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Usik Lee Spectral Element Method in Structural Dynamics


Spectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields. The book consists of three key sections. In the first part, background knowledge is set up for the readers by reviewing previous work in the area and by providing the fundamentals for the spectral analysis of signals. In the second part, the theory of spectral element method is provided, focusing on how to formulate spectral element models and how to conduct spectral element analysis to obtain the dynamic responses in both frequency- and time-domains. In the last part, the applications of SEM to various structural dynamics problems are introduced, including beams, plates, pipelines, axially moving structures, rotor systems, multi-layered structures, smart structures, composite laminated structures, periodic lattice structures, blood flow, structural boundaries, joints, structural damage, and impact forces identifications, as well as the SEM-FEM hybrid method. Presents all aspects of SEM in one volume, both theory and applications Helps students and professionals master associated theories, modeling processes, and analysis methods Demonstrates where and how to apply SEM in practice Introduces real-world examples across a variety of structures Shows how models can be used to evaluate the accuracy of other solution methods Cross-checks against solutions obtained by conventional FEM and other solution methods Comes with downloadable code examples for independent practice Spectral Element Method in Structural Dynamics can be used by graduate students of aeronautical, civil, naval architectures, mechanical, structural and biomechanical engineering. Researchers in universities, technical institutes, and industries will also find the book to be a helpful reference highlighting SEM applications to various engineering problems in areas of structural dynamics, wave propagations, and other related subjects. The book can also be used by students, professors, and researchers who want to learn more efficient and more accurate computational methods useful for their research topics from all areas of engineering, science and mathematics, including the areas of computational mechanics and numerical methods.

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Chongmin Song The Scaled Boundary Finite Element Method. Introduction to Theory and Implementation


An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.

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Wu Shen R. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics


A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element. The authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections: • Fundamentals explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory • Element Technology discusses four-node, three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage • Contact and Constraint Conditions covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions Throughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.

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Jian-Ming Jin The Finite Element Method in Electromagnetics


A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes: A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics The finite element analysis of wave propagation, scattering, and radiation in periodic structures The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystals Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.

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Anastasis C. Polycarpou Introduction to the Finite Element Method in Electromagnetics

А. В. Ермакова Метод дополнительных конечных элементов для расчета железобетонных конструкций по предельным состояниям


The work presents the theoretical basis of Additional Finite Element Method (AFEM), which is a variant of the Finite Element Method (FEM) for analysis of reinforced concrete structures at limit state. AFEM adds to the traditional sequence of problem by FEM the units of the two well-known methods of the structural design: method of additional loads and limit state method. The problem is solved by introduction of ideal failure models and additional design diagrams formed from additional finite elements, where each AFE describes the limit state reached by the main element. The main relations defining the properties of AFEs as well as the examples of the use of Additional Finite Element Method for analysis of reinforced concrete structures at limit state are given in the work too.

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Francis Castanié Spectral Analysis


This book deals with these parametric methods, first discussing those based on time series models, Capon’s method and its variants, and then estimators based on the notions of sub-spaces. However, the book also deals with the traditional “analog” methods, now called non-parametric methods, which are still the most widely used in practical spectral analysis.

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Группа авторов A Practical Guide to Reliable Finite Element Modelling


Many books have been written about the finite element method; little however has been written about procedures that assist a practicing engineer in undertaking an analysis in such a way that errors and uncertainties can be controlled. In A Practical Guide to Reliable Finite Element Modelling, Morris addresses this important area. His book begins by introducing the reader to finite element analysis (FEA), covering the fundamental principles of the method, whilst also outlining the potential problems involved. He then establishes consistent methods for carrying out analyses and obtaining accurate and reliable results, concluding with a new method for undertaking error control led analyses which is illustrated by means of two case studies. The book addresses a number of topics that: • Systematically cover an introduction to FEA, how computers build linear-static and linear-dynamic finite element models, the identification of error sources, error control methods and error-controlled analyses. • Enable the reader to support the design of complex structures with reliable, repeatable analyses using the finite element method. • Provide a basis for establishing good practice that could underpin a legal defence in the event of a claim for negligence. A Practical Guide to Reliable Finite Element Modelling will appeal to practising engineers engaged in conducting regular finite element analyses, particularly those new to the field. It will also be a resource for postgraduate students and researchers addressing problems associated with errors in the finite element method. This book is supported by an author maintained website at http://www.femec.co.uk

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Emmanuel Lefrançois Finite Element Method


This book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences. The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus. The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.

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Guido Dhondt The Finite Element Method for Three-Dimensional Thermomechanical Applications


Though many 'finite element' books exist, this book provides a unique focus on developing the method for three-dimensional, industrial problems. This is significant as many methods which work well for small applications fail for large scale problems, which generally: are not so well posed introduce stringent computer time conditions require robust solution techniques. Starting from sound continuum mechanics principles, derivation in this book focuses only on proven methods. Coverage of all different aspects of linear and nonlinear thermal mechanical problems in solids are described, thereby avoiding distracting the reader with extraneous solutions paths. Emphasis is put on consistent representation and includes the examination of topics which are not frequently found in other texts, such as cyclic symmetry, rigid body motion and nonlinear multiple point constraints. Advanced material formulations include anisotropic hyperelasticity, large strain multiplicative viscoplasticity and single crystal viscoplasticity. Finally, the methods described in the book are implemented in the finite element software CalculiX, which is freely available (www.calculix.de; the GNU General Public License applies). Suited to industry practitioners and academic researchers alike, The Finite Element Method for Three-Dimensional Thermomechanical Applications expertly bridges the gap between continuum mechanics and the finite element method.

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Spectral Element Method in Structural Dynamics: Lee, Usik ...

Spectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields. The book consists of three key sections. In the first part, background knowledge is set up for the readers by reviewing previous work in the area and by providing the ...

Wiley: Spectral Element Method in Structural Dynamics ...

Usik Lee. ISBN: 978-0-470-82374-3. 480 pages. October 2009. Read an Excerpt . Description. Spectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields. The book consists of three key sections. In the first part, background knowledge is ...

Spectral Element Method in Structural Dynamics | Wiley ...

Usik Lee is a Professor of Mechanical Engineering at Inha University. He has 22 years teaching, research, and industry experience in the area of structural dynamics, and over 12 years of experience in developing and teaching spectral element methods. He has published over 100 papers in international journals and is an Associate Fellow of ...

[PDF] Spectral Element Method in Structural Dynamics ...

DOI: 10.1002/9780470823767 Corpus ID: 15665389. Spectral Element Method in Structural Dynamics @inproceedings{Lee2009SpectralEM, title={Spectral Element Method in Structural Dynamics}, author={U. Lee}, year={2009} }

Determination of Nonideal Beam Boundary Conditions: A ...

Usik Lee . Inha University, Inchon 402-751, Republic of Korea. Search for more papers by this author ... Spectral element modeling for the beams treated with active constrained layer damping. International Journal of Solids and Structures, Vol. 38, No. 32-33. Modal analysis of the passive constrained layer beams based on spectrally formulated exact normal modes . Joohong Kim and Usik Lee; 22 ...

Frequency Domain Spectral Element Model for the Vibration ...

We propose a new spectral element model for finite rectangular plate elements with arbitrary boundary conditions. The new spectral element model is developed by modifying the boundary splitting method used in our previous study so that the four corner nodes of a finite rectangular plate element become active. Thus, the new spectral element model can be applied to any finite rectangular plate ...

Mixed Mimetic Spectral Elements for Atmospheric Simulation

Dave Lee Mixed Mimetic Spectral Elements for Atmospheric Simulation. Important references: Energy and Enstrphy conserving nite di erences I Sadourny, J. Atmos. Sci., 1975 I Arakara and Lamb, Monthly Weather Review, 1981 Fintie di erence Poisson brackets I Salmon, J. Atmos. Sci, 2004, 2007 Unstructured nite volumes I Thuburn, Ringler, Skamarock, Klemp. J. Comput. Phys. 2009 I Ringler, Thuburn ...

Spectral (Film) – Wikipedia

Musik: Junkie XL: Kamera: Bojan Bazelli: Schnitt: Jason Ballantine: Besetzung; Synchronisation; Spectral ist ein US-amerikanischer Military-Science-Fiction-Spielfilm des Regisseurs Nic Mathieu. Der von Legendary Pictures produzierte Film wurde am 9. Dezember 2016 auf Netflix veröffentlicht. Handlung. In einer von Krieg zerstörten Stadt wird eine Einheit der Delta Forces von einer ...

Visible Spectra of the Elements - umop

Visible Spectra of the Elements If the emission lines of the chemical elements were observed through a diffraction grating, they would probably look something like this: Periodic table format Interactive Format This image is based on spectrum line positions and intensities from MIT Wavelength Tables and the NIST Atomic Spectrum Database. A few spectra (neon, for instance) have had corrections ...

Atomic spectra - ITP

Atomic spectra Light emitted or absorbed by single atoms contributes only very little to the colours of our surroundings. Neon signs (or other gas discharge tubes) as used for advertising, sodium or mercury vapour lamps show atomic emission; the colours of fireworks are due to it. The aurora borealis (northern light) is very rare at our latitudes, and to appreciate the colours of cosmic ...

Spectral Element | Scientific.Net

Authors: Sung Jun You, In Joon Jang, Usik Lee Abstract: This paper develops a spectral element model for elastic-elastic two-layered beams. First, the axial-bending coupled equations of motion for an elastic two-layer laminated beam are derived. The spectral element model is then formulated by using the wave solutions satisfying governing equations in frequency-domain as the frequency ...

Research Article Frequency Domain Spectral Element Model ...

Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions IlwookPark,TaehyunKim,andUsikLee Department of Mechanical Engineering, Inha University, Inha-ro, Nam-gu, Incheon- , Republic of Korea Correspondence should be addressed to Usik Lee; ulee@inha.ac.kr

Spectral element method in structural dynamics - CityU ...

Spectral element method in structural dynamics. / Lee, Usik; Kim, Joohong; Leung, Andrew Y. T. In: Shock and Vibration Digest, Vol. 32, No. 6, 11.2000, p. 451-465 ...

Elementary - US-Serie - SAT.1

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Spectral element method: application to structural damage ...

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Atomic Spectroscopy Databases | NIST

Atomic Spectra Database - Version 5 A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team This database contains critically evaluated NIST data for radiative transitions and energy levels in atoms and atomic ions. Data are included for observed transitions of 99 elements and energy levels of 89 elements. ASD contains data on more than 1000 ...

Spectral Element Method (SEM) | Scientific.Net

Abstract: Spectral element method (SEM), ... Authors: Usik Lee, In Joon Jang, Il Wook Park Abstract: This paper presents a spectral element model for the spinning uniform shaft represented by the Timoshenko beam model. The bearing-supports are represented by equivalent springs. The variational approach is used to formulate the spectral element model from the frequency-dependent shape functions ...

Mixed Mimetic Spectral Elements for Geophysical Fluid Dynamics

Lee; LA-UR-17-24044 Mixed Mimetic Spectral Elements. Application to spectral elements I The standard (0 form) spectral element basis is given as f0(˘) = a0 i l i(˘) I Start from the premise that in 1D we wish to exactly satisfy the fundamental th. of calculus between nodes ˘ i and ˘ i+1: Z ˘ i+1 ˘i df0(˘) = f0(˘ i +1) f0(˘ i) = a0 i a 0 = b1 = Z ˘ i+1 ˘i g1(˘) I The corresponding 1 ...

Vibration Analysis of Thin Plate Structures Subjected to a ...

In, the spectral element model for a rectangular finite plate element was developed based on the Kantorovich-based finite strip element method where the rectangular finite plate element was divided into Nζfinite strip elements in the direction of coordinate ζand Nηfinite strip elements in the direction of coordinate η.

Spectral Element Method in Structural Dynamics: Amazon.co ...

Buy Spectral Element Method in Structural Dynamics by Usik Lee (ISBN: 9780470823743) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

AN INTRODUCTION TO SPECTRAL MUSIC was writing pieces starkly

AN INTRODUCTION TO SPECTRAL MUSIC In the early 1970s, a group of young French composers1 was writing pieces starkly different from the music of most of their contemporaries. The music of the young French composers was based on slow harmonic development, and was devoid of a prominent melody or a strong sense of pulse. The music was not, however, lacking in either focus or coherence. These ...

Dynamics of Rotor Systems - Spectral Element Method in ...

Summary This chapter contains sections titled: Governing Equations Spectral Element Modeling Finite Element Model Numerical Examples Appendix 8.A: Finite Element Matrices for the Transverse Bending...

Exact spectral element model for rectangular membranes ...

This study proposes an exact frequency-domain spectral element model for a rectangular membrane subjected to arbitrary boundary conditions. The frequency-domain general solution of a finite rectangular membrane element is first assumed in the trigonometric Fourier series with the spatial coordinates x and y.After all the trigonometric Fourier series terms that vanish at the four boundary edges ...

CiteSeerX — Spectral Element Analysis of the Continuum ...

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this paper, an FFT-based spectral element method (SEM) is introduced for the linear continuum dynamic systems subjected to arbitrary, non-zero initial conditions. In the FFT-based SEM, the original equations of motion subjected to arbitrary initial conditions are transformed into a new set of equations of motion ...

Equivalent continuum representation of lattice beams ...

Motivated from the inherent accuracy of spectral elements, a new dynamic continuum modeling method is introduced, in which the spectral elements are utilized to transform a large periodic lattice beam into a structurally equivalent continuum beam model. The present continuum modeling method involves the derivation of the transfer matrices for both a representative lattice cell of original ...

CiteSeerX — Spectral Element Model of a Spinning ...

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): A spectral element model for the spinning shafts with thick rigid disks is developed. The spinning shafts supported by bearings are represented by the uniform Timoshenko shaft models and the disks are considered to be wobbling about their centers. The bearings are represented by two translational springs and two ...

Static and Dynamic Interfacial Stresses Analysis for Three ...

(2014). Static and Dynamic Interfacial Stresses Analysis for Three-Layer Beam Structures Using Spectral Element Method. The Journal of Adhesion: Vol. 90, No. 7, pp. 618-648. doi: 10.1080/00218464.2013.827571

Spectral element methods : theory and applications

Spectral Element Methods: Theoryand Applications / F.N. van de Vosse andP.D. Minev. - Eindhoven: Eindhoven University of Technology, 1996. - 117 p. - (Eindhoven Univer­ sity of Technology Research Reports, ISSN 0167-9708, EUT Report 96-W-00l).- ISBN 90-386-0318-5 Abstract Some mathematical aspects offinite and spectral element discretizations for partial differ­ ential equations are ...

Spectral Elements - geophysik.uni-muenchen.de

Spectral element method 23 Spectral elements: summary ¾Spectral elements (SE) are a special form of the finite element method. ¾The key difference is the choice of the basis (form) functions inside the elements, with which the fields are described. ¾ It is the Lagrange polynomials with Gauss-Lobato-Legendre (GLL) collocation points that make the mass matrix diagonal ¾This leads to a fully ...

Spectral method - Wikipedia

Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the fast Fourier transform.The idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and then to choose the ...

Exact spectral element model for rectangular membranes ...

Article “Exact spectral element model for rectangular membranes subjected to transverse vibrations” Detailed information of the J-GLOBAL is a service based on the concept of Linking, Expanding, and Sparking, linking science and technology information which hitherto stood alone to support the generation of ideas. By linking the information entered, we provide opportunities to make ...

Talk:Spectral element method - Wikipedia

According to Lee (Spectral Element Method in Structural Dynamics, 2009, p. 6), spectral element method in a form that is presented by Patera 1984, is only a class of finite element method. In the spectral element method, as it is understood currently, the idea is to formulate problem in a frequency domain, solve it, and then transform it into time domain using inverse of FFT. In the current ...

The dynamic analysis of a cracked Timoshenko beam by the ...

The aim of this paper is to introduce a new finite spectral element of a cracked Timoshenko beam for modal and elastic wave propagation analysis. The proposed approach deals with the spectral element method. This method is suitable for analyzing wave propagation problems as well as for calculating modal parameters of the structure. In the paper, the results of the change in modal parameters ...

Trace Metal Analysis - SPECTROLAB | SPECTRO Analytical

For metal analysis, the SPECTROLAB OES is the leading metal analyzer across the global metals industry. Find out more about its ultimate performance.

spectral elements - arXiv

Email address: drlee@lanl.gov (D. Lee) Preprint submitted to Journal of Computational Physics January 12, 2018 arXiv:1707.00346v3 [math.NA] 11 Jan 2018. The present study explores the use of spectral elements using mixed basis functions in order to preserve mimetic properties for geophysical flows. These recently developed methods invoke the use of histopolation functions [11], which are ...

Spectral Elements - YouTube

Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.

Dynamics of an axially moving Bernoulli-Euler beam ...

The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model for an axially moving Bernoulli-Euler beam subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model is then verified ...

Spectral Element Methods | SpringerLink

Spectral element methods are introduced for one space dimension then generalized to two. Benchmark solutions include steady temperatures in a long cylindrical rod, propagation of a circular sound wave in a disk, and transmission and reflection of a plane wave at a material interface. Keywords Element Boundary Single Domain Spectral Element Spectral Element Method Riemann Solver These keywords ...

The Spectral-Element Method: Introduction

Spectral elements in spherical coordinates by Fichtner et al. (2009) Community code "specfem" widely used for simulaton and inversion (e.g., Peter et al. 2011). After 2017 Salvus revolutionizes computational seismology Computational Seismology 4 / 59. Introduction History Originated in fluid dynamics (Patera, 1984, Maday and Patera, 1989) First applications to seismic wave propagation by ...

Read Spectral Element Method in Structural Dynamics Online ...

Read Spectral Element Method in Structural Dynamics by Usik Lee for free with a 30 day free trial. Read unlimited* books and audiobooks on the web, iPad, iPhone and Android. Spectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields ...

Spektralmethode – Wikipedia

In der numerischen Mathematik ist die Spektralmethode ein Verfahren zur Lösung von partiellen Differentialgleichungen, wie den Navier-Stokes Gleichungen, mittels globaler Ansatzfunktionen.Ansatzfunktionen können z. B. Fourierreihen oder Tschebyscheff-Polynome sein. Im Laufe eines numerischen Lösungsverfahrens wird die physikalische Repräsentation eines Problems in den Spektralbereich ...

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Группа авторов The Finite Element Method


A comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines. Written by a renowned author and academician with the Chinese Academy of Engineering, The Finite Element Method would appeal to researchers looking to understand how the fundamentals of the FEM can be applied in other disciplines. Researchers and graduate students studying hydraulic, mechanical and civil engineering will find it a practical reference text.

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I. Smith M. Programming the Finite Element Method


This title demonstrates how to develop computer programmes which solve specific engineering problems using the finite element method. It enables students, scientists and engineers to assemble their own computer programmes to produce numerical results to solve these problems. The first three editions of Programming the Finite Element Method established themselves as an authority in this area. This fully revised 4th edition includes completely rewritten programmes with a unique description and list of parallel versions of programmes in Fortran 90. The Fortran programmes and subroutines described in the text will be made available on the Internet via anonymous ftp, further adding to the value of this title.

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Jaakko Astola T. Spectral Logic and Its Applications for the Design of Digital Devices


Spectral techniques facilitate the design and testing of today's increasingly complex digital devices There is heightened interest in spectral techniques for the design of digital devices dictated by ever increasing demands on technology that often cannot be met by classical approaches. Spectral methods provide a uniform and consistent theoretic environment for recent achievements in this area, which appear divergent in many other approaches. Spectral Logic and Its Applications for the Design of Digital Devices gives readers a foundation for further exploration of abstract harmonic analysis over finite groups in the analysis, design, and testing of digital devices. After an introduction, this book provides the essential mathematical background for discussing spectral methods. It then delves into spectral logic and its applications, covering: * Walsh, Haar, arithmetic transform, Reed-Muller transform for binary-valued functions and Vilenkin-Chrestenson transform, generalized Haar, and other related transforms for multiple-valued functions * Polynomial expressions and decision diagram representations for switching and multiple-value functions * Spectral analysis of Boolean functions * Spectral synthesis and optimization of combinational and sequential devices * Spectral methods in analysis and synthesis of reliable devices * Spectral techniques for testing computer hardware This is the authoritative reference for computer science and engineering professionals and researchers with an interest in spectral methods of representing discrete functions and related applications in the design and testing of digital devices. It is also an excellent text for graduate students in courses covering spectral logic and its applications.

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Группа авторов Partial Differential Equations and the Finite Element Method


A systematic introduction to partial differential equations and modern finite element methods for their efficient numerical solution Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM. A solid introduction to the theory of PDEs and FEM contained in Chapters 1-4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations. The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM. Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science. Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists.

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Wieslaw Ostachowicz Guided Waves in Structures for SHM


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