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Journal articles on the topic 'Quadratic Time Finite Element Method'

Author: Grafiati

Published: 6 September 2023

Last updated: 31 July 2025

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1

Agrawal, Manish, and C. S. Jog. "A quadratic time finite element method for nonlinear elastodynamics within the context of hybrid finite elements." Applied Mathematics and Computation 305 (July 2017): 203–20. http://dx.doi.org/10.1016/j.amc.2017.01.059.

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Tang, Qiong, Luohua Liu, and Yujun Zheng. "Continuous Finite Element Methods of Molecular Dynamics Simulations." Modelling and Simulation in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/904140.

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Molecular dynamics simulations are necessary to perform very long integration times. In this paper, we discuss continuous finite element methods for molecular dynamics simulation problems. Our numerical results aboutABdiatomic molecular system andA2Btriatomic molecules show that linear finite element and quadratic finite element methods can better preserve the motion characteristics of molecular dynamics, that is, properties of energy conservation and long-term stability. So finite element method is also a reliable method to simulate long-time classical trajectory of molecular systems.

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Mahesh, S., Schiffel Marco, Ramesh S. Sharma, MK Praveenkumar, Vishal Wadagavi, and Lakshminarasimhan Subbarao. "A machine learning approach to predict the stress results of quadratic tetrahedral elements." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 2 (2021): 1128–35. http://dx.doi.org/10.1177/09544062211010828.

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Industries are always looking for an effective and efficient way to reduce the computation time of simulation because of the huge expenditure involved. From basics of Finite Element Method (FEM), it is known that, linear order finite elements consume less computation time and are less accurate compared to higher order finite elements say quadratic elements. An approach to get the benefit of less computation cost of linear elements and the good accuracy of quadratic elements can be of a good thought. The methodology to get the accurate results of quadratic elements with the advantage of less si

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Akpobi, John A., and E. D. Akpobi. "Development of a Model for Analysing Radial Flow of Slightly Compressible Fluids." Advanced Materials Research 62-64 (February 2009): 629–36. http://dx.doi.org/10.4028/www.scientific.net/amr.62-64.629.

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In this work, we develop a finite element-finite difference method to solve the differential equation governing the radial flow of slightly compressible fluids. The finite element method is used to carry out spatial approximations so as to study the variation of fluid properties at the various nodes to which effect we divided the entire radial domain of the fluid into a mesh of four radial 1-D quadratic elements which exposes nine nodes to intense study. Time approximation is done with the aid of the Crank-Nicolson finite difference scheme.

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Harari, Isaac, and Danny Avraham. "High-Order Finite Element Methods for Acoustic Problems." Journal of Computational Acoustics 05, no. 01 (1997): 33–51. http://dx.doi.org/10.1142/s0218396x97000046.

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The goal of this work is to design and analyze quadratic finite elements for problems of time-harmonic acoustics, and to compare the computational efficiency of quadratic elements to that of lower-order elements. Non-reflecting boundary conditions yield an equivalent problem in a bounded region which is suitable for domain-based computation of solutions to exterior problems. Galerkin/least-squares technology is utilized to develop robust methods in which stability properties are enhanced while maintaining higher-order accuracy. The design of Galerkin/least-squares methods depends on the order

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Purba, Baby, Roesyanto Roesyanto, Gina Cyntia Raphita, and Rudianto Surbakti. "Analisis Konsolidasi dengan Metode Preloading dikombinasikan dengan PVD berdasarkan Perhitungan Analitis dan Plaxis 2d." Jurnal Syntax Admiration 3, no. 12 (2022): 1569–85. http://dx.doi.org/10.46799/jsa.v3i12.518.

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Soft soil has poor soil characteristics. These soils generally have high compressibility, low permeability and low carrying capacity. Soil improvement by preloading and PVD is one of the common soil improvement methods to speed up the process of soil consolidation. The initial loading is carried out with the aim of consolidating the soft soil layer with the same or more loading amount than the load that will be carried by the soil both during and after construction. While vertical drainage can speed up the consolidation process. This analysis aims to determine the magnitude of consolidation se

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7

Bentahar, Mohammed. "Fatigue Analysis of an Inclined Crack Propagation Problem by the X-FEM Method." International Journal of Applied and Structural Mechanics, no. 34 (June 30, 2023): 23–31. http://dx.doi.org/10.55529/ijasm.34.23.31.

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The extended finite element method (X-FEM) has been used to solve fracture mechanics, problems in materials with various behavior laws (for example, isotropic, orthotropic or piezoelectric materials... For each type of material, it is necessary to obtain “enrichment functions” which model the behavior of the fields of displacement and stresses in the vicinity of the front of crack. In this paper, fatigue crack propagation analysis was modeled, by the extended finite element method X-FEM to evaluate the total energy and strain energy at the angled crack length, and to have the development of th

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Tang, Y., and Y. Hua. "Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints." East Asian Journal on Applied Mathematics 3, no. 2 (2013): 138–53. http://dx.doi.org/10.4208/eajam.240313.280513a.

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AbstractA quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical examples are performed to confirm theoretical results.

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9

SINGH, CHANDAN, and EKTA WALIA. "FAST HYBRID SHADING: AN APPLICATION OF FINITE ELEMENT METHODS IN 3D RENDERING." International Journal of Image and Graphics 05, no. 04 (2005): 789–810. http://dx.doi.org/10.1142/s0219467805002002.

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This paper is an attempt to improve the quality of Gouraud shading with minimum increase in the computation requirements. It presents algorithms for intermediate quality shading i.e. the quality of shading is better than Gouraud shading and nearly comparable to the quality of bi-quadratic Phong shading, at the same time, algorithms are very fast as compared to bi-quadratic Phong shading. Three algorithms are discussed. The first algorithm uses hybrid shading in which bi-quadratic interpolation of intensity is performed on the edges of a triangle and linear interpolation of intensity is perform

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10

Pineda, E., M. H. Aliabadi, and Janis Zapata. "The Boundary Element Method Applied to Visco-Plastic Analysis." Key Engineering Materials 449 (September 2010): 37–45. http://dx.doi.org/10.4028/www.scientific.net/kem.449.37.

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This paper presents a new formulation of the Dual Boundary Element Method to visco-plastic problems in a two-dimensional analysis. Visco-plastic stresses and strains around the crack tip are obtained until the visco-plastic strain rate reaches the steady state condition. A perfect visco-plastic analysis is also carried out in linear strain hardening (H’=0) materials. Part of the domain, the part that is susceptible to yield is discretized into quadratic, quadrilateral continuous cells. The loads are used to demonstrate time effects in the analysis carried out. Numerical results are compared wi

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Sundararaman, KA, KP Padmanaban, M. Sabareeswaran, and S. Guharaja. "An integrated finite element method, response surface methodology, and evolutionary techniques for modeling and optimization of machining fixture layout for 3D hollow workpiece geometry." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 23 (2016): 4344–59. http://dx.doi.org/10.1177/0954406216668208.

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Machining fixtures play inevitable role in manufacturing to ensure the machining accuracy and workpiece quality. The layout of fixture elements, clamping forces, and machining forces significantly affect the workpiece elastic deformation during machining. The clamping and machining forces are necessary to immobilize and machine the workpiece, respectively. Finding the appropriate layout of fixture elements is the other possible way to reduce the workpiece deformation, which in turn improves the machining accuracy. The finite element method interfaced with evolutionary techniques is normally us

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Welington, Vital da Silva*1 Brunno Emidio Sobrinho1 Cleirton André Silva Freitas2 Brenda A. Távora Ribeiro3 Francisco F. S. de Morais Júnior3 Ramon S. Y. R. Costa Silva 4. "NUMERICAL ANALYSIS IN FINITE ELEMENTS OF LAMINATED PLATES IN STEEL APPLIED IN DIFFERENT TYPES OF COMPOSITE MATERIALS MODELED ABAQUS MODELING AND COMPARED WITH ANALYTICAL." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 7, no. 6 (2018): 531–51. https://doi.org/10.5281/zenodo.1299053.

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The structures formed by laminated composites have great application in civil engineering. Mainly covering of industries with trapezoidal tile with acoustic insulation. Another application of the composite system is in the green layers of the roof. So this paper discussed a formulation for stability analysis of laminated plates through the Finite Element Method. The formulation presented allows the use of triangular and quadrilateral elements with different interpolation orders. In the numerical examples, the quadratic finite element with quadratic interpolation C3D8R was used to study its beh

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13

Shang Hsu, Yang, and Igor Alexandre Deitos. "Enriched finite element modeling in the dynamic analysis of plane frame subject to random loads." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 18 (2020): 3629–49. http://dx.doi.org/10.1177/0954406220916487.

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This work contributes to the generalized finite element approach in free vibration, dynamic elastic, and elastoplastic analysis of plane frame subjected to random excitation generated by the wind action. The wind velocity is modeled mathematically by using power spectral density method in combination with Shinozuka’s model, along with the commonly employed wind spectra. From these spectra, the dynamic wind loading is determined from the sum of the mean and floating wind velocities. The governing equation is formulated by Euler–Bernoulli beam theory, and it is discretized by using the enriched

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14

GHADIMI, PARVIZ, MOHAMMAD HADI JABBARI, and ARSHAM REISINEZHAD. "FINITE ELEMENT MODELING OF ONE-DIMENSIONAL BOUSSINESQ EQUATIONS." International Journal of Modeling, Simulation, and Scientific Computing 02, no. 02 (2011): 207–35. http://dx.doi.org/10.1142/s1793962311000414.

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Finite element modeling of one-dimensional Beji and Nadaoka Boussinesq equation is presented. The continuous equations are spatially discretized using standard Galerkin method. Since the extended Boussinesq equations contain high-order derivatives, two different numerical techniques are proposed in this paper in order to simplify the discretization task of the third-order terms. In the first technique, an auxiliary equation is introduced to eliminate the third-order derivatives of the momentum equation while non-overlapping elements with linear interpolating functions are employed to account f

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15

Zhu, Bao, Hongwei Yang, and Jiefu Chen. "A novel finite element time domain method for nonlinear Maxwell's equations based on the parametric quadratic programming method." Microwave and Optical Technology Letters 57, no. 7 (2015): 1640–45. http://dx.doi.org/10.1002/mop.29170.

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16

Pineda, E., and M. H. Aliabadi. "Dual Boundary Element Analysis for Time-Dependent Fracture Problems in Creeping Materials." Key Engineering Materials 383 (June 2008): 109–21. http://dx.doi.org/10.4028/www.scientific.net/kem.383.109.

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This paper presents the development of a new boundary element formulation for analysis of fracture problems in creeping materials. For the creep crack analysis the Dual Boundary Element Method (DBEM), which contains two independent integral equations, was formulated. The implementation of creep strain in the formulation is achieved through domain integrals in both boundary integral equations. The domain, where the creep phenomena takes place, is discretized into quadratic quadrilateral continuous and discontinuous cells. The creep analysis is applied to metals with secondary creep behaviour. T

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17

Cui, Li Kun, Wei Wang, and Zhuo Li. "Computing Method and Circuit Realization of Neural Network on Finite Element Analysis." Applied Mechanics and Materials 195-196 (August 2012): 758–63. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.758.

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The finite element analysis in theory of elasticity is corresponded to the quadratic programming with equality constraint, which can be further transformed into the unconstrained optimization. In the paper, the question is solved by modified Hopfield neural network based on the energy function of the neural network equals to the objective function of the finite element method and the minimum point, which is the stable equilibrium point of the network system, is the solution. In addition the authors present the computer simulation and analogue circuit experiment to verify this method. The resul

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18

Fazio, P., K. Gowri, and K. H. Ha. "Rectangular hybrid elements for the analysis of sandwich plate structures." Canadian Journal of Civil Engineering 14, no. 4 (1987): 455–60. http://dx.doi.org/10.1139/l87-069.

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The structural behaviour of sandwich plate structures are characterized by transverse shear deformations in the core. The assumed stress hybrid finite element technique is particularly suitable for developing sandwich plate bending elements. In the present study, rectangular three-layer sandwich plate elements have been formulated using simple assumed stress functions. Numerical test problems have been solved to examine the convergence property and suitability of these elements. The results are compared with that of a complete quadratic stress mode element and with analytical solutions. Six de

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Nguyen, Nghia-Danh, and Shyh-Chour Huang. "Trawl Grid Structure Design and Analysis Using the Finite Element Method." Applied Sciences 13, no. 13 (2023): 7536. http://dx.doi.org/10.3390/app13137536.

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The structure of fishnet knots has been simplified in previous studies to facilitate the construction of numerical equations of the fishnet structure. This leads to errors in the dynamic analysis of the trawl mesh structure with water flow. In this study, the finite element method was used to analyze the interaction of the trawl mesh structure with the solid object in a dynamic explicit environment. At the same time, design variables were optimized through impact assessment and the displacement of grid cells. The results show that the polyamide (PA) material, a 0.4 mm cross-section, and a 25 m

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20

Bernat, J., S. Stępień, A. Stranz, G. Szymański, and J. K. Sykulski. "Infinite time horizon optimal current control of a stepper motor exploiting a finite element model." Bulletin of the Polish Academy of Sciences Technical Sciences 62, no. 4 (2014): 835–41. http://dx.doi.org/10.2478/bpasts-2014-0092.

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Abstract An optimal control theory based method is presented aiming at minimizing the energy delivered from source and the power loss in a stepper motor circuit. A linear quadratic current regulator with an infinite time horizon is employed and its appropriateness for this type of a problem explained. With the purpose of improving the accuracy of the control system, the self and mutual inductances of windings are calculated using a finite element model. The numerically computed results are verified experimentally.

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AL-saedi, Akeel A., and Jalil Rashidinia. "Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation." Electronic Research Archive 31, no. 7 (2023): 4248–65. http://dx.doi.org/10.3934/era.2023216.

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<abstract> <p>This paper presents a numerical scheme based on the Galerkin finite element method and cubic B-spline base function with quadratic weight function to approximate the numerical solution of the time-fractional Burger's equation, where the fractional derivative is considered in the Caputo sense. The proposed method is applied to two examples by using the $L_2$ and $ {L_\infty } $ error norms. The obtained results are compared with a previous existing method to test the accuracy of the proposed method.</p> </abstract>

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Wang, Shuo, Binbin Xiang, Wei Wang, et al. "Finite Element Model Updating Method for Radio Telescope Antenna Based on Parameter Optimization with Surrogate Model." Applied Sciences 14, no. 13 (2024): 5620. http://dx.doi.org/10.3390/app14135620.

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There are deviations between the radio telescope antenna finite element (FE) model, founded on the design stage, and the actual working antenna structure. The original FE model cannot accurately describe the antenna structure deformation characteristics under the environmental load, thereby compromising the accuracy of the active structural compensation. This article proposes an antenna FE model updating method founded on parameter optimization with a surrogate model. The updating method updates the modulus of elasticity parameters of different components of the antenna backup structure (BUS)

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Rojas-Quintero, Juan Antonio, François Dubois, and José Guadalupe Cabrera-Díaz. "Simpson’s Variational Integrator for Systems with Quadratic Lagrangians." Axioms 13, no. 4 (2024): 255. http://dx.doi.org/10.3390/axioms13040255.

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This contribution proposes a variational symplectic integrator aimed at linear systems issued from the least action principle. An internal quadratic finite-element interpolation of the state is performed at each time step. Then, the action is approximated by Simpson’s quadrature formula. The implemented scheme is implicit, symplectic, and conditionally stable. It is applied to the time integration of systems with quadratic Lagrangians. The example of the linearized double pendulum is treated. Our method is compared with Newmark’s variational integrator. The exact solution of the linearized dou

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Bernat, Jakub, Slawomir Jan Stepien, Artur Stranz, and Paulina Superczynska. "Infinite-time linear–quadratic optimal control of the BLDC motor exploiting a nonlinear finite element model." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 3 (2017): 633–48. http://dx.doi.org/10.1108/compel-09-2016-0419.

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Purpose This paper aims to present a nonlinear finite element model (FEM) of the Brushless DC (BLDC) motor and the application of the optimal linear–quadratic control-based method to determine the excitation voltage and current waveform considering the minimization of the energy injected to the input circuit and energy lost. The control problem is designed and analyzed using the feedback gain strategy for the infinite time horizon problem. Design/methodology/approach The method exploits the distributed parameters, nonlinear FEM of the device. First, dynamic equations of the BLDC motor are tran

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Karpik, Anna, Francesco Cosco, and Domenico Mundo. "Higher-Order Hexahedral Finite Elements for Structural Dynamics: A Comparative Review." Machines 11, no. 3 (2023): 326. http://dx.doi.org/10.3390/machines11030326.

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The finite element method (FEM) is widely used in many engineering applications. The popularity of FEM led to the development of several variants of formulations, and hexahedral meshes surged as one of the most computationally effective. After briefly reviewing the reasons and advantages behind the formulation of increasing order elements, including the serendipity variants and the associated reduced integration schemes, a systematic comparison of the most common hexahedral formulations is presented. A numerical benchmark was used to assess convergency rates and computational efficiencies when

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Karaagac, Berat, Yusuf Ucar, and Alaattin Esen. "Numerical solutions of the improved boussinesq equation by the galerkin quadratic B-spline finite element method." Filomat 32, no. 16 (2018): 5573–83. http://dx.doi.org/10.2298/fil1816573k.

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In this paper, we are going to obtain numerical solutions of the improved Boussinesq equation with the aid of Galerkin quadratic B-spline finite element method. To test the accuracy and efficiency of the current method, four test problems have been used. These are solitary wave movement, interaction of two solitary waves, wave break-up and blow-up of solutions. Their results have been compared with those available in the literature for different values of space and time steps. Also, the error norms L2 and L1 have been computed and presented in comparison.

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Liu, Qiyu, Qunxiong Zhu, Zhiqiang Geng, and Longjin Lv. "Time Optimal Control of a Thermoelastic System." Mathematical Problems in Engineering 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/6047670.

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This paper considers the numerical approximation for the time optimal control problem of a thermoelastic system with some control and state constraints. By the Galerkin finite element method (FEM), the original problem is projected into a semidiscrete optimal control problem governed by a system of ordinary differential equations. Then the optimal time and control parameterization method is applied to reduce the original system to an optimal parameter selection problem, in which both the optimal time and control are taken as decision variables to be optimized. This problem can be solved as a n

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Mukae, Shunichi, Takeshi Okuzono, and Kimihiro Sakagami. "On the Robustness and Efficiency of the Plane-Wave-Enriched FEM with Variable q-Approach on the 2D Room Acoustics Problem." Acoustics 4, no. 1 (2022): 53–73. http://dx.doi.org/10.3390/acoustics4010004.

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Partition of unity finite element method with plane wave enrichment (PW-FEM) uses a shape function with a set of plane waves propagating in various directions. For room acoustic simulations in a frequency domain, PW-FEM can be an efficient wave-based prediction method, but its practical applications and especially its robustness must be studied further. This study elucidates PW-FEM robustness via 2D real-scale office room problems including rib-type acoustic diffusers. We also demonstrate PW-FEM performance using a sparse direct solver and a high-order Gauss–Legendre rule with a recently devel

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Esen, Alaattin, and Orkun Tasbozan. "Numerical Solution of Time Fractional Schrödinger Equation by Using Quadratic B-Spline Finite Elements." Annales Mathematicae Silesianae 31, no. 1 (2017): 83–98. http://dx.doi.org/10.1515/amsil-2016-0015.

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Abstract In this article, quadratic B-spline Galerkin method has been employed to solve the time fractional order Schrödinger equation. Numerical solutions and error norms L2 and L∞ are presented in tables.

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KERUR, S. B., and ANUP GHOSH. "ACTIVE VIBRATION CONTROL OF COMPOSITE PLATE USING AFC ACTUATOR AND PVDF SENSOR." International Journal of Structural Stability and Dynamics 11, no. 02 (2011): 237–55. http://dx.doi.org/10.1142/s0219455411004075.

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A finite element formulation for active vibration control of laminated composite plate integrated with active fiber composite (AFC) layer acting as distributed actuator and PVDF layer as sensor is presented in this paper. An eight noded quadratic isoparametric element with five mechanical degrees of freedom and one electrical degree of freedom per node of the element is considered. Newmark time integration method is used to calculate the dynamic response and negative velocity feedback control algorithm is used to control the dynamic response of the laminated composite plate. The effect of piez

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Yigit Akargun, Hayri, and Cuneyt Sert. "Least-squares finite element solution of Euler equations with H-type mesh refinement and coarsening on triangular elements." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 7 (2014): 1487–503. http://dx.doi.org/10.1108/hff-01-2013-0006.

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Purpose – The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows. Design/methodology/approach – Unsteady Euler equations are discretized on meshes of linear and quadratic triangular and quadrilateral elements using LSFEM. Backward Euler scheme is used for time discretization. For the refinement of linear triangular elements, a modified version of the simple bisection algorithm is used. Mesh coarsening is performed with the edge collapsi

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Peng, Jia Chung, Yong Xiang Zhao, L. Y. Yu, and A. G. Yang. "Finite Element Analysis on Fatigue Stress History of a Railway Bogie Bolster." Advanced Materials Research 44-46 (June 2008): 195–200. http://dx.doi.org/10.4028/www.scientific.net/amr.44-46.195.

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An efficient finite element (FE) method, multivariate quadratic regression approach, is proposed for calculating the fatigue stress spectrum of engineering structures. The calculation starts from a dynamic load history. A regression function is established as a relation from the concurrent components of structural balance force systems into the structural stress. Parameters of the relation are measured by the stress data using an elastic-plastic FE method under selected groups of balance force systems. The selected systems should cover the possible load range with a similar service condition.

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WOLFF, SEBASTIAN, and CHRISTIAN BUCHER. "ON CONTINUOUS ASSUMED GRADIENT ELEMENTS OF SECOND ORDER." International Journal of Computational Methods 10, no. 01 (2013): 1340009. http://dx.doi.org/10.1142/s0219876213400094.

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This paper presents and compares continuous assumed gradient (CAG) methods when applied to structural elasticity. CAG elements are finite elements where the strain, i.e., the deformation gradient, is replaced by a C0-continuous interpolation. Similar approaches are found in nodal integration and SFEM. Recently, interpolation schemes for a continuous assumed deformation gradient were proposed for first order tetrahedral and hexahedral finite elements. These schemes try to balance accuracy and numerical efficiency. At the same time, the stability of the interpolation with respect to hourglassing

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Koubaiti, Ouadie, Said EL Fakkoussi, Jaouad El-Mekkaoui, Hassan Moustachir, Ahmed Elkhalfi, and Catalin I. Pruncu. "The treatment of constraints due to standard boundary conditions in the context of the mixed Web-spline finite element method." Engineering Computations 38, no. 7 (2021): 2937–68. http://dx.doi.org/10.1108/ec-02-2020-0078.

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Purpose This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous and non-homogeneous; Dirichlet boundary conditions. This paper considered the two-dimensional linear elasticity equation of Navier–Lamé with the condition CAB. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained; without using a numerical method as Lagrange multiplier. This study have developed mixed finite element; method using the B-splines Web-spline space. T

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LISTERUD, EIVIND, and WALTER EVERSMAN. "FINITE ELEMENT MODELING OF ACOUSTICS USING HIGHER ORDER ELEMENTS PART I: NONUNIFORM DUCT PROPAGATION." Journal of Computational Acoustics 12, no. 03 (2004): 397–429. http://dx.doi.org/10.1142/s0218396x0400233x.

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Cubic serendipity elements have been implemented into a nonuniform duct model of acoustic propagation in a moving medium. This model uses a convective potential formulation derived from the inviscid linearized mass and momentum equations. The model requires post-processing to calculate acoustic pressure. These elements outperform the quadratic serendipity elements in terms of computational efficiency based on visual observations and error norm analysis of acoustic pressure. CPU time reduction of up to 40% has been observed without sacrificing accuracy. Any penalty in numerical accuracy incurre

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Tota-Maharaj, Kiran, Ghassan Nounu, and Navin Ramroop. "Modelling of Quadratic-Surface Sludge Digesters by Smoothed Particle Hydrodynamics (SPH) – Finite Element (FE) Methods." Archives of Hydro-Engineering and Environmental Mechanics 67, no. 1-4 (2020): 35–53. http://dx.doi.org/10.1515/heem-2020-0003.

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Abstract The quadric-surfaced sludge digester (QSD), also known as the egg-shaped sludge digester, has proven its advantages over traditional cylindrical digesters recently. A reduction in operational cost is the dominant factor. Its shell can be described as a revolution of a parabola with the apex and base being either tapered or spherical. This shape provides a surface free of discontinuities, which is advantageous regarding the efficiency during mixing. Since the shape does not produce areas of inactive fluid motion within the tank, sludge settlement and an eventual grit build-up are avoid

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Chen, Enwei, Mengbo Li, Neil Ferguson, and Yimin Lu. "An adaptive higher order finite element model and modal energy for the vibration of a traveling string." Journal of Vibration and Control 25, no. 5 (2018): 996–1007. http://dx.doi.org/10.1177/1077546318808881.

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A nonlinear equation describing the transverse vibration of an axially traveling string with constant and time-varying length is obtained by developing a new finite element model described by quadratic shape functions. A novel nonlinear coordinate transform is introduced with regard to its nonlinear terms. Subsequently, a new hybrid Newmark-beta/time varying degree of freedom method, which can adjust the element number automatically according to the change of string length, is proposed to improve accuracy. The proposed method as well as normal numerical methods are compared with an analytical

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Rosati, I., G. Fabbrocino, and C. Rainieri. "An application of different surrogate models to model updating of a heritage structure." Journal of Physics: Conference Series 2647, no. 22 (2024): 222004. http://dx.doi.org/10.1088/1742-6596/2647/22/222004.

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Abstract The preservation of historic structures is of primary importance due to their significant cultural value. However, destructive tests as well as invasive interventions should be as much limited as possible. In this contest, Finite Element model updating can be applied as a non-destructive method to indirectly estimate selected unknown parameters through numerical model calibration. To this aim, an inverse problem has to be solved by minimizing the gap between corresponding experimental and numerical estimates of modal parameters. However, the application of Finite Element model updatin

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OLATOYINBO, Seyi Festus. "Verification of a High-Order FEM-based CFD Code using the Method of Manufactured Solutions." INCAS BULLETIN 15, no. 2 (2023): 75–89. http://dx.doi.org/10.13111/2066-8201.2023.15.2.8.

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A high-order computational fluid dynamics (CFD) code capable of solving compressible turbulent flow problems was developed. The CFD code employs the Flowfield Dependent Variation (FDV) scheme implemented in a Finite Element Method (FEM) framework. The FDV scheme is basically derived from the Lax-Wendroff Scheme (LWS) involving the replacement of LWS’s explicit time derivatives with a weighted combination of explicit and implicit time derivatives. The code utilizes linear, quadratic and cubic isoparametric quadrilateral and hexahedral Lagrange finite elements with corresponding piecewise shape

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Rafiee, Vahid, and Jawad Faiz. "RESPONSE SURFACE METHOD-BASED OPTIMIZATION OF OUTER ROTOR PERMANENT MAGNET SYNCHRONOUS MOTOR." Journal of Energy Technology 12, no. 3 (2024): 43–52. https://doi.org/10.18690/jet.12.3.43-52.2019.

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The Finite Element Method (FEM) is a prominent analysis approach. Although it is applicable for simulation and optimization of electrical machines, FEM is a very time-consuming technique. One of theapproaches to shorten the optimization runtime is the use of surrogate models instead of FEM. In this paper, the design and optimization of an outer rotor permanent magnet synchronous motor for ahybrid vehicle are investigated. Response surface methodology (RSM) with four input variables is integrated with a sequential quadratic programming algorithm for optimization. Before the optimization,the per

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Eisler, G. R., R. D. Robinett, D. J. Segalman, and J. D. Feddema. "Approximate Optimal Trajectories for Flexible-Link Manipulator Slewing Using Recursive Quadratic Programming." Journal of Dynamic Systems, Measurement, and Control 115, no. 3 (1993): 405–10. http://dx.doi.org/10.1115/1.2899116.

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The method of recursive quadratic programming, coupled with a homotopy method, has been used to generate approximate minimum-time and minimum tracking-error tip trajectories for two-link flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for a multi-link, multi-joint system with bending only in the horizontal-plane. Constraints on the trajectory include boundary conditions on link tip position, final joint velocities, accelerations and torque inputs to complete a rest-to-rest maneuver, straight-line tip tracking between bo

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Grandhi, R. V., H. Cheng, and S. S. Kumar. "Design of Forging Process Parameters With Deformation and Temperature Constraints." Journal of Manufacturing Science and Engineering 118, no. 3 (1996): 441–44. http://dx.doi.org/10.1115/1.2831051.

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This paper presents a methodology for designing optimal process parameters for forging operations. The nonlinear rigid viscoplastic finite element (FE) method is used for deformation and thermal analyses. From the FE model a state space system is developed for representing the coupled deformation and thermal behavior of the metal forming system. Constraints are imposed on the strain rate and temperature of the deforming work-piece for obtaining the desired physical/microstructural properties in the final product. The linear quadratic regulator (LQR) theory for finite time control is used in de

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Zeng, Detang, Xin Yu, Jingfang Huang, and Chunqing Tan. "Numerical Computation for a Kind of Time Optimal Control Problem for the Tubular Reactor System." Mathematical Problems in Engineering 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/9580470.

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This paper is devoted to the study of numerical computation for a kind of time optimal control problem for the tubular reactor system. This kind of time optimal control problem is aimed at delaying the initiation time τ of the active control as late as possible, such that the state governed by this controlled system can reach the target set at a given ending time T. To compute the time optimal control problem, we firstly approximate the original problem by finite element method and get a new approximation time optimal control problem governed by ordinary differential equations. Then, through t

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Karpik, Anna, Francesco Cosco, and Domenico Mundo. "Dynamic Error Estimation in Higher-Order Finite Elements." Designs 8, no. 4 (2024): 79. http://dx.doi.org/10.3390/designs8040079.

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The Finite Element Method (FEM) has emerged as a powerful tool for predicting the behavior of industrial products, including those with complex geometries or uncommon materials. Finite Element Analysis (FEA) is widely used to study structural vibration-related aspects such as stress, displacement, and velocity. Modal analysis, a standard technique for characterizing the vibrational behavior of structures, is essential for identifying resonance frequencies, optimizing component design, and assessing structural integrity. Finite Elements (FE) modal analysis enables engineers to evaluate numerica

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Siddharath, Yadav1 Er. Shubham Srivastava2 &. Rishabh Joshi3. "ANALYSIS OF CRACK IDENTIFICATION IN BEAM USING FINITE ELEMENT METHOD." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 8 (2018): 52–55. https://doi.org/10.5281/zenodo.1339354.

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Crack in any structure changes the dynamic behaviour of the structure and by examining this change location and severity of the crack can be identified. Non-destructive testing (NDT) methods are used for detecting the location and severity i.e. crack size but these techniques are costly and time consuming. Modal parameters like natural frequency, mode shape can be used to detect the crack in beams. The present work is aimed for detection of open transverse crack in a Euler Bernoulli beam. The crack considered is an open crack and the analysis is made for linear behaviour of the beam. Finite el

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Bonnet, Marc, Giulio Maier, and Castrenze Polizzotto. "Symmetric Galerkin Boundary Element Methods." Applied Mechanics Reviews 51, no. 11 (1998): 669–704. http://dx.doi.org/10.1115/1.3098983.

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This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that th

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Zhang, Huiqin, and Yanping Chen. "Two-grid finite element method with an H2N2 interpolation for two-dimensional nonlinear fractional multi-term mixed sub-diffusion and diffusion wave equation." AIMS Mathematics 9, no. 1 (2024): 160–77. http://dx.doi.org/10.3934/math.2024010.

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<abstract><p>In this paper, we studied the two-grid method (TGM) for two-dimensional nonlinear time fractional multi-term mixed sub-diffusion and diffusion wave equation. A fully discrete scheme with the quadratic Hermite and Newton interpolation (H2N2) method was considered in the temporal direction and the expanded finite element method is used to approximate the spatial direction. In order to reduce computational time, a dual grid method based on Newton iteration was constructed with order $ \alpha\in(0, 1) $ and $ \beta\in(1, 2) $. The global convergence order of the two-grid s

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WANG, FENGXIA. "MODEL REDUCTION WITH GEOMETRIC STIFFENING NONLINEARITIES FOR DYNAMIC SIMULATIONS OF MULTIBODY SYSTEMS." International Journal of Structural Stability and Dynamics 13, no. 08 (2013): 1350046. http://dx.doi.org/10.1142/s0219455413500466.

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This work investigates the implementation of nonlinear model reduction to flexible multibody dynamics. Linear elastic theory will lead to instability issues with rotating beam-like structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In order to reduce the computation cost in flexible multibody dynamics, which is extremely important for complex large system simulations, modal reduction is usually implemented to

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Bernat, Jakub, Slawomir Jan Stepien, Artur Stranz, and Paulina Superczynska. "Linear quadratic-based optimal current control of BLDC motor minimizing control error and considering accurate finite element model." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 35, no. 6 (2016): 2063–73. http://dx.doi.org/10.1108/compel-03-2016-0087.

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Purpose Brushless DC (BLDC) motors are commonly used in the industry. The improvement of power switching electronic elements, especially integrated circuits, has led to the development and improvement of control strategies. The purpose of this paper is to apply the well-known LQR control method for the highly accurate model of the BLDC motor, which is a must for the control system to be optimal and stable. Design/methodology/approach The employed distributed parameter finite element motor model uses a state vector which is dependent not only on time but also on space configuration, thus enabli

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Aghdam, Yones Esmaeelzade, Hamid Mesgarani, Zeinab Asadi, and Van Thinh Nguyen. "Investigation and analysis of the numerical approach to solve the multi-term time-fractional advection-diffusion model." AIMS Mathematics 8, no. 12 (2023): 29474–89. http://dx.doi.org/10.3934/math.20231509.

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<abstract><p>In this paper, a methodical approach is presented to approximate the multi-term fractional advection-diffusion model (MT-FAD). The Lagrange squared interpolation is used to discretize temporal fractional derivatives, and Legendre polynomials are shifted as an operator to discretize the spatial fractional derivatives. The advantage of these numerical techniques lies in the orthogonality of Legendre polynomials and its matrix operations. A quadratic implicit design as well as its stability and convergence analysis are evaluated. It should be noted that the theoretical pr

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