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Автор: Grafiati

Опубліковано: 6 вересня 2023

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1

JIN, SHI, XIAOMEI LIAO, and XU YANG. "THE VLASOV–POISSON EQUATIONS AS THE SEMICLASSICAL LIMIT OF THE SCHRÖDINGER–POISSON EQUATIONS: A NUMERICAL STUDY." Journal of Hyperbolic Differential Equations 05, no. 03 (September 2008): 569–87. http://dx.doi.org/10.1142/s021989160800160x.

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In this paper, we numerically study the semiclassical limit of the Schrödinger–Poisson equations as a selection principle for the weak solution of the Vlasov–Poisson in one space dimension. Our numerical results show that this limit gives the weak solution that agrees with the zero diffusion limit of the Fokker–Planck equation. We also numerically justify the multivalued solution given by a moment system of the Vlasov–Poisson equations as the semiclassical limit of the Schrödinger–Poisson equations.

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2

Labbé, Stéphane, and Lionel Paumond. "Numerical comparisons of two long-wave limit models." ESAIM: Mathematical Modelling and Numerical Analysis 38, no. 3 (May 2004): 419–36. http://dx.doi.org/10.1051/m2an:2004020.

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3

Liu, Ying Hua, Bing Ye Xu, and Xian He Du. "A Numerical Approach for Lower Bound Limit Analysis." Key Engineering Materials 626 (August 2014): 474–81. http://dx.doi.org/10.4028/www.scientific.net/kem.626.474.

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In this paper, a numerical procedure for plastic limit analysis of 3-D elastic-perfectly plastic bodies under complex loads is presented. The method is based on the lower-bound limit theorem and von Mises yield criterion so that the lower-bound limit analysis can be conducted by solving a nonlinear mathematical programming problem. A SQP algorithm and a dimension reduction-based technique are used to solve the discretized finite element optimization formulation. A conception of active constraint set is introduced, so that the number of constraints can be reduced greatly. The basis vectors of reduced residual stress spaces are constructed by performing an equilibrium iteration procedure of elasto-plastic finite element analysis. The numerical procedure is applied to carry out the plastic limit analysis of pipelines with part-through slots under internal pressure, bending moment and axial force. The effects of different sizes of part-through slots on the limit loads of pipelines are studied.

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4

Beran, P. S., N. S. Khot, F. E. Eastep, R. D. Snyder, and J. V. Zweber. "Numerical Analysis of Store-Induced Limit-Cycle Oscillation." Journal of Aircraft 41, no. 6 (November 2004): 1315–26. http://dx.doi.org/10.2514/1.404.

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5

Clarke, Samuel D., Colin C. Smith, and Matthew Gilbert. "Modelling discrete soil reinforcement in numerical limit analysis." Canadian Geotechnical Journal 50, no. 7 (July 2013): 705–15. http://dx.doi.org/10.1139/cgj-2012-0387.

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Soil reinforcement is widely used in geotechnical engineering. While there are various means of accounting for the presence of soil reinforcement in limit analysis and limit equilibrium type calculations, these are often highly problem-specific. In this paper, a general means of incorporating soil reinforcement within numerical limit analysis calculations is presented. A key feature of this implementation is that the reinforcement is modelled “in parallel” with the soil model, which allows the soil to flow past the reinforcement as might occur in soil nailing. To illustrate this, the “discontinuity layout optimization” (DLO) numerical limit analysis procedure is used, and the efficacy of the approach is evaluated via application to reinforced slope problems involving rigid soil nails under plane strain conditions. The analyses are calibrated against a two-part wedge analysis method, as presented in British Standard BS 8006:1995 or AASHTO’s LRFD bridge design specifications. It is shown that the DLO-based procedure produces identical results only when the two-part wedge collapse mechanism is prescribed in advance (achieved by artificially strengthening the soil except along pre-defined failure planes). A more critical mechanism is otherwise predicted, with the soil strength at collapse required to be approximately 10% higher than predicted by the two-part wedge method (or alternatively, soil nail lengths required to be approximately 20% greater).

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6

Kuznetsov, Yu A., W. Govaerts, E. J. Doedel, and A. Dhooge. "Numerical Periodic Normalization for Codim 1 Bifurcations of Limit Cycles." SIAM Journal on Numerical Analysis 43, no. 4 (January 2005): 1407–35. http://dx.doi.org/10.1137/040611306.

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7

Jiang, Kai Yu, Jing Cao, and Yue Ma. "Slope Stability Analysis Based on Limit Equilibrium and Numerical Analysis." Applied Mechanics and Materials 256-259 (December 2012): 198–202. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.198.

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Based on the background of a foundation pit slope of the tertiary strong weathered basalt(TSWB), a quantitative analysis of the slope stability is proposed by combination of the limit equilibrium and the numerical analysis. The analysis also considers the effects of the natural state and soaking state Then, as an example, an ultra-deep foundation pit slope (UFPS) is analyzed under the background of TSWB. The Janbu method is used in the limit equilibrium because it can meet all the equilibrium conditions, including the force and moment equilibrium equation. The Lagrangian difference method which based on shear strength reduction is adopted in numerical analysis. Some meaningful conclusions can be obtained through comparing analysis the calculation results of Janbu method with finite difference method. These conclusions can be given a reference to similar projects.

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8

Cáceres, María-José, José-Antonio Carrillo, and Pierre Degond. "The Child–Langmuir limit for semiconductors: a numerical validation." ESAIM: Mathematical Modelling and Numerical Analysis 36, no. 6 (November 2002): 1161–76. http://dx.doi.org/10.1051/m2an:2003011.

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9

Antão, A. N., and M. Vicente da Silva. "Three-dimensional Limit Analysis with Lade-Duncan criterion." Géotechnique Letters 12, no. 2 (June 1, 2022): 1–21. http://dx.doi.org/10.1680/jgele.22.00015.

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Анотація:

The paper describes the three-dimensional numerical implementation of the Lade-Duncan criterion in a finite element limit analysis (FELA) code. Validation is done using examples with a known solution. To conclude the proposed numerical tool is applied to the calculation of the ultimate bearing capacity of square footing.

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10

Bambach, Markus, M. Todorova, and Gerhard Hirt. "Experimental and Numerical Analysis of Forming Limits in CNC Incremental Sheet Forming." Key Engineering Materials 344 (July 2007): 511–18. http://dx.doi.org/10.4028/www.scientific.net/kem.344.511.

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Asymmetric incremental sheet forming (AISF) is a relatively new manufacturing process for the production of low volumes of sheet metal parts. Forming is accomplished by the CNC controlled movements of a simple ball-headed tool that follows a 3D trajectory to gradually shape the sheet metal blank. Due to the local plastic deformation under the tool, there is almost no draw-in from the flange region to avoid thinning in the forming zone. As a consequence, sheet thinning limits the amount of bearable deformation, and thus the range of possible applications. Much attention has been given to the maximum strains that can be attained in AISF. Several authors have found that the forming limits are considerably higher than those obtained using a Nakazima test and that the forming limit curve is approximately a straight line (mostly having a slope of -1) in the stretching region of the FLD. Based on these findings they conclude that the “conventional” forming limit curves cannot be used for AISF and propose dedicated tests to record forming limit diagrams for AISF. Up to now, there is no standardised test and no evaluation procedure for the determination of FLCs for AISF. In the present paper, we start with an analysis of the range of strain states and strain paths that are covered by the various tests that can be found in the literature. This is accomplished by means of on-line deformation measurements using a stereovision system. From these measurements, necking and fracture limits are derived. It is found that the fracture limits can be described consistently by a straight line with negative slope. The necking limits seem to be highly dependent on the test shapes and forming parameters. It is concluded that standardisation in both testing conditions and the evaluation procedures is necessary, and that a forming limit curve does not seem to be an appropriate tool to predict the feasibility of a given part design.

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11

Figueiredo, Fabio C., and Lavinia A. Borges. "Limit analysis and frictional contact: formulation and numerical solution." Meccanica 55, no. 6 (May 3, 2020): 1347–63. http://dx.doi.org/10.1007/s11012-020-01167-5.

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12

Chung, Eric, Bernardo Cockburn, and Guosheng Fu. "The Staggered DG Method is the Limit of a Hybridizable DG Method." SIAM Journal on Numerical Analysis 52, no. 2 (January 2014): 915–32. http://dx.doi.org/10.1137/13091573x.

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13

Antonucci, Clara, Massimo Gobbino, and Nicola Picenni. "On the gap between the Gamma-limit and the pointwise limit for a nonlocal approximation of the total variation." Analysis & PDE 13, no. 3 (March 19, 2020): 627–49. http://dx.doi.org/10.2140/apde.2020.13.627.

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14

CARLIER, GUILLAUME, MYRIAM COMTE, IOAN IONESCU, and GABRIEL PEYRÉ. "A PROJECTION APPROACH TO THE NUMERICAL ANALYSIS OF LIMIT LOAD PROBLEMS." Mathematical Models and Methods in Applied Sciences 21, no. 06 (June 2011): 1291–316. http://dx.doi.org/10.1142/s0218202511005325.

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Анотація:

This paper proposes a numerical scheme to approximate the solution of (vectorial) limit load problems. The method makes use of a strictly convex perturbation of the problem, which corresponds to a projection of the deformation field under bounded deformation and incompressibility constraints. The discretized formulation of this perturbation converges to the solution of the original landslide problem when the amplitude of the perturbation tends to zero. The projection is computed numerically with a multi-step gradient descent on the dual formulation of the problem.

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15

Sysala, Stanislav, Radim Blaheta, Alexej Kolcun, Jiří Ščučka, Kamil Souček, and Peng Zhi Pan. "Computation of Composite Strengths by Limit Analysis." Key Engineering Materials 810 (July 2019): 137–42. http://dx.doi.org/10.4028/www.scientific.net/kem.810.137.

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The paper is focused on computation of a compressive strength of composite materials by limit analysis. This method enables to determine the strength or other types of limit loads by solution of a specific optimization problem. It is also capable to predict failure zones. Abilities of the method are investigated on a particular composite -- a laboratory prepared sample consisting of a hard coal matrix and a polyurethane binder. This sample is chosen due to available CT images of the inner structure and laboratory experiments. Appropriate yield criteria are proposed for the coal and the binder in order to define the limit analysis problem. This problem is penalized and then discretized by higher order finite elements. For numerical solution, the semismooth Newton method and adaptive mesh refinements are also used. Numerical experiments in 2D for various CT scans and material parameters are performed.

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16

Arnold, Anton, Naoufel Ben Abdallah, and Claudia Negulescu. "WKB-Based Schemes for the Oscillatory 1D Schrödinger Equation in the Semiclassical Limit." SIAM Journal on Numerical Analysis 49, no. 4 (January 2011): 1436–60. http://dx.doi.org/10.1137/100800373.

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17

Carles, Rémi. "On Fourier Time-Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Limit." SIAM Journal on Numerical Analysis 51, no. 6 (January 2013): 3232–58. http://dx.doi.org/10.1137/120892416.

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18

Christiansen, Edmund, and Ole S. Pedersen. "Automatic mesh refinement in limit analysis." International Journal for Numerical Methods in Engineering 50, no. 6 (2001): 1331–46. http://dx.doi.org/10.1002/1097-0207(20010228)50:6<1331::aid-nme46>3.0.co;2-s.

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19

Bunov, Artem A., and Nina V. Kornilova. "Steel structures: numerical analysis of fire proofing." Stroitel'stvo: nauka i obrazovanie [Construction: Science and Education] 12, no. 3 (September 30, 2022): 60–71. http://dx.doi.org/10.22227/2305-5502.2022.3.3.

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Анотація:

Introduction. A set of calculations validating the conditions of limit states is to accompany the design of buildings and structures. Calculations of standard and non-standard combinations of loads and impacts are performed. Special loads include temperature effects from explosions and fires. Such effects greatly reduce the bearing capacity of metal structures. To protect metal structures from temperature effects, optimally selected fire proofing materials (varnishes, paints, various types of cladding) should be used. Numerical calculation methods allow analyzing the performance of building structures, exposed to temperature effects, and help select the necessary characteristics and thicknesses of fire proofing materials. Materials and methods. A metal hinged beam is used to analyze the influence of fire proofing, or lining made of fire-resistant gypsum sheets (FRGSh). Analytical and numerical methods of calculations were used to obtain the fire resistance limit of beams with cladding. The analytical method is based on the laboratory studies of fire resistance, as a result of which nomograms were obtained. The numerical method is implemented by Lira 10.12 software package. Results. Analytical and numerical methods were used to identify the fire-resistance limits for a beam that had FRGSh cladding. Temperature field mosaics in the elements along the thickness of the structure, as well as graphs of temperature changes and temperature fields in time were obtained using the numerical method. The obtained results showed good convergence. Conclusions. The use of numerical methods makes it possible to quickly and optimally select the required thickness of fire proofing for a steel structure. Calculation results are highly dependent on the characteristics of the materials in question, as well as the heat transfer environment.

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20

Qin, Li, and Hai Jian Zhang. "Gobi Inclined Excavation Based Numerical Analysis." Applied Mechanics and Materials 459 (October 2013): 631–36. http://dx.doi.org/10.4028/www.scientific.net/amm.459.631.

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Анотація:

Gobi inclined excavation foundation is based the advantages of good direct excavation, this paper mainly studied the angle inclined excavation foundation problems. Through the force, the size of the displacement, the optimal measure the tilt angle. And determine the limit load in the text.

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21

Pisano, A. A., and P. Fuschi. "A numerical approach for limit analysis of orthotropic composite laminates." International Journal for Numerical Methods in Engineering 70, no. 1 (2007): 71–93. http://dx.doi.org/10.1002/nme.1872.

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22

Klar, Axel. "An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit." SIAM Journal on Numerical Analysis 36, no. 5 (January 1999): 1507–27. http://dx.doi.org/10.1137/s0036142997321765.

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23

Liu, Jian-Guo, and Luc Mieussens. "Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit." SIAM Journal on Numerical Analysis 48, no. 4 (January 2010): 1474–91. http://dx.doi.org/10.1137/090772770.

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24

Munoz, Ana Isabel, and Jose Ignacio Tello. "MATHEMATICAL ANALYSIS AND NUMERICAL SIMULATION IN MAGNETIC RECORDING." Mathematical Modelling and Analysis 19, no. 3 (June 1, 2014): 334–46. http://dx.doi.org/10.3846/13926292.2014.924081.

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Анотація:

The head-tape interaction in magnetic recording is described in the literature by a coupled system of partial differential equations. In this paper we study the limit case of the system which reduces the problem to a second order nonlocal equation on a one-dimensional domain. We describe the numerical method of resolution of the problem, which is reformulated as an obstacle one to prevent head-tape contact. A finite element method and a duality algorithm handling Yosida approximation tools for maximal monotone operators are used in order to solve numerically the obstacle problem. Numerical simulations are introduced to describe some qualitative properties of the solution. Finally some conclusions are drawn.

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25

Yang, Rui, Yu Liu, Peng Fei Wen, and Jun Hua Zhang. "Numerical Analysis of Sheet Metal Forming Limit for Local Forming." Advanced Materials Research 1028 (September 2014): 76–83. http://dx.doi.org/10.4028/www.scientific.net/amr.1028.76.

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Анотація:

Generally, the forming limit diagram is widely applied to predict the sheet necking and fracture in the conventional sheet forming process. In recent years, the fact that the forming limit is much higher using Incremental sheet forming (ISF) than that obtained in conventional sheet forming, has become a research hotspot in forming mechanism of local forming process. In this paper, the geometrical imperfection in the thickness was presumed to represent local weakening zone and the BAMMAN_DAMAGE material model which using void to describe non homogenization caused by geometric imperfection, were used respectively to investigate the effect of geometry imperfection on the sheet forming limit. Based on the W.C. Emmens’ experiment, the reason and mechanism of enhancement of forming limit during incremental forming was studied through the numerical simulation method. And the variations of stress and strain during the forming process were also studied.

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26

Degond, Pierre, Jian-Guo Liu, and Marie-Hélène Vignal. "Analysis of an Asymptotic Preserving Scheme for the Euler–Poisson System in the Quasineutral Limit." SIAM Journal on Numerical Analysis 46, no. 3 (January 2008): 1298–322. http://dx.doi.org/10.1137/070690584.

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27

Cai, Yongyong, and Yan Wang. "Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime." SIAM Journal on Numerical Analysis 57, no. 4 (January 2019): 1602–24. http://dx.doi.org/10.1137/18m121931x.

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28

Xu, Bing Ye, Ying Hua Liu, Xian He Du, and Gang Chen. "Numerical Limit Load Analysis of Pipelines with Local Wall-Thinning." Key Engineering Materials 626 (August 2014): 482–88. http://dx.doi.org/10.4028/www.scientific.net/kem.626.482.

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Анотація:

Local wall-thinning, which can be found frequently on the surfaces of pipelines, may not only reduce the load-carrying capacities of pipelines, but also cause serious industrial accidents. In this paper, through a large number of computational examples, the effects of axial, circumferential, small area and large area local wall-thinning with different sizes on load-carrying capacities and failure modes of pipelines under both internal pressure and bending moment were investigated and evaluated. By data fitting, an engineering computational formula for plastic limit loads of pipelines with local wall-thinning was presented.

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29

Hjiaj, M., A. V. Lyamin та S. W. Sloan. "Numerical limit analysis solutions for the bearing capacity factor Nγ". International Journal of Solids and Structures 42, № 5-6 (березень 2005): 1681–704. http://dx.doi.org/10.1016/j.ijsolstr.2004.08.002.

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30

Zhang, Xiao-tian, Guang-hui Jia, and Hai Huang. "A fast numerical approach for Whipple shield ballistic limit analysis." Acta Astronautica 93 (January 2014): 112–20. http://dx.doi.org/10.1016/j.actaastro.2013.06.014.

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31

Liu, Y. H., Z. Z. Cen, and B. Y. Xu. "Numerical limit analysis of cylindrical shells with part-through slots." International Journal of Pressure Vessels and Piping 64, no. 1 (January 1995): 73–82. http://dx.doi.org/10.1016/0308-0161(94)00071-p.

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32

Degl'Innocenti, Silvia, and Cristina Padovani. "A numerical method for the limit analysis of masonry structures." Structural Engineering and Mechanics 18, no. 1 (July 25, 2004): 1–20. http://dx.doi.org/10.12989/sem.2004.18.1.001.

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33

Antão, Armando N., Teresa G. Santana, Mário Vicente da Silva, and Nuno M. da Costa Guerra. "Passive earth-pressure coefficients by upper-bound numerical limit analysis." Canadian Geotechnical Journal 48, no. 5 (May 2011): 767–80. http://dx.doi.org/10.1139/t10-103.

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Анотація:

A three-dimensional (3D) numerical implementation of the limit analysis upper-bound theorem is used to determine passive horizontal earth-pressure coefficients. An extension technique allowing determination of the 3D passive earth pressures for any width-to-height ratios greater than 7 is presented. The horizontal passive earth-pressure coefficients are presented and compared with solutions published previously. Results of the ratio between the 3D and two-dimensional horizontal passive earth-pressure coefficients are shown and found to be almost independent of the soil-to-wall friction ratio. A simple equation is proposed for calculating this passive earth-pressure ratio.

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34

Pisano, A. A., P. Fuschi, and D. De Domenico. "Numerical limit analysis of steel-reinforced concrete walls and slabs." Computers & Structures 160 (November 2015): 42–55. http://dx.doi.org/10.1016/j.compstruc.2015.08.004.

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35

Kammoun, Zied, Franck Pastor, Hichem Smaoui, and Joseph Pastor. "Large static problem in numerical limit analysis: A decomposition approach." International Journal for Numerical and Analytical Methods in Geomechanics 34, no. 18 (November 29, 2010): 1960–80. http://dx.doi.org/10.1002/nag.887.

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36

Herfelt, Morten A., Peter N. Poulsen, Linh C. Hoang, and Jesper F. Jensen. "Numerical limit analysis of keyed shear joints in concrete structures." Structural Concrete 17, no. 3 (September 2016): 481–90. http://dx.doi.org/10.1002/suco.201500161.

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37

Karczewska, Anna. "On the Limit Measure to Stochastic Volterra Equations." Journal of Integral Equations and Applications 15, no. 1 (March 2003): 59–77. http://dx.doi.org/10.1216/jiea/1181074945.

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38

Daud, Ruslizam, M. S. Abdul Majid, Mohd Afendi, N. A. M. Amin, Ahmad Kamal Ariffin, and Shahrum Abdullah. "Strong Shielding Interaction Analysis Using J-Integral." Applied Mechanics and Materials 695 (November 2014): 511–15. http://dx.doi.org/10.4028/www.scientific.net/amm.695.511.

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Анотація:

Numerical accuracy in assessing the strong shielding interaction that promotes cracking process based on continuum mechanics is presented in this paper. Crack interaction limit (CIL) and crack unification limit (CUL) are investigated based on strain energy release rate approach. The case of two interacting edge crack in finite body is simulated using finite element analysis and J-integral. As a result, the trend of CIL and CUL is presented to prove the limit and unification of energy release can be numerically shown at higher and lower crack-to-width ratio at two crack interval ratio b = 1 and b = 0. It can be concluded that the CIL and CUL is geometrically dependent.

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39

Maekawa, Yasunori. "Gevrey stability of Rayleigh boundary layer in the inviscid limit." Journal of Elliptic and Parabolic Equations 7, no. 2 (October 20, 2021): 417–38. http://dx.doi.org/10.1007/s41808-021-00128-7.

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40

Lyamin, Andrei V., Scott W. Sloan, Kristian Krabbenhøft, and Mohammed Hjiaj. "Lower bound limit analysis with adaptive remeshing." International Journal for Numerical Methods in Engineering 63, no. 14 (2005): 1961–74. http://dx.doi.org/10.1002/nme.1352.

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41

Witte, V. De, F. Della Rossa, W. Govaerts, and Yu A. Kuznetsov. "Numerical Periodic Normalization for Codim 2 Bifurcations of Limit Cycles: Computational Formulas, Numerical Implementation, and Examples." SIAM Journal on Applied Dynamical Systems 12, no. 2 (January 2013): 722–88. http://dx.doi.org/10.1137/120874904.

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42

Safari, Mehdi, Seyed Jamal Hosseinipour, and Hamed Deilami Azodi. "Experimental and Numerical Analysis of Forming Limit Diagram (FLD) and Forming Limit Stress Diagram (FLSD)." Materials Sciences and Applications 02, no. 05 (2011): 496–502. http://dx.doi.org/10.4236/msa.2011.25067.

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43

Guermond, Jean-Luc, and Guido Kanschat. "Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit." SIAM Journal on Numerical Analysis 48, no. 1 (January 2010): 53–78. http://dx.doi.org/10.1137/090746938.

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44

Binesh, S. M., and A. Gholampour. "Mesh-Free Lower Bound Limit Analysis." International Journal of Computational Methods 12, no. 01 (January 23, 2015): 1350105. http://dx.doi.org/10.1142/s0219876213501053.

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Анотація:

A novel numerical approach is developed for computing lower bound limit load in soil mechanics problems under plane strain condition. In the presented technique, there is no need to mesh in the traditional sense, and a lower bound solution is obtained. To develop the lower bound optimization problem, a statically admissible stress field is constructed by Shepard's shape functions in conjunction with the stabilized nodal integration scheme. The linearized Mohr–Coulomb criterion is adopted to satisfy the plastic admissibility of the generated stress field. The obtained optimization problem with a considerable reduced number of constraints has been solved by the linear programming technique. Based on the derived formulations, a computer code has been developed and the accuracy and efficiency of proposed method is demonstrated by solving some examples at the end of the paper.

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45

Helmberg, G. "A Limit Function for Equidistant Fourier Interpolation." Journal of Approximation Theory 81, no. 3 (June 1995): 389–96. http://dx.doi.org/10.1006/jath.1995.1058.

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46

Klymenko, O. V., and I. B. Svir. "Modelling Complex Chemical Processes in Homogeneous Solutions: Automatic Numerical Simulation." Nonlinear Analysis: Modelling and Control 11, no. 3 (September 1, 2006): 247–61. http://dx.doi.org/10.15388/na.2006.11.3.14746.

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Two algorithms for the determination of the necessary limit of local error for the numerical solution of ordinary differential equation (ODE) systems describing homogeneous chemical and biochemical processes, and for the evaluation of their stiffness are developed. The approach for finding the necessary limit of local error of a numerical ODE solver is justified by the proof of the corresponding theorems. The application of the new algorithms implemented in version 2.1 of KinFitSim software to the simulation of real chemical systems is considered on the example of Belousov-Zhabotinsky reaction.

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47

Bažant, Zdeněk P., and Feng-Bao Lin. "Non-local yield limit degradation." International Journal for Numerical Methods in Engineering 26, no. 8 (August 1988): 1805–23. http://dx.doi.org/10.1002/nme.1620260809.

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48

Qin, Fang, Lele Zhang, Geng Chen, and Christoph Broeckmann. "Lower bound limit and shakedown analysis of orthotropic material." Mathematics and Mechanics of Solids 25, no. 11 (June 7, 2020): 2037–49. http://dx.doi.org/10.1177/1081286520918004.

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We present in this study a new approach for predicting the plastic and shakedown limits of structures composed of orthotropic materials. In this approach, the Hill yield criterion is introduced to Melan’s theorem. By formulating the problem by means of the finite element method and solving the resulting large-scale nonlinear optimization problem we successfully predict the plastic and shakedown limits of structures having complex geometries made from multi-orthotropic materials. Several numerical examples are elaborated in this study for evaluating the accuracy, general applicability, as well as the efficiency of the established numerical scheme. Overall, the study confirms that the direct method can be extended and adopted as a viable means for design and analysis of structures made of orthotropic materials.

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49

Poelstra, Klaas Hendrik, Ben Schweizer, and Maik Urban. "The geometric average of curl-free fields in periodic geometries." Analysis 41, no. 3 (May 18, 2021): 179–97. http://dx.doi.org/10.1515/anly-2020-0053.

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Анотація:

Abstract In periodic homogenization problems, one considers a sequence ( u η ) η {(u^{\eta})_{\eta}} of solutions to periodic problems and derives a homogenized equation for an effective quantity u ^ {\hat{u}} . In many applications, u ^ {\hat{u}} is the weak limit of ( u η ) η {(u^{\eta})_{\eta}} , but in some applications u ^ {\hat{u}} must be defined differently. In the homogenization of Maxwell’s equations in periodic media, the effective magnetic field is given by the geometric average of the two-scale limit. The notion of a geometric average has been introduced in [G. Bouchitté, C. Bourel and D. Felbacq, Homogenization of the 3D Maxwell system near resonances and artificial magnetism, C. R. Math. Acad. Sci. Paris 347 2009, 9–10, 571–576]; it associates to a curl-free field Y ∖ Σ ¯ → ℝ 3 {Y\setminus\overline{\Sigma}\to\mathbb{R}^{3}} , where Y is the periodicity cell and Σ an inclusion, a vector in ℝ 3 {\mathbb{R}^{3}} . In this article, we extend previous definitions to more general inclusions, in particular inclusions that are not compactly supported in the periodicity cell. The physical relevance of the geometric average is demonstrated by various results, e.g., a continuity property of limits of tangential traces.

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50

Vetchanin, E. V., and I. S. Mamaev. "Numerical analysis of the periodic controls of an aquatic robot." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 32, no. 4 (December 2022): 644–60. http://dx.doi.org/10.35634/vm220410.

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Анотація:

A model governing the motion of an aquatic robot with a shell in the form of a symmetrical airfoil NACA0040 is considered. The motion is controlled by periodic oscillations of the rotor. It is numerically shown that for physically admissible values of the control parameters in the phase space of the system, there exists only one limit cycle. The limit cycle that occurs under symmetric control corresponds to the motion of the robot near a straight line. In the case of asymmetric controls, the robot moves near a circle. An algorithm for controlling the course of the robot motion is proposed. This algorithm uses determined limit cycles and transient processes between them.

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