FEM-notes-refs.bib

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@ARTICLE{aberg1997,
  author = {M. Aberg and P. Gudmundson},
  title = {{T}he usage of standard finite element codes for computation of dispersion
	relations in materials with periodic microstructure},
  journal = {Journal of the Acoustical Society of America},
  year = {1997},
  volume = {102},
  pages = {2007-2013},
  abstract = {A method with which standard finite element programs can be used to
	compute dispersion relations in periodic composites is proposed.
	The method is applied to two composite microstructures: a two-phase
	laminate and a fiber composite. The dispersion relations computed
	for the laminate are compared with a known analytical solution and
	the agreement is very good. The dispersion relations computed for
	the fibrous composite are compared with an existing approximate model
	and experimental results from the literature. The agreement between
	the approximate model, the experiments, and the computations is very
	good in the wave guide case and satisfactory for the wave reflect
	case.},
  keywords = {Abaqus, Finite Element, Periodic Materials, Real formulation, Homogenization},
  owner = {Nico},
  timestamp = {2012.04.04}
}

@BOOK{book:achenbach_waves,
  title = {{W}ave {P}ropagation in {E}lastic {S}olids},
  publisher = {North Holland Publishing Company},
  year = {1973},
  author = {J.D. Achenbach},
  pages = {425},
  keywords = {Elastodynamics, Wave Propagation, Continuum Mechanics},
  owner = {nguarinz},
  timestamp = {2011.11.28}
}

@BOOK{book:arfken,
  title = {{M}athematical {M}ethods for {P}hysicists},
  publisher = {Academic Press},
  year = {2005},
  author = {George B. Arfken and Hans J. Weber and Frank Harris},
  pages = {1200},
  edition = {6},
  keywords = {Mathematical Physics, Theoretical Physics},
  owner = {nguarinz},
  review = {Mathematical Methods For Physicists provides aspiring engineers and
	scientists with key insights into mathematical concepts that they
	may need to understand as elementary researchers and students. The
	authors have ensured that the first chapter covers all the vital
	concepts needed by the readers to understand the latter chapters.
	This seventh edition consists of mathematical relations and proofs
	that are of great importance in the field of Physics},
  timestamp = {2011.11.28}
}

@BOOK{book:BEMBanerjee,
  title = {{T}he {B}oundary {E}lement {M}ethods in {E}ngineering},
  publisher = {Mcgraw-Hill College},
  year = {1994},
  author = {Banerjee, Prasanta Kumar},
  pages = {496},
  edition = {2},
  month = {1},
  comment = {ISBN-10: 0077077695 ISBN-13: 978-0077077693},
  keywords = {Boundary Element Method, BEM, IBEM, Computational Mechanics},
  owner = {nguarinz},
  review = {The last two decades have seen the emergence of a versatile and powerful
	method of computational engineering mechanics, namely the boundary
	element method. This book which incorporates the massive development
	of the BEM technology that has occurred in the last decade, describes
	the formulation of boundary element methods for almost all applications
	of the method. For ease of use, a simple utilitarian and tutorial
	approach is adopted in the initial chapters, introducing the basic
	background needed to learn the method. Simple but detailed instructions
	for its application to heat transfer and stress analyses are then
	dealt with, before moving on to more complex formulations in the
	later chapters. Fully supported by numerous case studies, this is
	a comprehensive guide to the subject.},
  timestamp = {2011.02.11}
}

@BOOK{book:bathe,
  title = {{F}inite {E}lement {P}rocedures},
  publisher = {Prentice Hall},
  year = {1995},
  author = {Klaus-Jurgen Bathe},
  pages = {1037},
  edition = {2},
  month = {6},
  comment = {ISBN-10: 0133014584 ISBN-13: 978-0133014587},
  keywords = {Finite Element Method, FEM, Numerical Analysis, Computational Mechanics},
  owner = {nguarin},
  review = {For courses in finite element methods, finite element analysis taught
	in departments of Civil, Mechanical, Aerospace, Agriculture, and
	Mechanics departments. Course for which this book is appropriate
	is usually taught to seniors or graduate students.Comprehensive --
	this text explores the full range of finite element methods used
	in engineering practice for actual applications in computer-aided
	design. It provides not only an introduction to finite element methods
	and the commonality in the various techniques, but explores state-of-the-art
	methods as well -- with a focus on what are deemed to become "classical
	techniques" -- procedures that will be standard and authoritative
	for finite element analysis for years to come.},
  timestamp = {2011.02.12}
}

@BOOK{book:brillouin2003,
  title = {Wave propagation in periodic structures: electric filters and crystal
	lattices},
  publisher = {Courier Dover Publications},
  year = {2003},
  author = {Brillouin, L{\'e}on},
  owner = {nguarin},
  timestamp = {2014.04.03}
}

@BOOK{book:burden-analisis,
  title = {{A}n\'alisis {N}um\'erico},
  publisher = {Thomson Learning},
  year = {2002},
  author = {Richard Burden and Douglas Faires},
  pages = {839},
  edition = {7},
  owner = {Nico},
  timestamp = {2012.04.21}
}

@BOOK{book:burden2011,
  title = {Numerical Analysis},
  publisher = {Brooks/Cole},
  year = {2011},
  author = {Burden, R.L. and Faires, J.D.},
  edition = {9},
  institution = {ISBN 978-0-5387335-1-9},
  owner = {nguarinz},
  review = {This well-respected text gives an introduction to the theory and application
	of modern numerical approximation techniques for students taking
	a one- or two-semester course in numerical analysis. With an accessible
	treatment that only requires a calculus prerequisite, Burden and
	Faires explain how, why, and when approximation techniques can be
	expected to work, and why, in some situations, they fail. A wealth
	of examples and exercises develop students' intuition, and demonstrate
	the subject's practical applications to important everyday problems
	in math, computing, engineering, and physical science disciplines.
	The first book of its kind built from the ground up to serve a diverse
	undergraduate audience, three decades later Burden and Faires remains
	the definitive introduction to a vital and practical subject.},
  timestamp = {2012.11.27}
}

@INPROCEEDINGS{clough1999early,
  author = {Clough, Ray W and Wilson, Edward L},
  title = {Early finite element research at Berkeley},
  booktitle = {Fifth US National Conference on Computational Mechanics},
  year = {1999},
  abstract = {ignificant finite element research was conducted at the University
	of California at Berkeley during the period 1957 to 1970. The initial
	research was a direct extension of classical methods of structural
	analysis which previously had been restricted to one-dimensional
	elements. The majority of the research conducted was motivated by
	the need to solve practical problems in Aerospace, Mechanical and
	Civil Engineering. During this short period the finite element method
	was extended to the solution of linear and nonlinear problems associated
	with creep, incremental construction or excavation, crack closing,
	heat transfer, flow of water in porous media, soil consolidation,
	dynamic response analysis and computer assisted learning of structural
	analysis. During the last six years of this period the fields of
	structural analysis and continuum mechanics were unified. The computer
	programs developed during this early period at Berkeley were freely
	distributed worldwide allowing practicing engineers to solve many
	new problems in structural mechanics. Hence, the research was rapidly
	transferred to the engineering profession. In many cases the research
	was used professionally prior to the publication of a formal paper},
  owner = {nicoguaro},
  timestamp = {2015.01.15},
  url = {http://www.ce.memphis.edu/7111/notes/class_notes/papers/fe-history.pdf}
}

@ARTICLE{courant43,
  author = {Courant, Richard},
  title = {Variational methods for the solution of problems of equilibrium and
	vibrations},
  journal = {Bull. Amer. Math. Soc},
  year = {1943},
  volume = {49},
  pages = {1--23},
  number = {1},
  owner = {nicoguaro},
  timestamp = {2015.01.15},
  url = {http://mmph.narod.ru/doc/Courant.pdf}
}

@MANUAL{Calculix_manual,
  title = {CalculiX CrunchiX User’s Manual, version 2.7},
  author = {Guido Dhondt},
  year = {2014},
  owner = {nguarin},
  timestamp = {2015.06.11}
}

@ARTICLE{gander2012euler,
  author = {Gander, Martin J and Wanner, Gerhard},
  title = {From Euler, Ritz, and Galerkin to Modern Computing.},
  journal = {SIAM Review},
  year = {2012},
  volume = {54},
  pages = {627--666},
  number = {4},
  abstract = {The so-called Ritz--Galerkin method is one of the most fundamental
	tools of modern computing. Its origins lie in Hilbert's “direct”
	approach to the variational calculus of Euler--Lagrange and in the
	thesis of Walther Ritz, who died 100 years ago at the age of 31 after
	a long battle with tuberculosis. The thesis was submitted in 1902
	in Göttingen, during a period of dramatic developments in physics.
	Ritz tried to explain the phenomenon of Balmer series in spectroscopy
	using eigenvalue problems of partial differential equations on rectangular
	domains. While this physical model quickly turned out to be completely
	obsolete, his mathematics later enabled him to solve difficult problems
	in applied sciences. He thereby revolutionized the variational calculus
	and became one of the fathers of modern computational mathematics.
	We will see in this article that the path leading to modern computational
	methods and theory involved a long struggle over three centuries
	requiring the efforts of many great mathematicians.},
  doi = {10.1137/100804036},
  owner = {nicoguaro},
  publisher = {Citeseer},
  timestamp = {2015.01.15},
  url = {http://www.unige.ch/~gander/Preprints/Ritz.pdf}
}

@MANUAL{gmsh_manual,
  title = {Gmsh Reference Manual. Gmsh 2.9: A Three-Dimensional Finite Element
	Mesh Generator With Built-in Pre-and Post-Processing Facilities},
  author = {Geuzaine, C and Remacle, J},
  month = {4},
  year = {2015},
  owner = {nguarin},
  timestamp = {2015.06.11},
  url = {http://geuz.org/gmsh/doc/texinfo/gmsh.pdf}
}

@ARTICLE{gmsh2009,
  author = {Geuzaine, Christophe and Remacle, Jean-Fran{\c{c}}ois},
  title = {Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing
	facilities},
  journal = {International Journal for Numerical Methods in Engineering},
  year = {2009},
  volume = {79},
  pages = {1309--1331},
  number = {11},
  abstract = {Gmsh is an open-source 3-D finite element grid generator with a build-in
	CAD engine and post-processor. Its design goal is to provide a fast,
	light and user-friendly meshing tool with parametric input and advanced
	visualization capabilities. This paper presents the overall philosophy,
	the main design choices and some of the original algorithms implemented
	in Gmsh.},
  doi = {10.1002/nme.2579},
  keywords = {computer-aided design; mesh generation; post-processing; finite element
	method; open-source software},
  owner = {nguarin},
  publisher = {Wiley Online Library},
  timestamp = {2015.06.11},
  url = {http://geuz.org/gmsh/doc/preprints/gmsh_paper_preprint.pdf}
}

@BOOK{book:PDE_gockenbach,
  title = {{P}artial {D}ifferential {E}quations: {A}nalytical and {N}umerical
	{M}ethods},
  publisher = {SIAM},
  year = {2002},
  author = {Mark S. Gockenbach},
  owner = {nguarinz},
  timestamp = {2012.03.27}
}

@MASTERSTHESIS{MSc_thesis-Guarin2012,
  author = {Nicol\'as Guar\'in-Zapata},
  title = {{S}imulaci\'on {N}um\'erica de {P}roblemas de {P}ropagaci\'on de
	{O}ndas: {D}ominios {I}nfinitos y {S}emi-infinitos},
  school = {Universidad EAFIT},
  year = {2012},
  abstract = {Espa\~nol:
	
	Se presenta el desarrollo de dos herramientas computacionales para
	la simulaci\'on de propagaci\'on de ondas en s\'olidos infinitos
	y semi-infinitos. Ambas herramientas est\'an basadas en el M\'etodo
	de los Elementos Finitos (FEM). En una primera parte se presenta
	el acople de FEM con un M\'etodo de Elementos de Frontera (BEM) para
	la soluci\'on del problema de esparcimiento en una heterogeneidad
	en la parte superior de un semi-espacio. Se us\'o un criterio para
	comprimir las matrices de BEM para disminuir los recursos computacinoales
	requeridos y poder tratar problemas de mayor tama\~no.
	
	En la segunda parte se describe la formulaci\'on e implementaci\'on
	de una herramienta de an\'alisis para la propagaci\'on de ondas en
	materiales con heterogeneidades peri\'odicas. \'Esta pretende servir
	para caracterizar las propiedades globales del material cuando por
	\'el se propaga una onda con cierta frecuencia dada. Para esto se
	usaron diversos conceptos de la f\'isica del estado s\'olido y la
	soluci\'on se fundamenta en el teorema de Bloch.
	
	
	English:
	
	We present the development of two computational tools for the simulation
	wave propagation in infinite and semi-infinite solids. Both tools
	are based on the Finite Element Method (FEM). In the first part it
	is shown the couplinf of the FEM with a Boundary Element Method (BEM)
	for the solution of the scattering problem due to heterogeneity in
	the top of a half-space. We used a criterion for the compression
	of the resulting matrices from the BEM to decrease the computational
	costs and could handle bigger problems.
	
	En the second part is is described the formulation and implementation
	of an analysis tool for the wave propagation in periodic heterogeneous
	materials. This is useful to caracterize the bulk properties when
	it is a wave traveling through the material with a particular frequency.
	For this we used diverse concepts from the solid state physics and
	the solution is baes on the Bloch's theorem.},
  keywords = {Wave propagation, Computational elastodynamics, Finite Element Method,
	Boundary element method, Seismic waves, Periodic materials, Waves
	in heterogeneous materials},
  owner = {nguarinz},
  timestamp = {2012.09.29}
}

@MANUAL{Abaqus_manual,
  title = {ABAQUS User’s Manual: Version 6.12},
  author = {Hibbit, Karlsson \& Sorensen},
  year = {2014},
  journal = {Hibbit, Karlsson \& Sorensen},
  owner = {nguarin},
  timestamp = {2015.06.11}
}

@BOOKLET{abaqus_theory,
  title = {ABAQUS theory manual, version 6.3},
  author = {Hibbitt, HD and Karlsson, BI and Sorensen, P},
  year = {2006},
  journal = {Pawtucket, Rhode Island, USA},
  owner = {nguarin},
  timestamp = {2015.03.26}
}

@ARTICLE{hladky-hennion1992,
  author = {Anne-Christine Hladky-Hennion and Jean-No\"el Decarpigny},
  title = {{A}nalysis of the scattering of a plane acoustic wave by a doubly
	periodic structure using the finite element method: {A}pplication
	to {A}lberich anechoic coatings},
  journal = {J. Acoust. Soc. Am},
  year = {1991},
  volume = {90},
  pages = {3356-3367},
  abstract = {The finite element approach has been previously used, with the help
	of the ATILA code, to model the scattering of acoustic waves by single
	periodic structures, such as compliant tube gratings [A. C. Hennion
	et al., J. Acoust. Soc. Am. 87, 1861–1870 (1990)]. In this paper,
	the same approach is extended to doubly periodic structures, such
	as Alberich anechoic coatings. To do this, only the unit cell of
	the periodic structure, including a small part of the surrounding
	fluid domain, has to be meshed, due to the use of classical Bloch
	type relations. Then, the effects of the remaining fluid domain are
	accounted for by matching the pressure field in the finite element
	mesh with simple plane wave expansions of the ingoing and outgoing
	waves. After an outline of the method, the paper describes the results
	obtained for the scattering of a plane wave by different periodic
	structures. Internal losses are taken into account and the incident
	plane wave impinges at normal or oblique incidence. Numerical results
	obtained for Alberich anechoic coatings are first analyzed to check
	the convergence and then compared to previous numerical results or
	to experimental results, demonstrating that the finite element approach
	is accurate and well suited to predict the behavior of these gratings.
	Moreover, careful attention is devoted to the analysis of the inclusion
	vibrations, to identify the origin of the resonance mechanisms.},
  owner = {Nico},
  timestamp = {2012.04.01}
}

@ARTICLE{hrennikoff1941solution,
  author = {Hrennikoff, Alexander},
  title = {Solution of problems of elasticity by the framework method},
  journal = {Journal of applied mechanics},
  year = {1941},
  volume = {8},
  pages = {169--175},
  number = {4},
  owner = {nicoguaro},
  timestamp = {2015.01.15}
}

@TECHREPORT{algebraic_waves,
  author = {Steven G. Johnson},
  title = {{N}otes on the algebraic structure of wave equations},
  institution = {Massachusetts Institute of Technology},
  year = {2010},
  owner = {nguarinz},
  timestamp = {2012.03.28}
}

@BOOK{book:kittel1986,
  title = {Introduction to solid state physics},
  publisher = {Wiley New York},
  year = {1986},
  author = {Kittel, Charles and McEuen, Paul},
  volume = {8},
  owner = {nguarin},
  timestamp = {2014.04.03}
}

@BOOK{book:kreyzsig_functional,
  title = {{I}ntroductory {F}unctional {A}nalysis with {A}pplications},
  publisher = {Wiley},
  year = {1989},
  author = {Erwin Kreyzsig},
  pages = {704},
  edition = {1},
  keywords = {Functional Analysis},
  owner = {nguarinz},
  timestamp = {2011.11.28}
}

@BOOK{book:FEM_Matlab,
  title = {The finite element method using MATLAB},
  publisher = {CRC press},
  year = {2000},
  author = {Kwon, Young W and Bang, Hyochoong},
  owner = {nicoguaro},
  review = {The finite element method (FEM) has become one of the most important
	and useful tools for scientists and engineers. This new book features
	the use of MATLAB to present introductory and advanced finite element
	theories and formulations. MATLAB is especially convenient to write
	and understand finite element analysis programs because a MATLAB
	program manipulates matrices and vectors with ease. The book is suitable
	for introductory and advanced courses in the Finite Element Method,
	as well as a reference for practicing engineers.},
  timestamp = {2015.01.15}
}

@PHDTHESIS{langlet-thesis,
  author = {Philippe Langlet},
  title = {{A}nalyse de la {P}ropagation des {O}ndes {A}coustiques dans les
	{M}ateriaux {P}eriodiques a l'aide de la {M}ethode des {E}lements
	{F}inis},
  school = {L'Universite de Valenciennes et du Hainaut-Cambresis},
  year = {1993},
  abstract = {La propagation d'une onde acoustique plane dans un matériau comportant
	des cavités ou des inclusions rangées périodiquement est susceptible
	de nombreuses applications, notamment dans les domaines de l'acoustique
	sous-marine, du traitement des signaux et de l'acoustique médicale.
	De tels matériaux son utilisés, par exemple, comme revêtements anéchoïques
	de structures immergées, comme lignes à retar ou filtres acoustiques.
	De même, les matériaux piézocomposites interviennent dans la conception
	de nouveaux transducteurs ultrasonores.
	
	Cette thèse concerne la modélisatin par la méthoe des éléments finis,
	à l'aide du code ATILA, de matériaux élastiques ou piézoélectriques,
	périodiques dans une, deux ou trois directions de l'espace. Les développements
	théoriques spécifiques nécessaires à la description de ces matériaux
	sont tout d'abord présentés. Une première validation est réalisée
	à travers quelques résultats obtenus pour matériaux périodiques,
	pour lesquels des formulations analytiques simples existent. Ensuite,
	la technique développée est appliquée à l'étude de la propagation
	des ondes dans les matériaux périodiques poreux ou résultats éléments
	finis obtenus sont comparés avec succès aux résultats de modèles
	antérieurs semi-analytiques et empiriques ou à des résultats expérimentaux.
	Les propiétés homogénéisées de matériaux poreux sont ensuite recherchées
	sur des solides anisotropes, cette procédure d'homogéneisation est
	menée en étudiant les fréquences de résonance de plaques perforées
	périodiquement. Enfin, l'ensemble des résultats conduit à proposer
	une extension de la méthode pur les problèmes couplés fluide-solide
	et pour l'étude des ondes évanescentes dans les bandes interdites.},
  keywords = {Acoustic wave propagation, Periodic Materials, Finite Element Method,
	Effective Properties, Porous Materials, Piezocomposites, Waveguides},
  owner = {Nico},
  timestamp = {2012.03.19}
}

@ARTICLE{leissa2005historical,
  author = {Leissa, Arthur W},
  title = {The historical bases of the Rayleigh and Ritz methods},
  journal = {Journal of Sound and Vibration},
  year = {2005},
  volume = {287},
  pages = {961--978},
  number = {4},
  abstract = {Rayleigh's classical book Theory of Sound was first published in 1877.
	In it are many examples of calculating fundamental natural frequencies
	of free vibration of continuum systems (strings, bars, beams, membranes,
	plates) by assuming the mode shape, and setting the maximum values
	of potential and kinetic energy in a cycle of motion equal to each
	other. This procedure is well known as “Rayleigh's Method.” In 1908,
	Ritz laid out his famous method for determining frequencies and mode
	shapes, choosing multiple admissible displacement functions, and
	minimizing a functional involving both potential and kinetic energies.
	He then demonstrated it in detail in 1909 for the completely free
	square plate. In 1911, Rayleigh wrote a paper congratulating Ritz
	on his work, but stating that he himself had used Ritz's method in
	many places in his book and in another publication. Subsequently,
	hundreds of research articles and many books have appeared which
	use the method, some calling it the “Ritz method” and others the
	“Rayleigh–Ritz method.” The present article examines the method in
	detail, as Ritz presented it, and as Rayleigh claimed to have used
	it. It concludes that, although Rayleigh did solve a few problems
	which involved minimization of a frequency, these solutions were
	not by the straightforward, direct method presented by Ritz and used
	subsequently by others. Therefore, Rayleigh's name should not be
	attached to the method.},
  owner = {nicoguaro},
  publisher = {Elsevier},
  timestamp = {2015.01.15}
}

@ARTICLE{meek96,
  author = {Meek, JL},
  title = {A brief history of the beginning of the finite element method},
  journal = {International journal for numerical methods in engineering},
  year = {1996},
  volume = {39},
  pages = {3761--3774},
  abstract = {This paper presents summaries of the works of several authors associated
	with the invention of the analysis technique now referred to as the
	finite element method. It stresses the notion of first development
	from which subsequent ideas evolved and gives what is believed to
	be an accurate record of the historical sequence of published papers
	in the international literature.},
  doi = {10.1002/(SICI)1097-0207(19961130)39:22<3761::AID-NME22>3.0.CO;2-5},
  keywords = {history; finite elements; structural mechanics},
  owner = {nicoguaro},
  timestamp = {2015.01.15},
  url = {http://people.sc.fsu.edu/~jpeterson/history_fem.pdf}
}

@MANUAL{FEMM_manual,
  title = {Finite Element Method Magnetics: Version 4.2 User's Manual},
  author = {David Meeker},
  year = {2010},
  owner = {nguarin},
  timestamp = {2015.06.11},
  url = {http://www.femm.info/Archives/doc/manual42.pdf}
}

@BOOK{algebra_lineal-poole,
  title = {\'{A}lgebra lineal: una introducci\'on moderna},
  publisher = {Cengage Learning Editores},
  year = {2007},
  author = {David Poole},
  pages = {712},
  edition = {2},
  note = {ISBN 9706865950},
  owner = {Nico},
  timestamp = {2012.04.05}
}

@BOOK{book:FEM_SEM,
  title = {{I}ntroduction to {F}inite and {S}pectral {E}lement {M}ethods using
	{M}atlab ({R})},
  publisher = {Chapman \& Hall\&CRC},
  year = {2005},
  author = {C. Pozrikidis},
  pages = {653},
  edition = {1},
  keywords = {Finite Element Method, Spectral Element Method, Matlab},
  owner = {nguarinz},
  review = {[This book] approaches the matter from the more practical side. …
	It gives a broad, digestible introduction into what everybody wishing
	to write an FE code needs to know. …This is a hands-on book in that
	it presupposes the reader to work the examples in MATLAB, for which
	a primer is provided. The actual work is greatly facilitated by the
	possibility to freely download software … -Monatshefte fur Mathematik,
	2007},
  timestamp = {2011.11.28}
}

@BOOK{book:numerical_recipes,
  title = {Numerical recipes 3rd edition: The art of scientific computing},
  publisher = {Cambridge university press},
  year = {2007},
  author = {Press, William H},
  owner = {nguarin},
  timestamp = {2015.03.26}
}

@BOOK{book:reddy_intro_FEM,
  title = {{A}n {I}ntroduction to the {F}inite {E}lement {M}ethod},
  publisher = {McGraw-Hill},
  year = {2005},
  author = {J.N. Reddy},
  pages = {912},
  edition = {3},
  keywords = {Finite Element Method, Numerical Methods},
  owner = {nguarinz},
  review = {J.N. Reddy's, An Introduction to the Finite Element Method, third
	edition is an update of one of the most popular FEM textbooks available.
	The book retains its strong conceptual approach, clearly examining
	the mathematical underpinnings of FEM, and providing a general approach
	of engineering application areas.
	
	Known for its detailed, carefully selected example problems and extensive
	selection of homework problems, the author has comprehensively covered
	a wide range of engineering areas making the book approriate for
	all engineering majors, and underscores the wide range of use FEM
	has in the professional world.
	
	A supplementary text Web site located at http://www.mhhe.com/reddy3e
	contains password-protected solutions to end-of-chapter problems,
	general textbook information, supplementary chapters on the FEM1D
	and FEM2D computer programs, and more!},
  timestamp = {2011.11.28}
}

@BOOK{book:reddy_functional_analysis,
  title = {{A}pplied {F}unctional {A}nalysis and {V}ariational {M}ethods in
	{E}ngineering},
  publisher = {Krieger Publishing},
  year = {1991},
  author = {J.N. Reddy},
  pages = {546},
  edition = {1},
  keywords = {Variational Method, Functional Analysis, Analytical Mechanics},
  owner = {nguarinz},
  timestamp = {2011.11.28}
}

@ARTICLE{ritz1909,
  author = {Ritz, Walter},
  title = {{\"U}ber eine neue Methode zur L{\"o}sung gewisser Variationsprobleme
	der mathematischen Physik.},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  year = {1909},
  volume = {135},
  pages = {1--61},
  abstract = {Die Randwertaufgaben der mathematischen Physik erfordern durchweg
	die Darstellung endlicher, stetiger Funktionen in vorgeschriebenen
	endlichen Bereichen. Nur ausnahmsweise gelingt hier eine Entwicklung
	nach Potenzreihen , und noch seltener ist dieselbe im ganzen Bereich
	numerisch brauchbar . Endlich scheitert , selbst in F\''allen , wo
	die Entwicklung prinzipiell möglich w\''are , ihre Berechnung h\''aufig
	an dem Umstand , dass sie die Lösung unendlich vieler linearen Gleichungen
	mit unendlich vielen bekannten erfordert. Sehr viel besser eignen
	sich Entwicklungen nach Polynomen, Fouriersche Reihen usw . f\''ur
	die Darstellung einer reellen Funktion w(x , y,..) in einem gegebenen
	Bereich, da hier f\''ur die Konvergenz im ganzen Bereich nur Eigenschaften
	der Stetigkeit usw . gefordert werden, die bei den Randwertaufgaben
	meist erf\''ullt sind . Bei numerisch gegebenem l\''u bietet die
	Bestimmung der Koeffizienten eines Polynoms #w_n= a_0 + a_1 x + \cdots
	$ von gegebenem Grade $n$ derart, dass w als Approximation von $w$
	gelten könne, keinerlei Schwierigkeit, und es kann die Genauigkeit
	bei gen\''ugend grossem n unbegrenzt gesteigert werden. Ist aber
	w als Integral einer Differentialgleichung , unter gewissen Nebenbedingungen,
	definiert , so gelingt die Berechnung der Koeffizienten a, zun\''achst
	nur in dem sehr speziellen Fall, wo eine Integration durch rasch
	konvergente Potenzreihen möglich ist Es erhebt sich die Forderung,
	die angen\''aherte Darstellung des Integrals im ganzen vorgeschriebenen
	Bereich durch ein Polynom von gegebenem Grade n buch in diesem Falle
	allgemein durchzuf\''uhren, in der Art, dass bei wachsendem n die
	Genauigkeit unbegrenzt wachsen, so dass schliesslich eine Entwicklung
	des Integrals Polynomen resultiert.},
  owner = {nicoguaro},
  timestamp = {2015.01.15}
}

@BOOK{book:sepulveda_fismat,
  title = {{F}ísica {M}atemática},
  publisher = {Editorial Universidad de Antioquia},
  year = {2009},
  author = {Alonso Sep\'ulveda},
  pages = {406},
  edition = {1},
  keywords = {Mathematical Physics, Theoretical Physics},
  owner = {nguarinz},
  timestamp = {2011.11.28}
}

@BOOK{shames1997elastic,
  title = {Elastic and inelastic stress analysis},
  publisher = {CRC Press},
  year = {1997},
  author = {Shames, Irving H},
  owner = {eafit},
  timestamp = {2015.08.11}
}

@ARTICLE{sukumar_bloch-2009,
  author = {N. Sukumar and J. E. Pask},
  title = {{C}lassical and enriched {F}inite element formulations for {B}loch-periodic
	boundary conditions},
  journal = {International Journal of Numerical Methods in Engineering},
  year = {2009},
  volume = {77},
  pages = {1121–1138},
  number = {8},
  month = {2},
  abstract = {In this paper, classical and enriched Finite element formulations
	to impose Bloch-periodic boundary conditions are proposed. Bloch-periodic
	boundary conditions arise in the description of wave-like phenomena
	in periodic media. We consider the quantum-mechanical problem in
	a crystalline solid, and derive the weak formulation and matrix equations
	for the SchrÄodinger and Poisson equations in a parallelepiped unit
	cell under Bloch-periodic and periodic boundary conditions, respectively.
	For such second-order problems, these conditions consist of value-
	and derivative-periodic parts. The value-periodic part is enforced
	as an essential boundary condition by construction of a value-periodic
	basis, whereas the derivative-periodic part is enforced as a natural
	boundary condition in the weak formulation. We show that the resulting
	matrix equations can be obtained by suitably specifying the connectivity
	of element matrices in the assembly of the global matrices or by
	modifying the Neumann matrices via row and column operations. The
	implementation and accuracy of the new formulation is demonstrated
	via numerical examples for the three-dimensional Poisson and Schrodinger
	equations using classical and enriched (partition-of-unity) higher-order
	Funite elements.},
  owner = {nguarinz},
  timestamp = {2012.03.29}
}

@MANUAL{feap_manual,
  title = {FEAP--A Finite Element Analysis Program, Version 8.4 User Manual},
  author = {Taylor, RL},
  year = {2013},
  journal = {University of California at Berkeley, Berkeley, CA},
  owner = {nguarin},
  timestamp = {2015.06.11}
}

@MISC{wiki:calculus_of_variations,
  author = {Wikipedia},
  title = {Calculus of variations --- Wikipedia{,} The Free Encyclopedia},
  year = {2015},
  note = {[Online; accessed 30-May-2015]},
  owner = {nguarin},
  timestamp = {2015.05.30},
  url = {http://en.wikipedia.org/w/index.php?title=Calculus_of_variations&oldid=663148595}
}

@MISC{wiki:constitutive_relation,
  author = {Wikipedia},
  title = {Constitutive equation --- Wikipedia{,} The Free Encyclopedia},
  year = {2015},
  note = {[Online; accessed 2-July-2015]},
  owner = {nguarin},
  timestamp = {2015.07.02},
  url = {https://en.wikipedia.org/w/index.php?title=Constitutive_equation&oldid=668139312}
}

@MISC{wiki:variational_principle,
  author = {Wikipedia},
  title = {Variational principle --- Wikipedia{,} The Free Encyclopedia},
  year = {2015},
  note = {[Online; accessed 30-May-2015]},
  owner = {nguarin},
  timestamp = {2015.05.30},
  url = {http://en.wikipedia.org/w/index.php?title=Variational_principle&oldid=646823082}
}

@BOOK{book:zienkiewicz_FEM2,
  title = {{T}he {F}inite {E}lement {M}ethod for {S}olid and {S}tructural {M}echanics},
  publisher = {Butterworth-Heinemann},
  year = {2005},
  author = {O.C. Zienkiewicz and R.L. Taylor},
  volume = {2},
  pages = {736},
  edition = {6},
  keywords = {Finite Element Method, Structural Mechanics, Continuum Mechanics,
	Numerical Methods},
  owner = {nguarinz},
  review = {This is the key text and reference for engineers, researchers and
	senior students dealing with the analysis and modelling of structures
	- from large civil engineering projects such as dams, to aircraft
	structures, through to small engineered components. Covering small
	and large deformation behaviour of solids and structures, it is an
	essential book for engineers and mathematicians. The new edition
	is a complete solids and structures text and reference in its own
	right and forms part of the world-renowned Finite Element Method
	series by Zienkiewicz and Taylor.
	
	New material in this edition includes separate coverage of solid continua
	and structural theories of rods, plates and shells; extended coverage
	of plasticity (isotropic and anisotropic); node-to-surface and 'mortar'
	method treatments; problems involving solids and rigid and pseudo-rigid
	bodies; and multi-scale modelling.
	
	* Dedicated coverage of solid and structural mechanics by world-renowned
	authors, Zienkiewicz and Taylor * New material including separate
	coverage of solid continua and structural theories of rods, plates
	and shells; extended coverage for small and finite deformation; elastic
	and inelastic material constitution; contact modelling; problems
	involving solids, rigid and discrete elements; and multi-scale modelling
	* Accompanied by online downloadable software},
  timestamp = {2011.11.28}
}

@BOOK{book:zienkiewicz_FEM1,
  title = {{T}he {F}inite {E}lement {M}ethod: {I}ts {B}asis and {F}undamentals},
  publisher = {Butterworth-Heinemann},
  year = {2005},
  author = {O.C. Zienkiewicz and R.L. Taylor and J.Z. Zhu},
  volume = {1},
  pages = {752},
  edition = {6},
  keywords = {Finite Element Method,Numerical Methods},
  owner = {nguarinz},
  review = {The Finite Element Method: Its Basis and Fundamentals offers a complete
	introduction to the basis of the finite element method, covering
	fundamental theory and worked examples in the detail required for
	readers to apply the knowledge to their own engineering problems
	and understand more advanced applications.
	
	This edition sees a significant rearrangement of the book's content
	to enable clearer development of the finite element method, with
	major new chapters and sections added to cover:
	
	 Weak forms
	
	 Variational forms
	
	 Multi-dimensional field problems
	
	 Automatic mesh generation
	
	 Plate bending and shells
	
	 Developments in meshless techniques
	
	Focusing on the core knowledge, mathematical and analytical tools
	needed for successful application, The Finite Element Method: Its
	Basis and Fundamentals is the authoritative resource of choice for
	graduate level students, researchers and professional engineers involved
	in finite element-based engineering analysis.
	
	 A proven keystone reference in the library of any engineer needing
	to understand and apply the finite element method in design and development.
	Founded by an influential pioneer in the field and updated in this
	seventh edition by an author team incorporating academic authority
	and industrial simulation experience. Features reworked and reordered
	contents for clearer development of the theory, plus new chapters
	and sections on mesh generation, plate bending, shells, weak forms
	and variational forms.},
  timestamp = {2011.11.28}
}

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