-3213(99)00827-5.

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28

Verruijt, Arnold. "Numerical and analytical solutions of poroelastic problems." Geotechnical Research 5, no. 1 (March 2018): 39–50. http://dx.doi.org/10.1680/jgere.15.00006.

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29

Poyedinchuk, A. Ye, Y. A. Tuchkin, and V. P. Shestopalov. "New numerical-analytical methods in diffraction theory." Mathematical and Computer Modelling 32, no. 9 (November 2000): 1029–46. http://dx.doi.org/10.1016/s0895-7177(00)00188-6.

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30

Dain, Sergio. "Axially symmetric spacetimes: numerical and analytical perspectives." Journal of Physics: Conference Series 314 (September 22, 2011): 012015. http://dx.doi.org/10.1088/1742-6596/314/1/012015.

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31

Takahashi, M. "Analytical and Numerical Investigations of Spin Chains." Progress of Theoretical Physics 91, no. 1 (January 1, 1994): 1–15. http://dx.doi.org/10.1143/ptp/91.1.1.

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32

Fernandes, Amâncio, and Joël Pouget. "Analytical and numerical approaches to piezoelectric bimorph." International Journal of Solids and Structures 40, no. 17 (August 2003): 4331–52. http://dx.doi.org/10.1016/s0020-7683(03)00222-1.

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33

Carcolé, E., S. Bosch, and J. Campos. "Analytical and Numerical Approximations in Fresnel Diffraction." Journal of Modern Optics 40, no. 6 (June 1993): 1091–106. http://dx.doi.org/10.1080/09500349314551161.

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34

Harbrecht, Helmut. "Analytical and numerical methods in shape optimization." Mathematical Methods in the Applied Sciences 31, no. 18 (December 2008): 2095–114. http://dx.doi.org/10.1002/mma.1008.

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35

Kawalko, S. F., and M. Kanda. "Numerical and analytical monopole nonplanarity correction factors." IEEE Transactions on Electromagnetic Compatibility 40, no. 2 (May 1998): 176–79. http://dx.doi.org/10.1109/15.673625.

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36

Teeter, D. A., J. R. East, R. K. Mains, and G. I. Haddad. "Large-signal numerical and analytical HBT models." IEEE Transactions on Electron Devices 40, no. 5 (May 1993): 837–45. http://dx.doi.org/10.1109/16.210188.

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37

Canova, A., and L. Giaccone. "Numerical and Analytical Modeling of Busbar Systems." IEEE Transactions on Power Delivery 24, no. 3 (July 2009): 1568–78. http://dx.doi.org/10.1109/tpwrd.2009.2014270.

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38

Alvarez, A. C., J. Bruining, W. J. Lambert, and D. Marchesin. "Analytical and numerical solutions for carbonated waterflooding." Computational Geosciences 22, no. 2 (December 6, 2017): 505–26. http://dx.doi.org/10.1007/s10596-017-9707-3.

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39

Serra, M. "Optimal arch: Approximate analytical and numerical solutions." Computers & Structures 52, no. 6 (September 1994): 1213–20. http://dx.doi.org/10.1016/0045-7949(94)90186-4.

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40

Markosová, M. "Analytical and numerical studies on deterministic sandpiles." Physica D: Nonlinear Phenomena 80, no. 1-2 (January 1, 1995): 41–47. http://dx.doi.org/10.1016/0167-2789(95)90611-u.

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41

Markošová, Mária. "Analytical and numerical studies on deterministic sandpiles." Physica D: Nonlinear Phenomena 80, no. 1-2 (January 1995): 41–47. http://dx.doi.org/10.1016/0167-2789(95)90055-1.

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42

Wang, Wei, and Geng Chen. "Analytical and numerical modeling for flexible pipes." China Ocean Engineering 25, no. 4 (December 2011): 737–46. http://dx.doi.org/10.1007/s13344-011-0059-9.

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43

Figueroa Díaz, Rafael Alfonso, Antonio de Jesús Balvantín García, José Ángel Diosdado de la Peña, Pedro Cruz Alcantar, Ismael Murillo Verduzco, and Pedro Alberto Pérez Olivas. "Stress analysis in a screw conveyor axis under a specific fault condition." Ingeniería Investigación y Tecnología 20, no. 3 (July 1, 2019): 1–11. http://dx.doi.org/10.22201/fi.25940732e.2019.20n3.031.

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This work presents an analytical and numerical methodology that allows determining stress distribution during the functioning of a screw conveyor utilized for conveying granular material. Different operating conditions were studied analytically and numerically. Initially, the reactions generated when the mechanism was fully braced with four supports along the longitudinal axis of the shaft were estimated. In addition, the system was analyzed with a typical fault in one of the central supports. The faults studied occur primarily due to the empirical modifications that companies make to these kinds of mechanisms and to the continuous operation of the conveyor system. Finally, a comparative analysis is presented between the analytical and the numerical results in order to validate the proposed methodology.

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44

Lazareva, D. V., and M. G. Suryaninov. "Mathematical model of complex technical asymmetric system based on numerical-analytical boundary elements method." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 2 (June 15, 2015): 133–37. http://dx.doi.org/10.15276/opu.2.46.2015.24.

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45

Pousti, Shahrouz, and Ali Jalali Marnani. "Numerical and Analytical Evaluation of Crude Oil Contamination Effect on Strip Foundation’s Bearing Capacity." International Journal of Scientific Research 3, no. 4 (June 1, 2012): 143–45. http://dx.doi.org/10.15373/22778179/apr2014/49.

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46

Mehrabi, Hamed, Richard (Chunhui) Yang, and Baolin Wang. "Effects of Tension–Compression Asymmetry on Bending of Steels." Applied Sciences 10, no. 9 (May 11, 2020): 3339. http://dx.doi.org/10.3390/app10093339.

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Stainless steels (SUS) and dual-phase (DP) steels have tension-compression asymmetry (TCA) in mechanical responses to full loading cycles. This phenomenon can significantly influence sheet metal forming of such metals, however, it is difficult to describe this behaviour analytically. In this research, a novel analytical method for asymmetric elastic-plastic pure bending using the Cazacu–Barlat 2004 asymmetric yield function is proposed. It only uses material parameters in tension along with an asymmetry coefficient related to the yield function. Bending operations of SUS304 and DP980 are investigated as two case studies. In the pure bending for both SUS304 and DP980, moment–curvature diagrams are analytically obtained. Furthermore, linear and nonlinear springback behaviours of SUS304 are analytically investigated. Moreover, using the analytical model as a user-defined material, a numerical model is developed for both steels under pure bending. In the V-bending case of SUS304 with and without TCA effects, the springback behaviours of the material are investigated numerically. In addition, considering friction effects, the analytical method is further modified for predicting springback behaviours in the V-bending of 16 types of SUS304 with various strengths are determined. All the analytical and numerical results have good agreement with those experimental results from literature for validation.

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Farshidianfar, Anooshirvan, and Amin Saghafi. "Bifurcation and Chaos Prediction in Nonlinear Gear Systems." Shock and Vibration 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/809739.

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The homoclinic bifurcation and transition to chaos in gear systems are studied both analytically and numerically. Applying Melnikov analytical method, the threshold values for the occurrence of chaotic motion are obtained. The influence of system parameters on the character of vibration is studied. The numerical simulation of the system including bifurcation diagram, phase plane portraits, Fourier spectra, and time histories is considered to confirm the analytical predictions for the occurrence of homoclinic bifurcation and chaos in nonlinear gear systems.

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48

Dai, Chuanjun, He Liu, Zhan Jin, Qing Guo, Yi Wang, Hengguo Yu, Qi Wang, Zengling Ma, and Min Zhao. "Dynamic Analysis of a Heterogeneous Diffusive Prey-Predator System in Time-Periodic Environment." Complexity 2020 (April 14, 2020): 1–13. http://dx.doi.org/10.1155/2020/7134869.

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In this paper, a heterogeneous diffusive prey-predator system is first proposed and then studied analytically and numerically. Some sufficient conditions are derived, including permanence and extinction of system and the boundedness of the solution. The existence of periodic solution and its stability are discussed as well. Furthermore, numerical results indicate that both the spatial heterogeneity and the time-periodic environment can influence the permanence and extinction of the system directly. Our numerical results are consistent with the analytical analysis.

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Khdir, Younis Kh. "Analytical and Numerical Investigation of Hardening Behavior of Porous Media." Polytechnic Journal 9, no. 2 (October 30, 2019): 1–10. http://dx.doi.org/10.25156/ptj.v9n2y2019.pp1-10.

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In this study, a comparative analysis is presented between a new proposed analytical model and numerical results for macroscopic behavior of porous media with isotropic hardening in its matrix. The macroscopic behavior of a sufficiently large representative volume element (RVE), with 200 identical spherical voids, was simulated numerically using finite element method and compared with elementary volume element that contains one void. The matrix of the porous material is considered as elasto-plastic with isotropic hardening obeys exponential law for isotropic hardening. A new parameter was added with exponential law for isotropic hardening to represent the new proposed analytical model for macroscopic isotropic porous hardening. The new added parameter B depended only on the porosity. The results of the new proposed analytical model were compared with numerical results for different types of cyclic loading. Very good agreements were found between the numerical results and the proposed analytical model.

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Edeki, S. O., E. A. Owoloko, A. S. Osheku, A. A. Opanuga, H. I. Okagbue, and G. O. Akinlabi. "Numerical solutions of nonlinear biochemical model using a hybrid numerical-analytical technique." International Journal of Mathematical Analysis 9 (2015): 403–16. http://dx.doi.org/10.12988/ijma.2015.412411.

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