Relevant bibliographies by topics / Quadratic Time Finite Element Method

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Quadratic Time Finite Element Method'

Author: Grafiati
Published: 6 September 2023

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

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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 (December 7, 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 simulation run time of linear elements is presented here. Machine Learning (ML) algorithms are found to be effective in making predictions based on some known data set. The present paper discusses a methodology to implement ML model to predict the results equivalent to that of quadratic elements based on the solutions obtained from the linear elements. Here, a ML model is developed using python code, the stress results from Finite Element (FE) model of linear tetrahedral elements is given as the input to it to predict the stress results of quadratic tetrahedral elements. Abaqus is used as the FEM tool to develop the FE models. A python script is used to extract the stresses and the corresponding node numbers. The results showed that the developed ML model is successful in prediction of the accurate stress results for the set of test data. The scatter plots showed that the Z-score method was effective in removing the singularities. The proposed methodology is effective to reduce the computation time for simulation.
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Harari, Isaac, and Danny Avraham. "High-Order Finite Element Methods for Acoustic Problems." Journal of Computational Acoustics 05, no. 01 (March 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 of interpolation employed, and in this case quadratic elements are designed to yield dispersion-free solutions to model problems. The accuracy of Galerkin/least-squares and traditional Galerkin elements is compared, as well as the accuracy of quadratic versus standard linear interpolation, incorporating the effects of representing the radiation condition in exterior problems. The efficiency of the various methods is measured in terms of the cost of computation, rather than resolution requirements. In this manner, clear guidelines for selecting the order of interpolation are derived. Numerical testing validates the superior performance of the proposed methods. This work is a first step to gaining a thorough analytical understanding of the performance of p refinement as a basis for the development of h-p finite element methods for large-scale computation of solutions to acoustic problems.
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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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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 (December 27, 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 settlement using analytical methods and finite element methods with PLAXIS 2D modeling, the effect of modeling using quadratic triangle elements (6 nodal points) and quartic triangle elements (15 nodal points) on the consolidation magnitude and calculation processing time. The method used in this thesis is the analytical method using Terzaghi's theory and the finite element method using PLAXIS 2D. From the results of the analysis it was found that the use of a quadratic triangle element with 6 nodal points and 15 nodal points did not have a significant effect on the reduction results, but had a large effect on the length of the calculation process. After analyzing using 2D modeling using a quadratic triangle element with 6 nodal points and a quartic triangle element with 15 nodal points, a decrease of -6.673 meters for 6 nodal points and -6.669 meters for 15 nodal points is obtained. There was no significant difference between the two methods, which was only 4 mm different. The time needed to calculate with 6 nodes is about 1 hour and 15 nodes is about 4 hours.
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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 the increment time concerning the different values of α which is equal to 15°, 30° and 45, this development has been studied numerically by solving the problem of finite elements by the computer code ABAQUS. Quadratic 4-node elements (CPS4R) were used.
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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 (October 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 performed on the scan line. Hybrid shading, in which bi-quadratic interpolation of normals is performed on the edges and linear interpolation of intensity is performed on the scan line, has been proposed in the second algorithm. In the third algorithm, bi-cubic interpolation of intensity is performed on the edges and linear interpolation of intensity is performed on the scan line. The paper also presents an incremental method for fast calculation of area coordinates and shape functions enhancing the speed of the algorithms.
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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 (May 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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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 with solution obtained from the Finite Element Method (FEM).
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Dissertations / Theses on the topic "Quadratic Time Finite Element Method"

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Valivarthi, Mohan Varma, and Hema Chandra Babu Muthyala. "A Finite Element Time Relaxation Method." Thesis, Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-17728.

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In our project we discuss a finite element time-relaxation method for high Reynolds number flows. The key idea consists of using local projections on polynomials defined on macro element of each pair of two elements sharing a face. We give the formulation for the scalar convection–diffusion equation and a numerical illustration.
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Alpert, David N. "Enriched Space-Time Finite Element Methods for Structural Dynamics Applications." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870451.

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Kashefi, Ali. "A Finite-Element Coarse-GridProjection Method for Incompressible Flows." Thesis, Virginia Tech, 2017. http://hdl.handle.net/10919/79948.

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Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping operators execute data transfer between the grids. The CGP framework is constructed upon spatial and temporal discretization schemes. This framework has been established for finite volume/difference discretizations as well as explicit time integration methods. In this article we present for the first time a version of CGP for finite element discretizations, which uses a semi-implicit time integration scheme. The mapping functions correspond to the finite-element shape functions. With the novel data structure introduced, the mapping computational cost becomes insignificant. We apply CGP to pressure correction schemes used for the incompressible Navier Stokes flow computations. This version is validated on standard test cases with realistic boundary conditions using unstructured triangular meshes. We also pioneer investigations of the effects of CGP on the accuracy of the pressure field. It is found that although CGP reduces the pressure field accuracy, it preserves the accuracy of the pressure gradient and thus the velocity field, while achieving speedup factors ranging from approximately 2 to 30. Exploring the influence of boundary conditions on CGP, the minimum speedup occurs for velocity Dirichlet boundary conditions, while the maximum speedup occurs for open boundary conditions. We discuss the CGP method as a guide for partial mesh refinement of incompressible flow computations and show its application for simulations of flow over a backward facing step and flow past a cylinder.
Master of Science
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Wang, Bao. "Numerical Simulation of Detonation Initiation by the Space-Time Conservation Element and Solution Element Method." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1293461692.

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Dosopoulos, Stylianos. "Interior Penalty Discontinuous Galerkin Finite Element Method for the Time-Domain Maxwell's Equations." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337787922.

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Nagai, Toshiki. "Space-time Extended Finite Element Method with Applications to Fluid-structure Interaction Problems." Thesis, University of Colorado at Boulder, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10844711.

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This thesis presents a space-time extended finite element method (space-time XFEM) based on the Heaviside enrichment for transient problems with moving interfaces, and its applications to the fluid-structure interaction (FSI) analysis. The Heaviside-enriched XFEM is a promising method to discretize partial differential equations with discontinuities in space. However, significant approximation errors are introduced by time stepping schemes when the interface geometry changes in time. The proposed space-time XFEM applies the finite element discretization and the Heaviside enrichment in both space and time with elements forming a space-time slab. A simple space-time scheme is introduced to integrate the weak form of the governing equations. This scheme considers spatial intersection configuration at multiple temporal integration points. Standard spatial integration techniques can be applied for each spatial configuration. Nitsche's method and the face-oriented ghost-penalty method are extended to the proposed space-time XFEM formulation. The stability, accuracy and flexibility of the space-time XFEM for various interface conditions including moving interfaces are demonstrated with structural and fluid problems. Moreover, the space-time XFEM enables analyzing complex FSI problems using moving interfaces, such as FSI with contact. Two FSI methods using moving interfaces (full-Eulerian FSI and Lagrangian-immersed FSI) are studied. The Lagrangian-immersed FSI method is a mixed formulation of Lagrangian and Eulerian descriptions. As solid and fluid meshes are independently defined, the FSI is computed between non-matching interfaces based on Nitsche's method and projection techniques adopted from computational contact mechanics. The stabilized Lagrange multiplier method is used for contact. Numerical examples of FSI and FSI-contact problems provide insight into the characteristics of the combination of the space-time XFEM and the Lagrangian-immersed FSI method. The proposed combination is a promising method which has the versatility for various multi-physics simulations and the applicability such as optimization.

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Vikas, Sharma. "Development of Space-Time Finite Element Method for Seismic Analysis of Hydraulic Structures." Kyoto University, 2018. http://hdl.handle.net/2433/235094.

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Kyoto University (京都大学)
0048
新制・課程博士
博士(農学)
甲第21374号
農博第2298号
新制||農||1066(附属図書館)
学位論文||H30||N5147(農学部図書室)
京都大学大学院農学研究科地域環境科学専攻
(主査)教授 村上 章, 教授 藤原 正幸, 教授 渦岡 良介
学位規則第4条第1項該当
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KALARICKEL, RAMAKRISHNAN PRAVEEN. "Reliability of finite element method for time harmonic electromagnetic problems involving moving bodies." Doctoral thesis, Università degli studi di Genova, 2018. http://hdl.handle.net/11567/930777.

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This work is mainly concerned about the time-harmonic electromagnetic problems involving moving bodies. Such a formulation is possible when the boundaries between different moving objects are stationary and the sources involved are time-harmonic. Even simple media present bianisotropic properties when they are in motion. This kind of problems find applications in diverse fields. Numerical solution is required for most of the practical problems. We examined the reliability of finite element simulator developed for solving such problems.
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Wang, Shumin. "Improved-accuracy algorithms for time-domain finite methods in electromagnetics." The Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1061225243.

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Campbell-Kyureghyan, Naira Helen. "Computational analysis of the time-dependent biomechanical behavior of the lumbar spine." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1095445065.

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Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xix, 254 p.; also includes graphics. Includes bibliographical references (p. 234-254).
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Books on the topic "Quadratic Time Finite Element Method"

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Ruas, Vitoriano. A quadratic finite element method for solving biharmonic problems in IRn. Rio de Janeiro, Brasil: Pontifícia Universidade Catolica do Rio de Janeiro, 1986.

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Lin-Jun, Hou, and Langley Research Center, eds. Periodic trim solutions with hp-version finite elements in time: Final report. Atlanta, Ga: School of Aerospace Engineering, Georgia Institute of Technology, 1990.

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Golla, David Frank. Dynamics of viscoelastic structures: a time-domain finite element formulation. [Downsview, Ont.]: [Institute for Aerospace Studies], 1985.

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Golla, D. F. Dynamics of viscoelastic structures - a time-domain, finite element formulation. [S.l.]: [s.n.], 1985.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., ed. Time-domain finite elements in optimal control with application to launch-vehicle guidance. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1991.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., ed. Time-domain finite elements in optimal control with application to launch-vehicle guidance. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1991.

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Golla, David Frank. Dynamics of viscoelastic structures: A time-domain finite element formulation. [Downsview, Ont.]: Institute for Aerospace Studies, 1986.

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George, Alan. An analysis of spectral envelope-reduction via quadratic assignment problems. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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George, Alan. An analysis of spectral envelope-reduction via quadratic assignment problems. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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Bless, Robert R. Time-domain finite elements in optimal control with application to launch-vehicle guidance. Hampton, Va: Langley Research Center, 1991.

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Book chapters on the topic "Quadratic Time Finite Element Method"

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Bajer, Czesław I., and Bartłomiej Dyniewicz. "Space-Time Finite Element Method." In Numerical Analysis of Vibrations of Structures under Moving Inertial Load, 123–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29548-5_6.

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Singh, Shalvi, and tam Chakraborty. "Quadratic Wachspress Shape functions for polygonal finite element method." In Aerospace and Associated Technology, 118–23. London: Routledge, 2022. http://dx.doi.org/10.1201/9781003324539-21.

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Raiyan Kabir, S. M., B. M. A. Rahman, and A. Agrawal. "Finite Element Time Domain Method for Photonics." In Recent Trends in Computational Photonics, 1–37. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55438-9_1.

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Thomée, Vidar. "The Discontinuous Galerkin Time Stepping Method." In Galerkin Finite Element Methods for Parabolic Problems, 181–208. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-03359-3_12.

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Cardoso, José Roberto. "Finite Element Method for Time-Dependent Electromagnetic Fields." In Electromagnetics Through the Finite Element Method, 129–40. Boca Raton : Taylor & Francis, 2016. | “A CRC title.”: CRC Press, 2016. http://dx.doi.org/10.1201/9781315366777-5.

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Witkowski, M. "The Fundamentals of the Space-Time Finite Element Method." In Engineering Software IV, 281–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-21877-8_22.

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Zahedi, Sara. "A Space-Time Cut Finite Element Method with Quadrature in Time." In Lecture Notes in Computational Science and Engineering, 281–306. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71431-8_9.

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Geers, T. L. "A Fully Consistent Formulation of Early-Time Approximations for Acoustic Media." In The finite element method in the 1990’s, 521–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-10326-5_53.

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Gurusamy, Arumugam. "Finite Element Method for Time Fractional Keller–Segel Chemotaxis System." In Lecture Notes in Electrical Engineering, 441–48. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45474-0_39.

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Hochbruck, Marlis, and Christian Stohrer. "Finite Element Heterogeneous Multiscale Method for Time-Dependent Maxwell’s Equations." In Lecture Notes in Computational Science and Engineering, 269–81. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65870-4_18.

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Conference papers on the topic "Quadratic Time Finite Element Method"

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Pressburger, Yoram, Renato Perucchio, and David A. Field. "A Two-Level Multigrid Algorithm for Solving 3-D Quadratic Finite Element Models." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0098.

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Abstract A two-level multigrid algorithm for solving a quadratic finite element models containing tetrahedral meshes is presented. The basic idea is to generate two nested finite element models, first a linear model and then a quadratic one embedded hierarchically into the linear one. The exact solution to the linear model is computed and a two-level iterative procedure is used to solve for the quadratic model. In particular, the Successive Over Relaxation (SOR) method is used for the smoothing iteration on the quadratic model in each two-level cycle. A numerical study is carried out to determine how the relaxation factor and the number of SOR iteration in each two-level cycle influence the convergence rate of the complete algorithm. The stopping criterion for the iteration is based on the notion that the error in the iterative procedure will be of the same order as the error in the finite element approximation. Finally, the efficiency of the algorithm is evaluated by comparing the computational time with that of an exact solver based on Gauss elimination. Results indicate that the present algorithm produces substantial saving of CPU time.
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Emery, Ashley F., and Walter Dauksher. "The Dispersion in Finite Element Solutions to the One-Dimensional Heat Equation." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-1085.

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Abstract A method for evaluating the numerically introduced dispersion in finite element solutions to the one-dimensional heat equation is presented. The dispersion is quantified for linear and quadratic elements as a function of time step, mesh refinement and capacitance matrix formulation. It is demonstrated that an analysis of the dispersion is a useful tool in estimating the accuracy and in understanding the behavior of the numerical algorithm.
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Apte, Shrinivas G., and Brian H. Dennis. "Pseudo Compressible Mixed Interpolation Finite Element Method for Solving Three Dimensional Navier-Stokes Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13484.

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A pseudo compressible finite element method for solving three dimensional incompressible Navier-Stokes equations is presented. A physical problem discretized using tetrahedral elements with linear and quadratic interpolation functions for pressure and velocity variables respectively is then marched in time by using implicit time marching scheme based on finite differencing. The possible formation of indefinite matrix due to incompressibility constraint is avoided by inserting an artificial/pseudo time dependent term (Chorin, 1974) into the continuity equation that is eliminated when steady state is reached. This definite matrix system can then be solved using standard pre-conditioners and iterative solvers. Solutions for pressure driven flows obtained using this method are validated with the ones obtained from a standard problem of flow over a cylinder and also with numerical benchmark case of a 3-D laminar flow around an obstacle. An object oriented C++ program was developed which uses exact integrals of shape functions in its calculations rather than numerical integrations. This program was tested with different values of artificial compressibility factor (β), Reynolds numbers (Re) and grid sizes (number of Elements) and time steps (dt). The effect of these parameters on the the number of linear solver iterations required for convergence is studied efficiently using the non-dimensional numbers Pseudo Compressibility Number (PCN) and Elemental Reynolds Number (ERe). Although the relationship between the linear solver performance and these two non dimensional numbers remain complicated, it is found that there exists an optimum range of PCN as a function of ERe for which the solution convergence can be obtained with the minimum number of iterations.
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Dargush, G. F., and M. M. Grigoriev. "Higher-Order Boundary Element Methods for Unsteady Convective Transport." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/htd-24105.

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Abstract Higher-order boundary element methods (BEM) are presented for time-dependent convective diffusion problems. The time-dependent convective diffusion free-space fundamental solutions originally proposed by Carslaw and Jaeger are used to obtain the boundary integral formulation. For the linear, quadratic and quartic time interpolation functions considered in this paper, a complete set of closed form time integrals for the one-dimensional formulation are developed. Boundary element method solutions are obtained for four problems of unsteady convection-diffusion, including shock wave propagation. It is shown that the BEM solutions are extremely accurate in contrast to finite-difference and finite-element methods. Moreover, no upwinding is needed for the boundary element methods, even for high Peclet number flows. Finally, the conventional BEM formulation is extended to a problem involving singular flux arising due to a sudden rise of temperature on the boundary. This infinite flux BEM formulation provides significantly more accurate numerical results than the conventional approach.
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Mehraban, Arash, Jed Brown, Valeria Barra, Henry Tufo, Jeremy Thompson, and Richard Regueiro. "Efficient Residual and Matrix-Free Jacobian Evaluation for Three-Dimensional Tri-Quadratic Hexahedral Finite Elements With Nearly-Incompressible Neo-Hookean Hyperelasticity Applied to Soft Materials on Unstructured Meshes in Parallel, With PETSc and libCEED." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-24522.

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Abstract Soft materials such as rubber, elastomers, and soft biological tissues mechanically deform at large strain isochorically for all time, or during their initial transient (when a pore fluid, typically incompressible such as water, does not have time to flow out of the deforming polymer or soft tissue porous skeleton). Simulating these large isochoric deformations computationally, such as with the Finite Element Method (FEM), requires higher order (typically quadratic) interpolation functions and/or enhancements through hybrid/mixed methods to maintain stability. Lower order (linear) finite elements with hybrid/mixed formulation may not perform stably for all mechanical loading scenarios involving large isochoric deformations, whereas quadratic finite elements with or without hybrid/mixed formulation typically perform stably, especially when large bending or folding deformations are being simulated. For topology-optimization design of soft robotics, for instance, the FEM solid mechanics solver must run efficiently and stably. Stability is ensured by the higher order finite element formulation (with possible enhancement), but efficiency for higher order FEM remains a challenge. Thus, this paper addresses efficiency from the perspective of computer science algorithms and programming. The proposed efficient algorithm utilizes the Portable, Extensible Toolkit for Scientific Computation (PETSc), along with the libCEED library for efficient compiler optimized tensor-product-basis computation to demonstrate an efficient nonlinear solution algorithm. For preconditioning, a scalable p-multigrid method is presented whereby a hierarchy of levels is constructed. In contrast to classical geometric multigrid, also known as h-multigrid, each level in p-multigrid is related to a different approximation polynomial order, p, instead of the element size, h. A Chebyshev polynomial smoother is used on each multigrid level. Algebraic MultiGrid (AMG) is then applied to the assembled Q1 (linear) coarse mesh on the nodes of the quadratic Q2 (quadratic) mesh. This allows low storage that can be efficiently used to accelerate the convergence to solution. For a Neo-Hookean hyperelastic problem, we examine a residual and matrix-free Jacobian formulation of a tri-quadratic hexahedral finite element with enhancement. Efficiency estimates on AVX-2 architecture based on CPU time are provided as a comparison to similar simulation (and mesh) of isochoric large deformation hyperelasticity as applied to soft materials conducted with the commercially-available FEM software program ABAQUS. The particular problem in consideration is the simulation of an assistive device in the form of finger-bending in 3D.
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Darbandi, M., and Y. Daghighi. "Computation of Rarefied Gaseous Flows in Micro to Nano Scale Channels With Slip to Transient Regimes Using General Second-Order Quadratic Elements." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62155.

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A new finite-volume-based finite-element method using the quadratic elements is developed in the present study, to analyze the flow in micro and nano sizes with higher-order slip boundary conditions. The method is applied to gaseous flow in micro and nanoscale-channels. The developed method is carried out over a wide range of Knudsen numbers, which cover not only the continuum slip flow regime with 0≤Kn≤0.1 but also it entire the range of transient regime with 0.1<Kn≤10. To make the present computational model capable of simulating micro and nano sizes with the help of the Navier-Stokes equations, the modified high-order slip boundary conditions are applied which need utilizing the advantages of general quadratic second order elements in the computational domain. In other words, this paper introduces a new developed method, which is applied on higher-order elements, and employing reliable boundary conditions that all of these issues are used for the first time in the Micro/Nano study as well. The results reveal excellent agreement with those represented by analytical, DSMC, and Boltzmann calculations. The proposed method (using finite-volume-element strategy which benefits from the advantages of general quadratic second-order elements) is proved to be an efficient, practical, and accurate tool, which robustly extends the capability of our primitive large scale Navier-Stokes solver to micro and nano-scale flow predictions in slip and transient regimes. It can be regarded as a super alternative to classical molecular dynamics-based methods.
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Murakami, Hidenori, Oscar Rios, and Takeyuki Ono. "Development of a Nonlinear, C1-Beam Finite-Element Code for Actuator Design of Slender Flexible Robots." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70106.

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For actuator design and motion simulations of slender flexible robots, planar C1-beam elements are developed for Reissner’s large deformation, shear-deformable, curbed-beam model. Internal actuation is mechanically modeled by a rate-form of beam constitutive relation, where actuation curvature is prescribed at each time. Geometrically, a curbed beam is modeled as a frame bundle, whereby at each point on beam’s curve of centroids a moving orthonormal frame is attached to a cross section. After a finite element discretization, a curve of centroids is modeled as a C1-curve, employing cubic shape functions for both planar coordinates with an arc-parameter. The cubic shape functions have already been utilized in linear Euler-Bernoulli beams for the interpolation of transverse displacement. To define the rotation angle of each cross section or the attitude of the moving frame, quadratic shape functions are used introducing a middle node, resulting in three angular nodal displacements. As a result, each beam element has total eleven nodal coordinates. The implementation of a nonlinear finite element code is facilitated by the principle of virtual work, which yields Reissner’s large deformation curbed beam model as the Euler-Lagrange equations. For time integration, the Newmark method is utilized. Finally, as applications of the code, a few inchworm motions induced by different actuation curvature fields are presented.
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Tiso, Paolo. "Effective Modal Derivatives Based Reduction Method for Geometrically Nonlinear Structures." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48315.

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Effective Model Order Reduction (MOR) for geometrically nonlinear structural dynamics problems can be achieved by projecting the Finite Element (FE) equations on a basis constituted by a set of vibration modes and associated second order modal derivatives. However, the number of modal derivatives generated by such approach is quadratic with respect to the number of chosen vibration modes, thus quickly making the dimension of the reduction basis large. We show that the selection of the most important second order modes can be based on the convergence of the underlying linear modal truncation approximation. Given a certain time dependency of the load, this method allows to select the most significant modal derivatives set before computing it.
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Kerur, Shravankumar B., and Anup Ghosh. "Active Control of Geometrically Nonlinear Transient Response of Smart Laminated Composite Plate Integrated With AFC Actuator and PVDF Sensor." In ASME 2010 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2010. http://dx.doi.org/10.1115/smasis2010-3647.

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A coupled electromechanical finite element formulation for active control of geometrically nonlinear transient response of laminated composite plate is studied. First order shear deformation theory and Von Karman type nonlinear strain displacements are used. The plate is discritised using eight noded quadratic isoparametric elements with five mechanical degrees of freedom and one electrical degree of freedom per node. Newton-Raphson iterative method in association with Newmark time integration method is used to solve the nonlinear finite element equilibrium equation. Negative velocity feedback control algorithm is used to control the dynamic response of the smart laminated composite plate. Active fiber composite (AFC) layer poled in fiber direction acting as distributed actuator and PVDF layer poled in thickness direction acting as sensor are considered. Present study involves two types of actuator sensor arrangements. Case I: the substrate is sandwiched between AFC actuator and PVDF sensor. Case II: AFC actuator and PVDF sensor are collocated on top of the substrate. The effect of piezoelectric fiber orientation in actuator layer on vibration control for both cross ply and angle ply laminates are examined.
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Mahto, S., and U. S. Dixit. "Optimized Design of Single Link Flexible Manipulator." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63106.

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In this work, size optimization of a single link flexible robotic manipulator is carried out by considering the link as an Euler-Bernoulli beam. Finite element method is used for obtaining the natural frequencies and time response. Sequential quadratic programming method is used to maximize fundamental frequencies of the manipulator for different designs. A comparative study of the optimized designs is carried out to find out their suitability for real world situation. Based on the numerical experimentation, suggestion for formulating optimization problem for varying tip loads is provided.
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Reports on the topic "Quadratic Time Finite Element Method"

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Ewsuk, K. G., J. G. Arguello, Jr, D. H. Zeuch, and A. F. Fossum. Real-Time Design of Improved Powder Pressing Dies Using Finite Element Method Modeling. Office of Scientific and Technical Information (OSTI), December 2000. http://dx.doi.org/10.2172/773876.

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Rieben, Robert N. A Novel High Order Time Domain Vector Finite Element Method for the Simulation of Electromagnetic Devices. Office of Scientific and Technical Information (OSTI), January 2004. http://dx.doi.org/10.2172/15014486.

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Michalopoulos, C. D. PR-175-420-R01 Submarine Pipeline Analysis - Theoretical Manual. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), December 1985. http://dx.doi.org/10.55274/r0012171.

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Describes the computer program SPAN which computes the nonlinear transient response of a submarine pipeline, in contact with the ocean floor, to wave and current excitation. The dynamic response of a pipeline to impact loads, such as loads from trawl gear of fishing vessels, may also be computed. In addition, thermal expansion problems for submarine pipelines may be solved using SPAN. Beam finite element theory is used for spatial discretization of the partial differential equations governing the motion of a submarine pipeline. Large-deflection, small-strain theory is employed. The formulation involves a consistent basis and added mass matrix. Quadratic drag is computed using a nonconventional approach that involves the beam shape functions. Soil-resistance loads are computed using unique pipeline-soil interaction models which take into account coupling of axial and lateral soil forces. The nonlinear governing equations are solved numerically using the Newmark Method. This manual presents the discretized equations of motion, the methods used in determining hydrodynamic and soil-resistance forces, and the solution method.
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Yan, Yujie, and Jerome F. Hajjar. Automated Damage Assessment and Structural Modeling of Bridges with Visual Sensing Technology. Northeastern University, May 2021. http://dx.doi.org/10.17760/d20410114.

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Recent advances in visual sensing technology have gained much attention in the field of bridge inspection and management. Coupled with advanced robotic systems, state-of-the-art visual sensors can be used to obtain accurate documentation of bridges without the need for any special equipment or traffic closure. The captured visual sensor data can be post-processed to gather meaningful information for the bridge structures and hence to support bridge inspection and management. However, state-of-the-practice data postprocessing approaches require substantial manual operations, which can be time-consuming and expensive. The main objective of this study is to develop methods and algorithms to automate the post-processing of the visual sensor data towards the extraction of three main categories of information: 1) object information such as object identity, shapes, and spatial relationships - a novel heuristic-based method is proposed to automate the detection and recognition of main structural elements of steel girder bridges in both terrestrial and unmanned aerial vehicle (UAV)-based laser scanning data. Domain knowledge on the geometric and topological constraints of the structural elements is modeled and utilized as heuristics to guide the search as well as to reject erroneous detection results. 2) structural damage information, such as damage locations and quantities - to support the assessment of damage associated with small deformations, an advanced crack assessment method is proposed to enable automated detection and quantification of concrete cracks in critical structural elements based on UAV-based visual sensor data. In terms of damage associated with large deformations, based on the surface normal-based method proposed in Guldur et al. (2014), a new algorithm is developed to enhance the robustness of damage assessment for structural elements with curved surfaces. 3) three-dimensional volumetric models - the object information extracted from the laser scanning data is exploited to create a complete geometric representation for each structural element. In addition, mesh generation algorithms are developed to automatically convert the geometric representations into conformal all-hexahedron finite element meshes, which can be finally assembled to create a finite element model of the entire bridge. To validate the effectiveness of the developed methods and algorithms, several field data collections have been conducted to collect both the visual sensor data and the physical measurements from experimental specimens and in-service bridges. The data were collected using both terrestrial laser scanners combined with images, and laser scanners and cameras mounted to unmanned aerial vehicles.
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Zhu, Xian-Kui, and Bruce Wiersma. PR-644-213803-R01 Fatigue Life Models for Pipeline Containing Dents and Gouges. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), December 2022. http://dx.doi.org/10.55274/r0012248.

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Fatigue failure is a time-delayed failure that is one of the major threats to the pipeline integrity. For crack-like gouges in dents, the crack grows due to pressure cycling and eventually fails by fatigue. This work, which was funded by PRCI via Project MD-4-16, developed a viable engineering approach and a pragmatic fatigue model for predicting fatigue life of dents and gouges in pipelines. In particular, an equivalent stress method was developed with use of finite element analysis (FEA), and the crack driving force was determined based on the FEA results and the stress intensity factors (SIF) from API 579. The proposed fatigue model was evaluated with full-scale fatigue test data for line pipes containing dents and gouges, and then refined. The results showed that the refined fatigue model can predict adequate fatigue lives of dents and gouges in pipelines due to cyclic pressure. This report has a corresponding webinar.
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Al-Qadi, Imad, Egemen Okte, Aravind Ramakrishnan, Qingwen Zhou, and Watheq Sayeh. Truck Platooning on Flexible Pavements in Illinois. Illinois Center for Transportation, May 2021. http://dx.doi.org/10.36501/0197-9191/21-010.

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Truck platoons have many benefits over traditional truck mobility. Truck platoons have the potential to improve safety and reduce fuel consumption between 5% and 15%, based on platoon configuration. In Illinois, trucks carry more than 50% of freight tonnage and constitute 25% of the traffic on interstates. Therefore, expected fuel savings would be significant for trucks. Deployment of truck platoons within interstate highways may have a direct effect on flexible pavement performance, as the time between consecutive axle loads (i.e., resting time) is expected to decrease significantly. Moreover, platoons could potentially accelerate pavement damage accumulation due to trucks’ channelized position, decreasing pavement service life and increasing maintenance and rehabilitation costs. The main objective of this project was to quantify the effects of truck platoons on pavements and to provide guidelines to control corresponding potential pavement damage. Finite-element models were utilized to quantify the impact of rest period on pavement damage. Recovered and accumulated strains were predicted by fitting exponential functions to the calculated strain profiles. The results suggested that strain accumulation was negligible at a truck spacing greater that 10 ft. A new methodology to control pavement damage due to truck platoons was introduced. The method optimizes trucks’ lateral positions on the pavements, and an increase in pavement service life could be achieved if all platoons follow this optimization method. Life cycle assessment and life cycle cost analysis were conducted for fully autonomous, human-driven, and mixed-traffic regimes. For example, for an analysis period of 45 years, channelized truck platoons could save life cycle costs and environmental impacts by 28% and 21% compared with human-driven trucks, respectively. Furthermore, optimum truck platoon configuration could reduce life cycle costs and environmental impacts by 48% and 36%, respectively, compared with human-driven trucks. In contrast, channelized traffic could increase pavement roughness, increasing fuel consumption by 15%, even though platooning vehicles still benefit from reduction in air drag forces. Given that truck platoons are expected to be connected only in the first phase, no actions are required by the agency. However, in the second phase when truck platoons are also expected to be autonomous, a protocol for driving trends should be established per the recommendation of this study.
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Ramakrishnan, Aravind, Ashraf Alrajhi, Egemen Okte, Hasan Ozer, and Imad Al-Qadi. Truck-Platooning Impacts on Flexible Pavements: Experimental and Mechanistic Approaches. Illinois Center for Transportation, November 2021. http://dx.doi.org/10.36501/0197-9191/21-038.

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Truck platoons are expected to improve safety and reduce fuel consumption. However, their use is projected to accelerate pavement damage due to channelized-load application (lack of wander) and potentially reduced duration between truck-loading applications (reduced rest period). The effect of wander on pavement damage is well documented, while relatively few studies are available on the effect of rest period on pavement permanent deformation. Therefore, the main objective of this study was to quantify the impact of rest period theoretically, using a numerical method, and experimentally, using laboratory testing. A 3-D finite-element (FE) pavement model was developed and run to quantify the effect of rest period. Strain recovery and accumulation were predicted by fitting Gaussian mixture models to the strain values computed from the FE model. The effect of rest period was found to be insignificant for truck spacing greater than 10 ft. An experimental program was conducted, and several asphalt concrete (AC) mixes were considered at various stress levels, temperatures, and rest periods. Test results showed that AC deformation increased with rest period, irrespective of AC-mix type, stress level, and/or temperature. This observation was attributed to a well-documented hardening–relaxation mechanism, which occurs during AC plastic deformation. Hence, experimental and FE-model results are conflicting due to modeling AC as a viscoelastic and the difference in the loading mechanism. A shift model was developed by extending the time–temperature superposition concept to incorporate rest period, using the experimental data. The shift factors were used to compute the equivalent number of cycles for various platoon scenarios (truck spacings or rest period). The shift model was implemented in AASHTOware pavement mechanic–empirical design (PMED) guidelines for the calculation of rutting using equivalent number of cycles.
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Andrawes, Bassem, Ernesto Perez Claros, and Zige Zhang. Bond Characteristics and Experimental Behavior of Textured Epoxy-coated Rebars Used in Concrete Bridge Decks. Illinois Center for Transportation, January 2022. http://dx.doi.org/10.36501/0197-9191/22-001.

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The deterioration of bridge decks is a problem typically associated with the corrosion of the reinforcing steel. This issue was partially controlled during the 1970s with the incorporation of the epoxy-coating protection system. However, research later demonstrated that the smooth surface resulting from the epoxy-coating application reduces most of the friction between the rebar and the surrounding concrete. Consequently, forces acting on the rib faces are reconfigured in such a way that the radial components increase, triggering the early development of cracks. To mitigate both the reduction of bonding and the formation of cracks, the Illinois Department of Transportation proposed a new type of coated bars: textured epoxy-coated (TEC) bars. Over the last few years, different projects have been executed to understand and improve the characteristics of TEC rebars. This report is a continuation of research performed at the University of Illinois Urbana-Champaign to evaluate the bond behavior of TEC bars. The experimental program starts by characterizing, qualitatively and quantitatively, the roughness of the TEC rebars. Next, their bond-slip interaction embedded in concrete is evaluated through pull-out tests. Finite element models of these tests are developed to validate the behavior observed as the textured reinforcement loses anchorage with concrete. Based on these results, the experimental program then aims to study the impact of the drying shrinkage, temperature change, and flexural demands on two large-scale bridge deck specimens reinforced, individually, with TEC and standard epoxy-coated bars. The results collected from both specimens using digital image correlation and strain gauges are compared to explore the differences exhibited by the traditional and the new type of reinforcement coatings in terms of stress distribution in bridge decks. Finally, given the specialized equipment and time-consuming procedure needed to calculate the roughness parameters of TEC bars, an empirical, weight-based approach is developed as a rapid method for assessing the rebars’ roughness on-site.
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Thompson and Lawson. L51888 Development of Coupons for Monitoring Cathodic Protection Systems. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), April 2002. http://dx.doi.org/10.55274/r0010179.

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The use of coupons has been discussed and utilized for some time and is more prevalent in Europe than in the United States. Externally buried coupons have been utilized for different reasons including corrosion rate measurements, but their primary use has been for monitoring the effectiveness of a CP system. A detailed review of coupon studies is presented below. Renewed interest in the coupon technology was prompted by several studies performed by CC Technologies for PRCI that examined the use of off-potential measurements for evaluating the effectiveness of the CP system. These studies examined possible errors in the off-potential measurements including: Potential transients following the interruption of the CP system (spiking phenomenon). Interference due to multiple pipelines in the same right-of-way. Errors caused by long-line currents. Errors in monitoring local pipe conditions due to averaging large areas of pipe when making ground level pipe-to-soil potential measurements. In addition to the above studies which show conditions for which the off-potential measurements may not accurately represent the conditions locally on the pipe surface, a relatively common condition is the inability to interrupt all sources of the CP current on pipelines in congested areas or those structures with sacrificial anode cathodic protection directly bonded to the structure. Interpretation of pipe-to-soil potentials is made more difficult in areas of stray and/or telluric current activity. Therefore, there is a desire to utilize coupons as a more general tool for evaluating the level of CP. The areas targeted in this study are those areas for which the off-potential measurements are either difficult to perform or to interpret and for which a better means is needed for monitoring the CP level of the structure. Beginning in 1992, PRCI funded a program for the development, proof of concept, and evaluation of the coupon technology as applied to monitoring cathodic protection effectiveness on underground pipelines. The objectives for this project were: To provide a proof of concept for the use of coupons as a method to monitor the effectiveness of CP without interruption of the CP System. (Phase I). To establish guidelines for the use of coupons as a monitoring methodology for determining the level of protection on a pipeline. (Phase II). To provide a better understanding of the relationship between the coupon and the surface condition of the pipe. (Phase III). To quantify the technology such that it can be used as an alternative to conventional monitoring practices, specifically as a means of applying an acceptable criteria for CP. (Phase III). The scope of work included laboratory tests involving large soil boxes containing simulated coated-pipe segments with full size coupon test stations, finite element modeling of coupons near the pipe, full scale pipe tests at the Sugar Grove Test Facility and CC Technologies' Dublin, Ohio Pipe Test Facility, and test sites on operating pipelines throughout the United States.
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THE CRACK DETECTION METHOD OF LONGITUDINAL RIB BUTT WELD OF STEEL BRIDGE BASED ON ULTRASONIC LAMB WAVE. The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.265.

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Ultrasonic Lamb wave is an efficient and fast new nondestructive testing technology. Due to its characteristics of wide detection range, high efficiency and strong defect identification ability, ultrasonic Lamb wave has developed rapidly in the field of nondestructive testing in recent years. Meanwhile, the longitudinal rib butt weld is one of the most important failure modes of steel bridge deck, which seriously endangers the safety and durability of long-span steel bridges. In this paper, the fatigue failure mode of longitudinal rib butt weld is considered, the propagation process of ultrasonic guided wave in longitudinal rib butt weld is studied by using finite element real-time simulation, and the influences of different weld and crack parameters on ultrasonic guided wave is analyzed. The results show that the method based on ultrasonic Lamb wave has good applicability to crack detection of longitudinal rib butt weld of steel bridge deck. And this method provides a new idea and method for steel structure damage detection and monitoring.
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