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Journal articles on the topic 'Boundary element methods – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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1

Sheng, X., C. J. C. Jones, and D. J. Thompson. "Modelling ground vibration from railways using wavenumber finite- and boundary-element methods." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2059 (2005): 2043–70. http://dx.doi.org/10.1098/rspa.2005.1450.

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A mathematical model is presented for ground vibration induced by trains, which uses wavenumber finite- and boundary-element methods. The track, tunnel and ground are assumed homogeneous and infinitely long in the track direction ( x -direction). The models are formulated in terms of the wavenumber in the x -direction and discretization in the yz -plane. The effect of load motion in the x -direction is included. Compared with a conventional, three-dimensional finite- or boundary-element model, this is computationally faster and requires far less memory, even though calculations must be perform

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Čavka, Damir, Dragan Poljak, and Andres Peratta. "Comparison Between Finite and Boundary Element Methods for Analysis of Electrostatic Field Around Human Head Generated by Video Display Units." Journal of Communications Software and Systems 7, no. 1 (2011): 22. http://dx.doi.org/10.24138/jcomss.v7i1.184.

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Boundary and finite element modeling approach to the assessment of electrostatic field on human head generated by Video Display Units (VDU’s) are compared and discussed. Attention is focused to the field distribution over the surface of the face. The mathematical formulation for the assessment of the electrostatic field is based on the Laplace equation for the electric scalar potential. The electrostatic field is calculated for two different models of face. Numerical results are presented and compared in order to estimate the accuracy and computational efficiency of the two methods for the con

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M, Berdnyk. "Mathematical modeling of temperature fields in antenna reflectors of space vehicles." Artificial Intelligence 27, jai2022.27(1) (2022): 212–18. http://dx.doi.org/10.15407/jai2022.01.212.

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The main factor that determines the distortion of the shape of the reflectors in outer space is the temperature deformation due to the uneven distribution of heat fluxes in the structural elements. Therefore, it is important to develop models and methods for calculating temperature fields in reflectors with uneven distribution of heat fluxes on the surface. The use of such methods will reduce the number of expensive field experiments. The paper first constructs a mathematical model for calculating temperature fields in a parabolic reflex antenna, in the form of a paraboloid of rotation rotatin

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Arora, Vikas. "Comparative study of finite element model updating methods." Journal of Vibration and Control 17, no. 13 (2011): 2023–39. http://dx.doi.org/10.1177/1077546310395967.

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The effects of vibrations present major hazards and operating limitations ranging from discomfort (including noise), malfunctioning, reduced performance, early breakdown and structural failure which, in the worst case can be catastrophic. Hence, accurate mathematical models are required to describe the vibration characteristics of structures, which subsequently can be used for design purposes to limit the negative effects of vibrations. Finite element (FE) predictions are often called into question when they are in conflict with test results. Inaccuracies in FE models and errors in results pre

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Soloveva, Anastasia A., and Sergey A. Solovev. "Reliability analysis of planar steel trusses based on p-box models." Vestnik MGSU, no. 2 (February 2021): 153–67. http://dx.doi.org/10.22227/1997-0935.2021.2.153-167.

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Introduction. The development of probabilistic approaches to the assessment of mechanical safety of bearing structural elements is one of the most relevant areas of research in the construction industry. In this research, probabilistic methods are developed to perform the reliability analysis of steel truss elements using the p-box (probability box) approach. This approach ensures a more conservative (interval-based) reliability assessment made within the framework of attaining practical objectives of the reliability analysis of planar trusses and their elements. The truss is analyzed as a pro

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Mello, Carlos Eduardo Ferraz de. "BEM numerical simulation of spillway flows." Rem: Revista Escola de Minas 67, no. 1 (2014): 21–26. http://dx.doi.org/10.1590/s0370-44672014000100003.

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The study of gravity-free surface flows presents difficulties, such as the nonlinearity of the dynamic boundary condition in the free surface, and also the fact that the location of this surface is not known a priori. Traditionally, this phenomenon has been investigated by physical models, but the progress of computer science and numeric methods has allowed more and more the successful use of mathematical models to simulate this type of flow. This work presents a boundary element method (BEM) numerical simulation of spillway flows with discontinuous linear elements. The solution procedure invo

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SHAW, RICHARD PAUL, PAUL VAN SLOOTEN, and MATTHEW NOBILE. "OPTIMAL SOURCE LOCATIONS FOR VARIOUS GEOMETRIES FOR ACOUSTIC REFLECTORS BY BOUNDARY ELEMENT METHODS." Journal of Computational Acoustics 02, no. 04 (1994): 423–39. http://dx.doi.org/10.1142/s0218396x94000245.

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A boundary element method (BEM) approach is used to solve the acoustic problem of a point source within an enclosure with a large opening to an infinite (without a baffle) or semi-infinite (with a baffle) acoustic space. Emphasis is placed on 2D models with the source located along the center line of three types of geometries: a wedge, a parabola, and a rectangular enclosure.

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Shabouei, M., and K. B. Nakshatrala. "Mechanics-Based Solution Verification for Porous Media Models." Communications in Computational Physics 20, no. 5 (2016): 1127–62. http://dx.doi.org/10.4208/cicp.oa-2016-0007.

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AbstractThis paper presents a new approach to verify the accuracy of computational simulations. We develop mathematical theorems which can serve as robusta posteriorierror estimation techniques to identify numerical pollution, check the performance of adaptive meshes, and verify numerical solutions. We demonstrate performance of this methodology on problems from flow thorough porous media. However, one can extend it to other models. We construct mathematical properties such that the solutions to Darcy and Darcy-Brinkman equations satisfy them. The mathematical properties include the total mini

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Wang, Changsheng, Yang Wang, Caixia Yang, Xiangkui Zhang, and Ping Hu. "8-node and 12-node plane elements based on assumed stress quasi-conforming method immune to distorted mesh." Engineering Computations 34, no. 8 (2017): 2731–51. http://dx.doi.org/10.1108/ec-11-2016-0404.

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Purpose Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties. Design/methodology/approach First, the fundamental analytical solutions which satisfied both the e

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Lin, Ray-Qing, Weijia Kuang, and Arthur M. Reed. "Numerical Modeling of Nonlinear Interactions Between Ships and Surface Gravity Waves, Part 1: Ship Waves in Calm Water." Journal of Ship Research 49, no. 01 (2005): 1–11. http://dx.doi.org/10.5957/jsr.2005.49.1.1.

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This paper presents a pseudo-spectral model for nonlinear ship-surface wave interactions. The algorithm used in the model is a combination of spectral and boundary element methods: the boundary element method is used to translate physical quantities between the nonuniform ship surface and the regular grid of the spectral representation; the spectral method is used throughout the remainder of the fluid domain. All possible wave-wave interactions are included in the model (up to N-wave interactions for the truncation order N of the spectral expansions). This paper focuses on the mathematical the

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Tamarova, Yuliya A., Petr A. Velmisov, Nikolai D. Aleksanin, and Nail I. Nurullin. "Investigation of dynamic processes in pressure measurement systems for gas-liquid media." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 23, no. 4 (2021): 461–71. http://dx.doi.org/10.15507/2079-6900.23.202104.461-471.

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Initial-boundary value problems for systems of differential equations are considered, which are mathematical models of the mechanical system "pipeline - pressure sensor". In such a system, to mitigate the effects of vibration accelerations and high temperatures, the sensor is located at a certain distance from the engine and is connected to it via a pipeline. The "pipeline - pressure sensor" system is designed to measure pressure in gas-liquid media, for example, to control the pressure of the working medium in the combustion chambers of engines. On the basis of the proposed models, the joint

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Miłkowska‐Piszczek, Katarzyna, and Jan Falkus. "Control and Design of the Steel Continuous Casting Process Based on Advanced Numerical Models." Metals 8, no. 8 (2018): 591. http://dx.doi.org/10.3390/met8080591.

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The process of continuous casting of steel is a complex technological task, including issues related to heat transfer, the steel solidification process, liquid metal flow and phase transitions in the solid state. This involves considerable difficulty in creating the optimal process control system, which would include the influence of all the physico‐chemical phenomena which may occur. In parallel, there is an intensive development of new mathematical models and an increase in computer performance, therefore complex numerical simulations requiring substantial computing time can be conducted. Th

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Gao, Xiang, Tailu Li, Yao Zhang, Xiangfei Kong, and Nan Meng. "A Review of Simulation Models of Heat Extraction for a Geothermal Reservoir in an Enhanced Geothermal System." Energies 15, no. 19 (2022): 7148. http://dx.doi.org/10.3390/en15197148.

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This paper reviews the heat transfer model for geothermal reservoirs, the fracture network in reservoirs, and the numerical model of hydraulic fracturing. The first section reviews the heat transfer models, which contain the single-porosity model, the dual-porosity model, and the multi-porosity model; meanwhile the mathematical equations of the porosity model are summarized. Then, this paper introduces the fracture network model in reservoirs and the numerical method of computational heat transfer. In the second section, on the basis of the conventional fracture theory, the PKN (Perkins–Kern–N

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Syrotkina, Olena Ihorivna, Mykhailo Oleksandrovych Aleksieiev, and Iryna Mykhailivna Udovyk. "GRAPHICAL AND ANALYTICAL METHODS FOR PROCESSING “BIG DATA” BASED ON THE ANALYSIS OF THEIR PROPERTIES." System technologies 3, no. 122 (2019): 78–90. http://dx.doi.org/10.34185/1562-9945-3-122-2019-10.

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This article addresses the subject of creating mathematical methods in order to optimize time and computing resources when processing “big data.” One of the ways of solving this problem is the creation of NoSQL systems, an advantage of which is the flexibility of data models as well as the possibility of horizontal scaling, parallel processing and the speed of obtaining results. From the viewpoint of “big data” analysis, there have been other methods developed such as machine learning, artificial intelligence, distributed processing of streams and events, and visual data research technology.Fu

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Bao, Yi, Song Cen, and Chenfeng Li. "Distortion-resistant and locking-free eight-node elements effectively capturing the edge effects of Mindlin–Reissner plates." Engineering Computations 34, no. 2 (2017): 548–86. http://dx.doi.org/10.1108/ec-04-2016-0143.

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Purpose A simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin–Reissner plates. Three distortion-resistant and locking-free eight-node plate elements are proposed by utilizing this method. Design/methodology/approach This method is based on the principle of minimum complementary energy, in which the trial functions for resultant fields are derived from two displacement functions, F and f, and satisfy all governing equations. Meanwhile, the element boundary displacements are determined by the locking-free arbitrary order T

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Ren, Lihai, Dangdang Wang, Chengyue Jiang, and Yuanzhi Hu. "Influence of Foramen Magnum Boundary Condition on Intracranial Dynamic Response Under Forehead Impact Using Human Body Finite Element Model." International Journal of Computational Methods 17, no. 07 (2019): 1950029. http://dx.doi.org/10.1142/s0219876219500294.

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The biofidelity is an essential requirement of the application of human head finite element (FE) models to investigate head injuries under mechanical loadings. However, the influence of the foramen magnum boundary condition (FMBC) on intracranial dynamic responses under head impacts has yet to be fully identified until now. This study aimed to investigate the effect of different modeling methods of the FMBC on intracranial dynamic responses induced by forehead impact, especially the axonal injury associated dynamic responses. The total human model for safety (THUMS) was applied in this study.

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Xia, Chen, Chengzhi Qi, and Xiaozhao Li. "Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain." Mathematical Problems in Engineering 2018 (October 10, 2018): 1–11. http://dx.doi.org/10.1155/2018/7982342.

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Transmitting boundaries are important for modeling the wave propagation in the finite element analysis of dynamic foundation problems. In this study, viscoelastic boundaries for multiple seismic waves or excitations sources were derived for two-dimensional and three-dimensional conditions in the time domain, which were proved to be solid by finite element models. Then, the method for equivalent forces’ input of seismic waves was also described when the proposed artificial boundaries were applied. Comparisons between numerical calculations and analytical results validate this seismic excitation

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Köppl, Tobias, Ettore Vidotto, Barbara Wohlmuth, and Paolo Zunino. "Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions." Mathematical Models and Methods in Applied Sciences 28, no. 05 (2018): 953–78. http://dx.doi.org/10.1142/s0218202518500252.

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Many biological and geological systems can be modeled as porous media with small inclusions. Vascularized tissue, roots embedded in soil or fractured rocks are examples of such systems. In these applications, tissue, soil or rocks are considered to be porous media, while blood vessels, roots or fractures form small inclusions. To model flow processes in thin inclusions, one-dimensional (1D) models of Darcy- or Poiseuille type have been used, whereas Darcy-equations of higher dimension have been considered for the flow processes within the porous matrix. A coupling between flow in the porous ma

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Kabanov, S. A., B. A. Zimin, and F. V. Mitin. "Development and Research of Mathematical Models of Deployment of Mobole Parts of Transformable Space Construction. Part II." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 2 (2020): 117–28. http://dx.doi.org/10.17587/mau.21.117-128.

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The process of deployment elements of constructions and adjustment of the radio-reflecting network of large-sized transformable space-based reflector is considered. The reflector consists of a frontal network, which is stretched on the power frame, cables, with which the front network is pulled to the rear network to set the desired shape of the reflecting surface. The problem of setting and determining the shape of the radio-reflective network is solved both in one plane and in three planes. In general, the task of adjusting the form of a radio reflecting reticle is solved by affecting the de

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Beirão da Veiga, L., F. Brezzi, L. D. Marini, and A. Russo. "Virtual Element Method for general second-order elliptic problems on polygonal meshes." Mathematical Models and Methods in Applied Sciences 26, no. 04 (2016): 729–50. http://dx.doi.org/10.1142/s0218202516500160.

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We consider the discretization of a boundary value problem for a general linear second-order elliptic operator with smooth coefficients using the Virtual Element approach. As in [A. H. Schatz, An observation concerning Ritz–Galerkin methods with indefinite bilinear forms, Math. Comput. 28 (1974) 959–962] the problem is supposed to have a unique solution, but the associated bilinear form is not supposed to be coercive. Contrary to what was previously done for Virtual Element Methods (as for instance in [L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo, Basic pri

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Solovyova, A. A., and S. A. Solovyov. "STRUCTURAL RELIABILITY ANALYSIS OF STEEL TRUSS ELEMENTS ON BUCKLING USING PBOX APPROACH." STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS, no. 1 (February 25, 2021): 45–53. http://dx.doi.org/10.37538/0039-2383.2021.1.45.53.

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Abstract. The reliability of load-bearing structural elements is one of the indicators of structural safety. The article presents methods for steel trusses bars reliability analysis according to the buckling criterion using p-boxes. A p-box consists of two boundary probability distribution functions that form the area of possible distribution functions. Such model used for modeling random variables in conditions of incomplete statistical data by quantity or quality. An algorithm for summing p-boxes of random load models is demonstrated on the example of a probabilistic estimate of the force in

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Miazio, Ł., and G. Zboiński. "A posteriori boundary layer detection and resolution in hpq-adaptive finite element methods for 3D-based hierarchical plate and shell models." Computers & Mathematics with Applications 129 (January 2023): 50–68. http://dx.doi.org/10.1016/j.camwa.2022.11.010.

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Morgun, Alla, Ivan Met, and Igor Shevchenko. "INFLUENCE OF THE DEGREE OF DISCRETIZATION OF THE TECHNICAL FACILITY ON THE RESULTS OF THE FORECAST FOR MHE." Modern technology, materials and design in construction 31, no. 2 (2022): 27–31. http://dx.doi.org/10.31649/2311-1429-2021-2-27-31.

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A significant difference between soils and homogeneous elastic bodies is that under action External loads residual deformations are always concomitant elastic, even at low loads. The sum of residual and elastic deformation is the total deformation of the soil base. The simultaneous presence in the soil of zones operating in both elastic and plastic zones requires the involvement of the theory of elasticity and plasticity to model its behavior [1-4]. It is known that the solution of the mixed problem of the theory of elasticity and the theory of soil plasticity brings the results of sedimentati

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Yaghoobi, Amin, and Mi G. Chorzepa. "Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis." Mathematics and Mechanics of Solids 23, no. 8 (2017): 1156–76. http://dx.doi.org/10.1177/1081286517711495.

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Peridynamics is an effective method in computational solid mechanics for dealing with discontinuities. However, its computational cost limits its applications, especially when used in the most general form, non-ordinary state-based peridynamics. This paper considers two approaches which decrease the computational cost. The first approach accounts for symmetry boundary conditions in a peridynamic body. In nonlocal peridynamics, boundary conditions are applied to an area. Therefore, when modeling the symmetry boundary condition, assuming fixed particles around the symmetry axis yields incorrect

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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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Christen, David, Duncan James Webster, and Ralph Müller. "Multiscale modelling and nonlinear finite element analysis as clinical tools for the assessment of fracture risk." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1920 (2010): 2653–68. http://dx.doi.org/10.1098/rsta.2010.0041.

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The risk of osteoporotic fractures is currently estimated based on an assessment of bone mass as measured by dual-energy X-ray absorptiometry. However, patient-specific finite element (FE) simulations that include information from multiple scales have the potential to allow more accurate prognosis. In the past, FE models of bone were limited either in resolution or to the linearization of the mechanical behaviour. Now, nonlinear, high-resolution simulations including the bone microstructure have been made possible by recent advances in simulation methods, computer infrastructure and imaging, a

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Berdnyk, M. H. "Mathematical modeling of temperature fields of spacecraft antenna reflectors with a new inte-gral transformation." Mathematical machines and systems 3 (2022): 158–65. http://dx.doi.org/10.34121/1028-9763-2022-3-158-165.

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Prediction of the mechanical properties of the reflector, and above all, the deviation of the highly accurate shape of the reflecting surface (RSS) from the given one is the main goal of designing spacecraft antennas. Distortion of the RSS is determined by the stress-deformed state of the elements of the reflector structures under the conditions of orbital operation. At the same time, the main factor determining the distortion of reflectors with RSS in open space is temperature deformation due to the uneven distribution of solar heat fluxes among structural elements. Therefore, the development

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ArianMaram, Moloud, Mahmoud Ghiasi, Hassan Ghassemi, and Hamid Reza Ghafari. "Hydrodynamic Analysis of 3D Hydrofoil Using Nonuniform Rational B-Spline and Boundary Element Method." Mathematical Problems in Engineering 2021 (October 25, 2021): 1–8. http://dx.doi.org/10.1155/2021/7252949.

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In this paper, two different 3D hydrofoils with profiles NACA0012 are simulated in the potential flow. Boundary element method (BEM) and nonuniform rational B-spline (NURBS) are coupled to reduce error and increase accuracy. The computer code is developed in different submergence depths (d), flow velocities (U), and various angles of attack (AoA), and the pressure is obtained by NURBS formulation. The pressure on a 3D hydrofoil with NACA412 profile iscompared with other existing methods. The validity of result is revealed. The accuracy of the results is acceptable. The competition of the two m

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Frittelli, Massimo, Anotida Madzvamuse, and Ivonne Sgura. "Bulk-surface virtual element method for systems of PDEs in two-space dimensions." Numerische Mathematik 147, no. 2 (2021): 305–48. http://dx.doi.org/10.1007/s00211-020-01167-3.

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AbstractIn this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general nonlinear boundary conditions. For such a system we propose a novel method, based on coupling a virtual element method (Beirão Da Veiga et al. in Math Models Methods Appl Sci 23(01):199–214, 2013. https://doi.org/10.1051/m2an/2013138) in the bulk domain to a surface finite element method (Dziuk and Elliott in Acta Numer 22:289–396, 2013. https://doi.org/10.1017/s0962492913000056) on the surface. The proposed

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Chang, Y. C., D. Y. Lin, H. C. Cheng, and M. C. Chiu. "Numerical Assessment of Rectangular Straight/Reverse Mufflers at High-Order-Modes." Journal of Mechanics 34, no. 3 (2016): 325–36. http://dx.doi.org/10.1017/jmech.2016.123.

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AbstractThere has been wide-spread use of plane wave theory in muffler design in industry. However, This has led to an underestimation of acoustical performances at higher frequencies. To overcome the above drawback, the finite element and boundary element methods have been developed. Nevertheless, the time consumed in calculating the noise level is unacceptable. Moreover, considering the acoustical effect and necessity of space-constrained situation in industry, a compact design of reverse mufflers which may improve the acoustical efficiency is then proposed.In this paper, a numerical assessm

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Kanick, Stephen Chad, William J. Doyle, Samir N. Ghadiali, and William J. Federspiel. "On morphometric measurement of oxygen diffusing capacity in middle ear gas exchange." Journal of Applied Physiology 98, no. 1 (2005): 114–19. http://dx.doi.org/10.1152/japplphysiol.00203.2004.

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An accurate mathematical model of transmucosal gas exchange is prerequisite to understanding middle ear (ME) physiology. Current models require experimentally measured gas species time constants for all extant conditions as input parameters. However, studies on pulmonary gas exchange have shown that a morphometric model that incorporates more fundamental physiochemical and anatomic parameters accurately simulates transport from which the species time constants can be derived for all extant conditions. Here, we implemented a variant of that model for ME gas exchange that requires the measuremen

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Hajiazizi, Mohammad, and Adel Graili. "A novel hybrid meshless method for seepage flows in non-homogeneous and anisotropic soils." Engineering Computations 35, no. 2 (2018): 867–86. http://dx.doi.org/10.1108/ec-07-2017-0245.

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Purpose The purpose of this paper is to extend the scaled boundary radial point interpolation method (SBRPIM), as a novel semi-analytical scheme, to the analysis of the steady state confined seepage flows. Design/methodology/approach This method combines the advantages of the scaled boundary finite element method and the BRPIM. In this method, only boundary nodes are used, no fundamental solution of the problem is required, and as the shape functions constructed based on the RPIM satisfy the Kronecker delta function property, the boundary conditions of problems can be imposed accurately and ea

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NAZAROVA, Zinaida Mikhailovna. "Formation of a stable price for energy resources by solving a non-linear dynamic problem as an element of socio-economic stability of the economy." NEWS of the Ural State Mining University 1, no. 1 (2020): 170–81. http://dx.doi.org/10.21440/2307-2091-2020-1-170-181.

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Relevance. The authors note that the formation of a stable price for natural resources and the possibility of smoothing the price during fluctuations not only in demand for them, but also changes in the supply schedule for economic and other reasons require the development of an economic model; they are very relevant. The purpose of the study: identifying the possibilities of forecasting energy prices in the event of price fluctuations and the formation of various levels of demand in the market and taking into account market and non-market methods for its regulation. Results of the study. Stud

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Bobriakova, Elena, Artem Gundar, Sergiy Ivanov, et al. "Mathematical model of a vertical-axial wind motor in a viscous gas flow." Aerospace technic and technology, no. 1 (February 24, 2022): 12–24. http://dx.doi.org/10.32620/aktt.2022.1.02.

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The development of vertical axial wind turbines in Ukraine is in its infancy for many reasons: the lack of systematic theoretical and experimental studies of the aerodynamic characteristics of various schemes of wind turbines, the lack of an appropriate experimental base in technical universities, design organizations, insufficient number of available publications in foreign literature due to high competition between by monopoly firms. At present, various numerical methods are widely used to solve urgent problems of aero hydrodynamics, which are used for the approximate solution of boundary va

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Harizanov, Stanislav, Raytcho Lazarov, and Svetozar Margenov. "A survey on numerical methods for spectral Space-Fractional diffusion problems." Fractional Calculus and Applied Analysis 23, no. 6 (2020): 1605–46. http://dx.doi.org/10.1515/fca-2020-0080.

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AbstractThe survey is devoted to numerical solution of the equation $ {\mathcal A}^\alpha u=f $, 0 < α<1, where $ {\mathcal A} $ is a symmetric positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain Ω in ℝd. The fractional power $ {\mathcal A}^\alpha $ is a non-local operator and is defined though the spectrum of $ {\mathcal A} $. Due to growing interest and demand in applications of sub-diffusion models to physics and engineering, in the last decade, several numerical approaches have been proposed, studied, and tested. We consider

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RAHMAN, MAHBUBUR, YIXIANG XU, JAMES B. P. LIM, et al. "BEHAVIOR OF STEEL PORTAL FRAMES IN FIRE: COMPARISON OF IMPLICIT AND EXPLICIT DYNAMIC FINITE ELEMENT METHODS." International Journal of Structural Stability and Dynamics 13, no. 04 (2013): 1250058. http://dx.doi.org/10.1142/s0219455412500587.

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The use of finite element methods to determine the collapse behavior of steel portal frames in fire requires temperature, large deformation, complex geometry, boundary conditions and degradation of material stiffness to be taken into account. For such analyses, the cost of computation is important as well as the accuracy, robustness and stability of the analyses. The implicit dynamic method is a rigorous technique that considers the equilibrium of every time step. However, convergence may become an issue, particularly if the frame undergoes structural instability while using a direct time incr

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Legusha, F., and Yu Popov. "Acoustic wave absorption in a waveguide with impedance boundary conditions." Transactions of the Krylov State Research Centre 2, no. 396 (2021): 113–21. http://dx.doi.org/10.24937/2542-2324-2021-2-396-113-121.

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Object and purpose of research. The study of the acoustic pulse changes regularities during its propagation in con-fined media is one of the fundamental problems of acoustics, which allows to pose and solve the inverse problem of determining the dissipative and resonant properties of these media. The physical processes occurring during the propagation of a pulse in a cylindrical waveguide with rigid walls were investigated. Materials and methods. To analyze the mechanism of dissipation, experimental studies of pulse propagation in a hy-droacoustic tube were carried out, and the theoretical des

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Xu, Wenhan, Hong Xu, Jie Chen, et al. "Combining Numerical Simulation and Deep Learning for Landslide Displacement Prediction: An Attempt to Expand the Deep Learning Dataset." Sustainability 14, no. 11 (2022): 6908. http://dx.doi.org/10.3390/su14116908.

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Effective landslide hazard prevention requires accurate landslide prediction models, and the data-driven approaches based on deep learning models are gradually becoming a hot research topic. When training deep learning models, it is always preferable to have a large dataset, while most available landslide monitoring data are limited. For data missing or data sparseness problems, conventional interpolation methods based on mathematical knowledge lack mechanism interpretability. This paper proposes that numerical simulations can be used to expand the deep learning dataset we need. Taking the Jiu

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Lebedev, V. D., N. V. Kuzmina, and G. A. Filatova. "Study of mathematical approaches to determine frequency-dependent impedance of over-head power transmission line." Vestnik IGEU, no. 3 (June 30, 2022): 24–34. http://dx.doi.org/10.17588/2072-2672.2022.3.024-034.

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Mathematical modeling of a power transmission line (PTL) is an important issue for a wide range of tasks in the electric power industry. Mathematical modeling is necessary when studying the transient processes in electric power systems. Analytical expressions that allow modeling power transmission lines in a wide frequency range, including low frequencies and direct current, make it possible to study the operation of relay protection and automation devices in various modes and improve the accuracy of devices of fault location. It is important not only to obtain analytical expressions to determ

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TADEU, ANTÓNIO, LUÍS GODINHO, and JULIETA ANTÓNIO. "DYNAMIC RESPONSE OF A THREE-DIMENSIONAL FLUID CHANNEL BOUNDED BY AN ELASTIC FLOOR IN THE PRESENCE OF A SUBMERGED INCLUSION VIA BEM." Journal of Computational Acoustics 13, no. 01 (2005): 203–27. http://dx.doi.org/10.1142/s0218396x0500261x.

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Numerical methods for computing the three-dimensional pressure field in a flat fluid channel bounded either by a rigid boundary, an elastic semi-infinite medium or by a layer of sediment, subjected to incoherent line sources are presented. After verification Greens functions are incorporated in a Boundary Element Method (BEM) code that simulates the pressure variation inside the fluid channel in the vicinity of a rigid or elastic inclusion, avoiding the discretization of the fluid and solid channel interfaces. After the verification of the solution, the models developed are then used to simula

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Nicolaidou, Evangelia, Thomas L. Hill, and Simon A. Neild. "Indirect reduced-order modelling: using nonlinear manifolds to conserve kinetic energy." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (2020): 20200589. http://dx.doi.org/10.1098/rspa.2020.0589.

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Nonlinear dynamic analysis of complex engineering structures modelled using commercial finite element (FE) software is computationally expensive. Indirect reduced-order modelling strategies alleviate this cost by constructing low-dimensional models using a static solution dataset from the FE model. The applicability of such methods is typically limited to structures in which (a) the main source of nonlinearity is the quasi-static coupling between transverse and in-plane modes (i.e. membrane stretching); and (b) the amount of in-plane displacement is limited. We show that the second requirement

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Biglar, Mojtaba, Tomasz Trzepieciński, Feliks Stachowicz, and Magdalena Gromada. "Application of the grain boundary formulation and image processing-based algorithm in micro-mechanical analysis of piezoelectric ceramic." Mathematics and Mechanics of Solids 25, no. 7 (2017): 1384–404. http://dx.doi.org/10.1177/1081286517735696.

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The main subject of this paper is the micro-mechanical analysis of a piezoelectric ceramic. In micro-mechanical analyses, it is very important to have knowledge about the real and natural micro-structure of materials. Therefore, the barium titanate powder was prepared using the solid-state technique, and pellets and beams were manufactured by uniaxial and isostatic pressing. The boundary element method (BEM) is used in order to be combined with three different grain boundary formulations for investigation of micro-mechanics and crack nucleation and evaluation in piezoelectric ceramic. In order

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Peirce, A. "Implicit level set algorithms for modelling hydraulic fracture propagation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2078 (2016): 20150423. http://dx.doi.org/10.1098/rsta.2015.0423.

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Hydraulic fractures are tensile cracks that propagate in pre-stressed solid media due to the injection of a viscous fluid. Developing numerical schemes to model the propagation of these fractures is particularly challenging due to the degenerate, hypersingular nature of the coupled integro-partial differential equations. These equations typically involve a singular free boundary whose velocity can only be determined by evaluating a distinguished limit. This review paper describes a class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encounte

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Starovoitov, E. I., M. A. Zhuravkov, and P. F. Pronina. "BENDING OF AN ELASTIC THREE-LAYER PLATE WITH A HOLE CONNECTED TO THE SOIL FOUNDATION." Series of Geology and Technical Sciences 445, no. 1 (2021): 164–71. http://dx.doi.org/10.32014/2021.2518-170x.23.

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The relevance of this paper is explained by a demand for the development of mechanical and mathematical models and methods for calculating the stress-strain state of the sandwich structural elements. The statement of the boundary value problem on the deformation of a circular sandwich plate with a central hole, connected to the soil foundation, was given. To describe the kinematics of an asymmetric plate pack, the broken line hypotheses are accepted. In a relatively thick lightweight core, the normal does not change its length, remains rectilinear, but rotates through some additional angle. Tu

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Yu, H. S., and X. Yuan. "On a class of non-coaxial plasticity models for granular soils." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2067 (2005): 725–48. http://dx.doi.org/10.1098/rspa.2005.1590.

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The non-coaxiality of the directions of principal stresses and principal plastic strain rates in granular soils under stress rotations has long been observed and recognized in soil tests using both simple shear and hollow cylinder apparatuses. A few constitutive theories have also been proposed in the literature to account for the effect of stress rotations and the subsequent non-coaxial soil behaviour, particularly in the context of shear band analysis. However, the lack of corresponding general numerical methods makes it difficult to investigate the influence of non-coaxial stress–strain beh

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STAROVOITOV, Eduard I., Denis V. LEONENKO, and Alexander A. OREKHOV. "Bending of an elastoplastic circular sandwich plate on an elastic foundation in a temperature field." INCAS BULLETIN 13, S (2021): 233–44. http://dx.doi.org/10.13111/2066-8201.2021.13.s.21.

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Today, the development of the general theory of quasi-static deformation of three-layer structural elements, including plates, is not yet complete and is being intensively studied. Mathematical models of deformation under complex thermo-force and thermo-irradiation loads are created. The problems of strength, stability, and dynamic behaviour are considered. In strength calculations of three-layer structural elements, it is necessary to take kinematic hypotheses for each layer separately, which complicates the mathematical side of the problem but leads to significant refinement of the stress-st

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Yakovlev, E. V., A. L. Ovsepyan, S. A. Zhivolupov, A. A. Smirnov, and E. N. Gnevyshev. "Possibilities of personalized finite element segmental analysis of the cervical spine for predicting the course of dorsopathy." Meditsinskiy sovet = Medical Council, no. 14 (August 10, 2022): 38–56. http://dx.doi.org/10.21518/2079-701x-2022-16-14-38-56.

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Introduction. The use of mathematical modeling methods in clinical practice will make it possible to identify the pathogenetic forms of dorsopathies and thus reasonably use the concept of targeted treatment in the management of patients of this category.Aim. To evaluate the possibilities of finite element segmental analysis of the cervical spine for personalized treatment and prediction of the course of dorsopathies.Material and methods. Based on the combined data of computed and magnetic resonance imaging of the patient (female, born in 1951), a model of the C5 – C7 segment was generated, inc

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Brailko, N. N., and I. M. Tkachenko. "STUDY OF THE STRESS-STRAIN STATE OF THE "FILLING-TOOTH" SYSTEM IN CERVICAL DEFECTS OF THE TEETH." Актуальні проблеми сучасної медицини: Вісник Української медичної стоматологічної академії 20, no. 4 (2020): 108–14. http://dx.doi.org/10.31718/2077-1096.20.4.108.

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The problem of preserving restorations in defects in the cervical region, even with high-quality preparation and restoration, is also relevant in the modern world. The tensions in the teeth lead to the formation of cracks in the enamel and dentin, loss of tightness and marginal adhesion of the fillings, resorption and loss. Therefore, to ensure high-quality results of treatment of hard tissue defects in the cervical region of the teeth, it is appropriate to take into account the physical processes occurring around the "filling-tooth" system, namely, the stress-strain state. To assess the stres

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Kristensen, Philip K., Christian F. Niordson, and Emilio Martínez-Pañeda. "An assessment of phase field fracture: crack initiation and growth." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2203 (2021): 20210021. http://dx.doi.org/10.1098/rsta.2021.0021.

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The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith’s energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization—without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and e

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Lockington, David, Zhaokun Wang, Nan Qi, et al. "Modelling floppy iris syndrome and the impact of pupil size and ring devices on iris displacement." Eye 34, no. 12 (2020): 2227–34. http://dx.doi.org/10.1038/s41433-020-0782-7.

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Abstract Introduction The aim of this paper was to further develop a previously described finite element model which equates clinical iris billowing movements with mechanical buckling behaviour, simulating floppy iris syndrome. We wished to evaluate the impact of pupil dilation and mechanical devices on normal iris and floppy iris models. Methods Theoretical mathematical modelling and computer simulations were used to assess billowing/buckling patterns of the iris under loading pressures for the undilated and dilated normal iris, the undilated and dilated floppy iris, and additionally with a m

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