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Journal articles on the topic 'Differential quadrature-based elements'

Author: Grafiati

Published: 6 September 2023

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1

Verma, Anjali, and Ram Jiwari. "Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 7 (2015): 1574–89. http://dx.doi.org/10.1108/hff-08-2014-0240.

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Purpose – The purpose of this paper is to present the computational modeling of second-order two-dimensional nonlinear hyperbolic equations by using cosine expansion-based differential quadrature method (CDQM). Design/methodology/approach – The CDQM reduced the equations into a system of second-order differential equations. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations. Findings – The computed numerical results are compared with the results presented by other workers (Mohanty et al., 1996; Mohanty, 2004) and it is found that th

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2

Kucharov, Olim, Fozil Turaev, Sergey Leonov, and Kholida Komilova. "Numerical study of nonlinear problems in the dynamics of thin-walled structural elements." E3S Web of Conferences 264 (2021): 05056. http://dx.doi.org/10.1051/e3sconf/202126405056.

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Mathematical model of the problem of vibration of thin-walled structural elements has been constructed based on Kirchhoff-Love theory. The problem is reduced, using the Bubnov-Galerkin method, to the solution of a set of nonlinear integro-differential Volterra type equations with weakly-singular kernels of relaxation. A numerical method based on the use of quadrature formulae being used for their solution. The influence of rheological parameters of the material on the values of critical velocity and amplitude-frequency characteristics of viscoelastic thin-walled structural elements is analyzed

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3

JANCHAI, Prawech. "Voltage-mode Second-order Filter and Quadrature Oscillator Based-on Differential Difference Current Conveyors and Only Grounded Elements." PRZEGLĄD ELEKTROTECHNICZNY 1, no. 9 (2020): 64–69. http://dx.doi.org/10.15199/48.2020.09.13.

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4

Orlov, Victor, and Magomedyusuf Gasanov. "The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular Point." Axioms 12, no. 9 (2023): 844. http://dx.doi.org/10.3390/axioms12090844.

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This paper presents the final stage in the study of the analytical approximate solution to a class of nonlinear differential equations unsolvable in quadrature in the general case in the neighborhood of a perturbed value of a moving singular point. An a priori error estimation is proven. The scope of application of the analytical approximate solution is extended; the formula for calculating this scope is obtained. The proof of the theorem is based on the application of elements of differential calculus. Theoretical results are supported by numerical calculations, which validate their reliabili

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5

Khudayarov, Bakhtiyar, Fozilzhon Turaev, and Olimzhon Kucharov. "Computer simulation of oscillatory processes of viscoelastic elements of thin-walled structures in a gas flow." E3S Web of Conferences 97 (2019): 06008. http://dx.doi.org/10.1051/e3sconf/20199706008.

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Results of numerical investigation of dynamic behavior of deformed wing aircraft in a gas flow are presented in the paper. Vibrations with respect to deflections are described by a system of integro-differential equations in partial derivatives. Using the Bubnov-Galerkin method, the problem is reduced to a system of ordinary integro-differential equations, where time is an independent variable. The solutions of integro-differential equations are determined by a numerical method based on the use of quadrature formulas. Computational algorithms and a package of applied programs have been created

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6

Mirzaev, Sayibdjan, Majid Yusupov, Barna Rakhmankulova, Feruza Umarova, and Gulnaz Abdikayimova. "Vertical vibrations of traction engine with viscoelastic suspension." E3S Web of Conferences 365 (2023): 01022. http://dx.doi.org/10.1051/e3sconf/202336501022.

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The tasks of a traction engine with suspension elements and additional devices for converting movement (DCM) are considered. The object of protection, the estimated dynamic state, is solid with mass M and moment of inertia J relative to the center of gravity. To account the suspension material's rheological properties, the Boltzmann-Volterra principle is used. Mathematical models of the problem under consideration are obtained, which are described by the systems of integro-differential equations. A solution method based on quadrature formulas is developed, and a computer program is compiled ba

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7

Kiarasi, Faraz, Masoud Babaei, Kamran Asemi, Rossana Dimitri, and Francesco Tornabene. "Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions." Applied Sciences 11, no. 21 (2021): 10434. http://dx.doi.org/10.3390/app112110434.

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The present work studies the buckling behavior of functionally graded (FG) porous rectangular plates subjected to different loading conditions. Three different porosity distributions are assumed throughout the thickness, namely, a nonlinear symmetric, a nonlinear asymmetric and a uniform distribution. A novel approach is proposed here based on a combination of the generalized differential quadrature (GDQ) method and finite elements (FEs), labeled here as the FE-GDQ method, while assuming a Biot’s constitutive law in lieu of the classical elasticity relations. A parametric study is performed sy

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8

Petrov, Andrey, Sergey Aizikovich, and Leonid A. Igumnov. "Modeling of Wave Propagation in the Unsaturated Soils Using Boundary Element Method." Key Engineering Materials 743 (July 2017): 158–61. http://dx.doi.org/10.4028/www.scientific.net/kem.743.158.

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Problems of wave propagation in poroelastic bodies and media are considered. The behavior of the poroelastic medium is described by Biot theory for partially saturated material. Mathematical model is written in term of five basic functions – elastic skeleton displacements, pore water pressure and pore air pressure. Boundary element method (BEM) is used with step method of numerical inversion of Laplace transform to obtain the solution. Research is based on direct boundary integral equation of three-dimensional isotropic linear theory of poroelasticity. Green’s matrices and, based on it, bounda

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9

Furqan, Muhammad, Faisal Ahmed, Reinhard Feger, Klaus Aufinger, Walter Hartner, and Andreas Stelzer. "A SiGe-based fully-integrated 122-GHz FMCW radar sensor in an eWLB package." International Journal of Microwave and Wireless Technologies 9, no. 6 (2017): 1219–30. http://dx.doi.org/10.1017/s1759078717000095.

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High-performance SiGe HBTs and advancements in packaging processes have enabled system-in-package (SiP) designs for millimeter-wave applications. This paper presents a 122-GHz bistatic frequency modulated continuous wave (FMCW) radar SiP. The intended applications for the SiP are short-range distance and angular position measurements as well as communication links between cooperative radar stations. The chip is realized in a 130-nm SiGe BiCMOS technology and is based on a fully differential frequency-multiplier chain with in phase quadrature phase receiver and a binary phase shift keying modul

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10

Wang, Haijun, Weihua Jiang, Qing Hu, Jianjun Zhang, and Yanqing Jia. "Differential Evolution Algorithm-Aided Time-Varying Carrier Frequency Offset Estimation for OFDM Underwater Acoustic Communication." Journal of Marine Science and Engineering 10, no. 12 (2022): 1826. http://dx.doi.org/10.3390/jmse10121826.

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Orthogonal frequency division multiplexing (OFDM) is the preferred scheme for high-speed communication in the field of underwater acoustic communication. However, it is very sensitive to the carrier frequency offset (CFO). This study used a time-varying CFO estimation method aided by the differential evolution (DE) algorithm to accurately estimate the CFO of an OFDM system. This method was based on the principle that the received OFDM signal with inter-carrier interference could be considered by a Multi Carrier-code division multiple access (MC-CDMA) system on the receiver side because MC-CDMA

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11

Farazin, Ashkan, Chunwei Zhang, and Azher M. Abed. "Vibrations of composite structures: Finite element and analytical investigation." Polymers and Polymer Composites 30 (January 2022): 096739112211129. http://dx.doi.org/10.1177/09673911221112956.

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In this examination, the free vibrations of complete composite shells with rectangular openings based on first-order shear deformation theory have been studied. The equations are generally written in such a way that they can be converted to any of Donnell, Love, or Sanders theories. To study the shell with the opening of the problem-solving space, it is elementalized in such a way that the boundary conditions and loading are uniform at the edges of each element. For each element, the governing equations, the boundary conditions of the edges, and the compatibility conditions at the common bound

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12

Algül, İlke, and Ahmet Sinan Oktem. "Analytical and Numerical Solutions to Static Analysis of Moderately Thick Cross-Ply Plates and Shells." Applied Sciences 12, no. 24 (2022): 12547. http://dx.doi.org/10.3390/app122412547.

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This study aimed to provide a static solution to the boundary value problem presented by symmetric (0°/90°/0°) and antisymmetric (0°/90°) cross-ply composite, moderately thick shallow shells and plates (a special case of the shells) subjected to mixed-type unsolved boundary conditions. The boundary-discontinuous double Fourier series (BDM) method, in which displacements are expressed in trigonometric functions, is employed in a well-established framework. The analytical solution obtained using the BDM is compared with the successful integration of the generalized differential quadrature (GDQ)

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13

Nie, G. J., and Zheng Zhong. "Second-Order Elasto-Plastic Analysis of Frames by Differential Quadrature Element Method." Key Engineering Materials 340-341 (June 2007): 1321–26. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.1321.

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A new differential quadrature element model is presented for the second-order elasto-plastic analysis of frames in this study. The new model is based on the differential quadrature method (DQM) and the finite-cut technique. Firstly the basic equilibrium differential equations of members, the compatibility conditions of joints and the equilibrium equations of joints for the second-order analysis of frames are established. The differential quadrature method is used to discretize the basic equations and then the stiffness equations of the whole structure can be derived. While the corresponding bo

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14

Kővári, Zs, K. G. Strassmeier, K. Oláh, et al. "Surface magnetic activity of the fast-rotating G5 giant IN Comae, central star of the faint planetary nebula LoTr 5." Astronomy & Astrophysics 624 (April 2019): A83. http://dx.doi.org/10.1051/0004-6361/201834810.

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Context. On the asymptotic giant branch, low to intermediate mass stars blow away their outer envelopes, forming planetary nebulae. Dynamic interaction between the planetary nebula and its central progenitor is poorly understood. The interaction is even more complex when the central object is a binary star with a magnetically active component, as is the case for the target in this paper. Aims. We aim to quantify the stellar surface activity of the cool binary component of IN Com and aim to explain its origin. In general, we need a better understanding of how central binary stars in planetary n

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15

Doss, L. Jones Tarcius, and A. P. Nandini. "Discrete Mixed Petrov-Galerkin Finite Element Method for a Fourth-Order Two-Point Boundary Value Problem." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/962070.

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A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal ordera priorierror estimates are obtained without any restriction on the mesh.

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16

Bayat, Mohammad, and Mohammad Mohammadi Aghdam. "Micromechanical analysis of unidirectional composites using a least-squares-based differential quadrature element method." Journal of Mechanics of Materials and Structures 7, no. 2 (2012): 119–35. http://dx.doi.org/10.2140/jomms.2012.7.119.

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17

Chang-New Chen. "Differential Quadrature, Generalized Methods, Related Discrete Element Analysis Methods And EDQ Based Time Integration Method." Recent Patents on Engineering 1, no. 2 (2007): 163–76. http://dx.doi.org/10.2174/187221207780832147.

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18

Xing, Yufeng, Mingbo Qin, and Jing Guo. "A Time Finite Element Method Based on the Differential Quadrature Rule and Hamilton’s Variational Principle." Applied Sciences 7, no. 2 (2017): 138. http://dx.doi.org/10.3390/app7020138.

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19

Zhao, Jingjun, Jingyu Xiao, and Yang Xu. "Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/857205.

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A finite element method (FEM) for multiterm fractional partial differential equations (MT-FPDEs) is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem. The Diethelm fractional backward difference method (DFBDM), based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the m

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20

Arifeen, Shams Ul, Sirajul Haq, and Farhan Golkarmanesh. "Computational Study of Multiterm Time-Fractional Differential Equation Using Cubic B-Spline Finite Element Method." Complexity 2022 (November 23, 2022): 1–15. http://dx.doi.org/10.1155/2022/3160725.

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Due to the symmetry feature in nature, fractional differential equations precisely measure and describe biological and physical processes. Multiterm time-fractional order has been introduced to model complex processes in different physical phenomena. This article presents a numerical method based on the cubic B-spline finite element method for the solution of multiterm time-fractional differential equations. The temporal fractional part is defined in the Caputo sense while the B-spline finite element method is employed for space approximation. In addition, the four-point Gauss−Legendre quadrat

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21

Shafiei, Navvab, Mohammad Kazemi, and Laleh Fatahi. "Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method." Mechanics of Advanced Materials and Structures 24, no. 3 (2016): 240–52. http://dx.doi.org/10.1080/15376494.2015.1128025.

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22

Ansari, R., J. Torabi, and R. Hassani. "Vibration analysis of FG-CNTRC plates with an arbitrarily shaped cutout based on the variational differential quadrature finite element method." Materials Research Express 6, no. 12 (2019): 125086. http://dx.doi.org/10.1088/2053-1591/ab5b57.

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23

Boutiba, Malika, Selma Baghli-Bendimerad, and Abbès Benaïssa. "Three Approximations of Numerical Solution's by Finite Element Method for Resolving Space-Time Partial Differential Equations Involving Fractional Derivative's Order." Mathematical Modelling of Engineering Problems 9, no. 5 (2022): 1179–86. http://dx.doi.org/10.18280/mmep.090503.

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In this paper, we apply to a class of partial differential equation the finite element method when the problem is involving the Riemann-Liouville fractional derivative for time and space variables on a bounded domain with bounded conditions. The studied equation is obtained from the standard time diffusion equation by replacing the first order time derivative by  for 0<<1 and for the second standard order space derivative by  for 1<<2 respectively. The existence of the unique solution is proved by the Lax-Milgram Lemma. We present here three schemes to approximate numerically t

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24

Mohammadian, Mostafa, Seyed Mahmoud Hosseini, and Mohammad Hossein Abolbashari. "Lateral vibrations of embedded hetero-junction carbon nanotubes based on the nonlocal strain gradient theory: Analytical and differential quadrature element (DQE) methods." Physica E: Low-dimensional Systems and Nanostructures 105 (January 2019): 68–82. http://dx.doi.org/10.1016/j.physe.2018.08.022.

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25

Mohammadian, Mostafa, and Seyed Mahmoud Hosseini. "A size-dependent differential quadrature element model for vibration analysis of FG CNT reinforced composite microrods based on the higher order Love-Bishop rod model and the nonlocal strain gradient theory." Engineering Analysis with Boundary Elements 138 (May 2022): 235–52. http://dx.doi.org/10.1016/j.enganabound.2022.02.017.

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26

Trabelssi, M., and S. El-Borgi. "A novel formulation for the weak quadrature element method for solving vibration of strain gradient graded nonlinear nanobeams." Acta Mechanica, September 26, 2022. http://dx.doi.org/10.1007/s00707-022-03321-4.

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AbstractA novel formulation of the weak form quadrature element method, referred to as the locally adaptive weak quadrature element method, is proposed to develop elements for nonlinear graded strain gradient Timoshenko and Euler–Bernoulli nanobeams. The equations of motion are obtained based on Hamilton principle while accounting for the position of the physical neutral axis. The proposed elements use Gauss quadrature points to ensure full integration of the variational statement. The proposed formulation develops matrices based on the differential quadrature method which employs Lagrange-bas

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27

Trabelssi, M., and S. El-Borgi. "Vibration of nonlocal strain gradient functionally graded nonlinear nanobeams using a novel locally adaptive strong quadrature element method." Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, November 21, 2022, 239779142211294. http://dx.doi.org/10.1177/23977914221129426.

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The primary objective of this paper is to propose a novel method to derive Differential Quadrature Method matrices with several degrees of freedom at the boundaries that can be used to build Strong Quadrature Elements to solve fourth and higher-order equations of motion. The proposed method, referred to as Locally adaptive Strong Quadrature Element Method, is applied to higher-order equations of motion for nonlinear graded Timoshenko and Euler-Bernoulli nanobeams formulated using the Second Strain Gradient Theory or the Nonlocal Strain Gradient Theory. To limit the formulation complexity, the

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28

Mohamed, Nurul Akmal, Nur Fadhilah Ibrahim, Mohd Rozni Md Yusof, Nurul Farihan Mohamed, and Nurul Huda Mohamed. "IMPLEMENTATIONS OF BOUNDARY–DOMAIN INTEGRO-DIFFERENTIAL EQUATION FOR DIRICHLET BVP WITH VARIABLE COEFFICIENT." Jurnal Teknologi 78, no. 6-5 (2016). http://dx.doi.org/10.11113/jt.v78.9003.

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In this paper, we present the numerical results of the Boundary-Domain Integro-Differential Equation (BDIDE) associated to Dirichlet problem for an elliptic type Partial Differential Equation (PDE) with a variable coefficient. The numerical constructions are based on discretizing the boundary of the problem region by utilizing continuous linear iso-parametric elements while the domain of the problem region is meshed by using iso-parametric quadrilateral bilinear domain elements. We also use a semi-analytic method to handle the integration that exhibits logarithmic singularity instead of using

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29

Sun, Guangjun, Hongjing Li, Tong Wang, and Qiang Xu. "Out-of-Plane Free Vibration Analysis of Continuous Curved Girders with Combined Linetypes Using Differential Quadrature Element Method." International Journal of Structural Stability and Dynamics, January 24, 2022. http://dx.doi.org/10.1142/s0219455422500602.

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In this study, the out-of-plane free vibration equations of circular curved and clothoid transition curved girders with various boundary conditions were derived. The continuous curved girder with combined linetypes was discretized into separate curved girder elements. Based on the differential quadrature element method (DQEM), the Chebyshev–Gauss–Labatto unequal mesh division was applied to discretize the vibration equations of the continuous curved girder into those of the curved girder elements, along with the boundary conditions, internal geometric compatibility conditions, and force balanc

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30

Ansari, Reza, Ramtin Hassani, Emad Hasrati, and Hessam Rouhi. "Studying nonlinear vibrations of composite conical panels with arbitrary-shaped cutout reinforced with graphene platelets based on higher-order shear deformation theory." Journal of Vibration and Control, June 24, 2021, 107754632110248. http://dx.doi.org/10.1177/10775463211024847.

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In this article, the vibrational behavior of conical panels in the nonlinear regime made of functionally graded graphene platelet–reinforced composite having a hole with various shapes is investigated in the context of higher-order shear deformation theory. To achieve this aim, a numerical approach is used based on the variational differential quadrature and finite element methods. The geometrical nonlinearity is captured using the von Karman hypothesis. Also, the modified Halpin–Tsai model and rule of mixture are applied to calculate the material properties of graphene platelet–reinforced com

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31

Michel, Sixtine, Davide Torlo, Mario Ricchiuto, and Rémi Abgrall. "Spectral Analysis of High Order Continuous FEM for Hyperbolic PDEs on Triangular Meshes: Influence of Approximation, Stabilization, and Time-Stepping." Journal of Scientific Computing 94, no. 3 (2023). http://dx.doi.org/10.1007/s10915-022-02087-0.

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AbstractIn this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the polynomial space (Lagrangian on equispaced, Lagrangian on quadrature points (Cubature) and Bernstein), the stabilization techniques (streamline-upwind Petrov–Galerkin, continuous interior penalty, orthogonal subscale stabilization) and the time discretization (Runge–Kutta (RK), strong stability preserving RK and deferred correction). This is an extension of the one dimensional study by Michel et al. (J Sci Comput 89(2):31, 2021. https://doi.o

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32

Jin, Bangti, and Zhi Zhou. "Recovery of a space-time-dependent diffusion coefficient in subdiffusion: stability, approximation and error analysis." IMA Journal of Numerical Analysis, September 26, 2022. http://dx.doi.org/10.1093/imanum/drac051.

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Abstract In this work we study an inverse problem of recovering a space-time-dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian–Caputo fractional derivative of order $\alpha \in (0,1)$ in time. The main technical challenges of both theoretical and numerical analyses lie in the limited smoothing properties due to the fractional differential operator and high degree of nonlinearity of the forward map from the unknown diffusion coefficient to the distributed observation. We establish two conditional stabil

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33

Tornabene, Francesco, Nicholas Fantuzzi, Francesco Ubertini, and Erasmo Viola. "Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey." Applied Mechanics Reviews 67, no. 2 (2015). http://dx.doi.org/10.1115/1.4028859.

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A survey of several methods under the heading of strong formulation finite element method (SFEM) is presented. These approaches are distinguished from classical one, termed weak formulation finite element method (WFEM). The main advantage of the SFEM is that it uses differential quadrature method (DQM) for the discretization of the equations and the mapping technique for the coordinate transformation from the Cartesian to the computational domain. Moreover, the element connectivity is performed by using kinematic and static conditions, so that displacements and stresses are continuous across t

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Ford, Neville, Jingyu Xiao, and Yubin Yan. "A finite element method for time fractional partial differential equations." Fractional Calculus and Applied Analysis 14, no. 3 (2011). http://dx.doi.org/10.2478/s13540-011-0028-2.

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AbstractIn this paper, we consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained. The numerical examples at the end of the paper show that the experimental results are consistent with our theoretical results.

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35

Houalef, Ihab Eddine, Ismail Bensaid, Ahmed Saimi, and Abdelmadjid Cheikh. "Free Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Higher Order Refined Composite Beams Using Differential Quadrature Finite Element Method." European Journal of Computational Mechanics, February 6, 2023. http://dx.doi.org/10.13052/ejcm2642-2085.3143.

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Present paper deals on the free vibration investigation of carbon nanotube-reinforced composite (CNTs) beams, based on refined third order shear deformation finite element beam theory. The particularity of this model is that, it can capture shear deformation effect without using of any shear correction factor by satisfying shear stress free at free edges. The carbon nanotubes are supposed to be immersed in a polymeric matrix with functionally graded pattern across the thickness direction of the beam, and their material properties are evaluated using the rule of mixture. The differential equati

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Saimi, Ahmed, Ismail Bensaid, and Ahmed Fellah. "Effect of crack presence on the dynamic and buckling responses of bidirectional functionally graded beams based on quasi-3D beam model and differential quadrature finite element method." Archive of Applied Mechanics, May 4, 2023. http://dx.doi.org/10.1007/s00419-023-02429-w.

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