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Dissertations / Theses on the topic 'Finite element method. Fracture mechanics'

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Published: 4 June 2021

Last updated: 4 February 2022

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1

Pluma, Reyes Jorge A. "Fracture Control Modeling With The Finite Element Method." DigitalCommons@CalPoly, 2019. https://digitalcommons.calpoly.edu/theses/2096.

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This thesis investigates the feasibility and usability of the finite element method approach in the design of crack arresting devices. Current design and manufacturing practices are improving structures' susceptibility to fracture, in particular brittle fracture; however, cracks in structures are still observed within their lifespans due to severe unexpected service conditions, poor designs, or faulty manufacturing. Crack arrester systems can be added during service to prolong the longevity of structures with sub-critical or critical flaws. Fracture properties of different specific structures

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2

蘇啓亮 and Kai-leung Su. "Fractal two-level finite element method for elastic crack analysis." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31235323.

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3

Su, Kai-leung. "Fractal two-level finite element method for elastic crack analysis /." Hong Kong : University of Hong Kong, 1996. http://sunzi.lib.hku.hk/hkuto/record.jsp?B14777290.

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4

SANTANA, WLASMIR CAVALCANTI DE. "A ROBUST GENERALIZED FINITE ELEMENT METHOD APPLIED TO FRACTURE MECHANICS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2004. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4716@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Apesar da extensa aplicabilidade do Método de Elementos Finitos na representação e solução de problemas dos mais diversos campos da Engenharia, há ainda classes de problemas em que o seu uso encontra severas dificuldades. Uma delas está relacionada com a simulação da evolução temporal da geometria ou de condições de contorno móveis na Mecânica Computacional. Exemplos típicos destes problemas envolvem grandes deformações, propagação de trincas na mecânica da fratura, escoamentos bi-fásicos , transferência de calor em meios

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5

Sun, Huaiyang, and 孫懷洋. "Fractal finite element method for anisotropic crack problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B26720474.

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6

Johnsen, Eivind. "Application method of the least squares finite element method to fracture mechanics." Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/16435.

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7

Ogiso, Tadashi. "Finite element alternating analysis for stiffened fuselage with cracks." Thesis, Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/18992.

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8

Bird, Gareth Edward. "The coupled dual boundary element-scaled boundary finite element method for efficient fracture mechanics." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/6996/.

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A novel numerical method is presented for applications to general fracture mechanics problems in engineering. The coupled dual boundary element-scaled boundary finite element method (DBE-SBFEM) incorporates the numerical accuracy of the SBFEM and the geometric versatility of the DBEM. Background theory, detailed derivations and literature reviews accompany the extensions made to the methods constituents necessary for their coupling as part of the present work. The coupled DBE-SBFEM, its constituent components and their application to linear elastic fracture mechanics are critically assessed an

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9

Chidgzey, Steven R. "Advances in the development of the scaled boundary method for applications in fracture mechanics." University of Western Australia. School of Civil and Resource Engineering, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0176.

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[Truncated abstract] The scaled boundary method is a powerful, though undervalued, computational analysis method. The complex mathematics of the original derivation of the method has rendered it unattractive to researchers. However, the method has proven more efficient than conventional computational analysis methods for problems involving unbounded domains and for problems involving stress singularities. The advantages of the scaled boundary method in dealing with stress singularities make it uniquely suited to the analysis of fracture mechanics problems. This study will extend the capabiliti

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10

Hinks, Thomas. "The application of the finite element method and the boundary element method to fatigue and fracture." Thesis, Cranfield University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302734.

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11

Sammur, Mohammed F. R. "Finite element methods applied to elasto-plastic fracture mechanics." Thesis, Queen Mary, University of London, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.423455.

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12

Kamble, Mithil. "Development of a Polygonal Finite Element Solver and Its Application to Fracture Problems." University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1504873845916901.

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13

McNary, Michael. "Implementation of the extended finite element method (XFEM) in the Abaqus software package." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29665.

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Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009.<br>Committee Chair: Cherkaoui, Mohammed; Committee Member: Neu, Richard; Committee Member: van der Sluis, Olaf. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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14

Pratap, Rudra 1964. "A NEW RESIDUAL FINITE-ELEMENT FORMULATION FOR ELASTODYNAMIC PROBLEMS." Thesis, The University of Arizona, 1987. http://hdl.handle.net/10150/276552.

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In the research undertaken a finite element formulation has been developed for an elastodynamic problem using a least squares approach. The special requirements of the problem demanded a study of suitability of various elements. The emergence of the final element is a result of both theoretical and numerical study of three different elements. The approximation function is assumed on the basis of the order of the governing differential equations. Then the square of the error resulting from the approximate solution is minimized over the entire domain as well as the boundaries in the same functio

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15

Khattab, Hussein A. "Finite element response modeling of crack geometries induced by hydraulic fracturing /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487261919112032.

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16

Marrón, Armando. "Scarf joint modeling and analysis of composite materials." Monterey, Calif. : Naval Postgraduate School, 2009. http://handle.dtic.mil/100.2/ADA502236.

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Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, June 2009.<br>Thesis Advisor(s): Kwon, Young W. "June 2009." Description based on title screen as viewed on July 10, 2009. DTIC Identifiers: Scarf joint, energy release rate, virtual crack closure method, overlap joint. Author(s) subject terms: Scarf joint, finite element method, energy release rate, virtual crack closure method, ansys, composites, overlap joint, fracture mechanics. Includes bibliographical references (p. 59). Also available in print.

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17

Jin, Hui, and Hao Wu. "Finite Element Modelling of Fracture in dowel-type timber connections." Thesis, Linnéuniversitetet, Institutionen för maskinteknik (MT), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-34783.

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Dowel-type steel to timber connections are commonly used in timber structure. The load carrying capacity and the stress distribution within the connection area are complicated and the failure behavior of a connection depends on many parameters. The main purpose of this thesis was to verify, using the data obtained from previous experiments, the conventional design method of European Code 5(EC5) (hand calculation) for dowel type joints subjected to pure bending moment and other alternative design methods based on the finite element method (FEM) including the use of the mean stress approach and

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18

Solanki, Kiran N. "TWO AND THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS OF PLASTICITY-INDUCED FATIGUE CRACK CLOSURE ? A COMPREHENSIVE PARAMETRIC STUDY." MSSTATE, 2002. http://sun.library.msstate.edu/ETD-db/theses/available/etd-11102002-143748/.

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Finite element analyses are frequently used to model growing fatigue cracks and the associated plasticity-induced crack closure. Two-dimensional, elastic-perfectly plastic finite element analyses of middle-crack tension (M(T)), bend (SEB), and compact tension (C(T)) geometries were conducted to study fatigue crack closure and to calculate the crack opening values under plane-strain and plane-stress conditions. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus similar initial forward plastic zone sizes. Mesh refinement studies were performed

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19

Alizada, Alaskar [Verfasser]. "The eXtended Finite Element Method (XFEM) with Adaptive Mesh Refinement for Fracture Mechanics / Alaskar Alizada." Aachen : Shaker, 2012. http://d-nb.info/1052408818/34.

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20

Li, Shanhu. "Extended voronoi cell finite element model for damage in brittle matrix composites." The Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1135317411.

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21

Zeng, Wei. "Advanced Development of Smoothed Finite Element Method (S-FEM) and Its Applications." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439309306.

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22

Chirputkar, Shardool U. "Bridging Scale Simulation of Lattice Fracture and Dynamics using Enriched Space-Time Finite Element Method." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1313753940.

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23

ESTEVES, ARMANDO M. "Modelamento do contínuo de simulações micromecânicas com base em novas teorias de comportamento plástico do material." reponame:Repositório Institucional do IPEN, 2005. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11277.

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24

Woodward, Huw. "On the application of the method of difference potentials to linear elastic fracture mechanics." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/on-the-application-of-the-method-of-difference-potentials-to-linear-elastic-fracture-mechanics(fec9a25c-0e37-4e53-ac35-ba85233c7dae).html.

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The Method of Difference Potentials (DPM) has proven an efficient tool for the solution of boundary value problems (BVPs) in various fields of research including acoustics and fluid mechanics. The method converts the solution of problems of complex geometry to the multiple solutions of a simple, well defined auxiliary problem, on which efficient solvers can be used, and which also avoids the numerical computation of stiffness matrices. So far, most problems solved by the method have been considered for regular domains. Here the method is considered for the solution of Linear Elastic Fracture M

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25

Wu, Jian. "Numerical modelling and optimization of new RHS column-to-I beam connections." Thesis, Swansea University, 2013. https://cronfa.swan.ac.uk/Record/cronfa43170.

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26

Zarate-Escudero, Francisco Antonio. "The application of numerical methods to problems in the physics of fracture." Thesis, Queen Mary, University of London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.283663.

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27

Bellinger, Nicholas C. (Nicholas Charles) Carleton University Dissertation Engineering Mechanical. "Linear elastic fracture mechanics analysis of flat oval Bourdon tubes using finite element methods." Ottawa, 1987.

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28

Wagner, David. "A Finite Element-based Adaptive Energy Response Function Method for Curvilinear Progressive Fracture." Thesis, The University of Texas at San Antonio, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10845946.

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<p> An adaptive arbitrary-order curvilinear progressive 2D crack growth algorithm is presented. The method uses the ZFEM hypercomplex finite element program to compute arbitrary order derivatives of strain energy with respect to self-similar or perpendicular crack extensions, and then constructs a family of Taylor series functions of strain energy versus crack growth direction. An adaptive algorithm automatically selects the best high-degree polynomial to extrapolate a curvilinear crack path, and adjusts the length of the crack growth increment added during each simulation step to maintain the

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29

Al-Edani, Ameen Ahmed Nassar. "Efficient fracture mechanics programming system for linear and non-linear problems using finite-element and boundary-element methods." Thesis, Cranfield University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276169.

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30

Nešpůrek, Lukáš. "STOCHASTIC CRACK PROPAGATION MODELLING USING THE EXTENDED FINITE ELEMENT METHOD." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-233900.

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Tato disertační práce vychází z výzkumu v rámci francouzsko-českého programu doktorátu pod dvojím vedením na pracovišti Institut français de mécanique avancée v Clermont-Ferrand a na Ústavu fyziky materiálu AV v Brně. Úvodní výzkumný úkol na brněnském pracovišti se zabýval numerickou analýzou pole napětí v okolí čela trhliny v tenké kovové fólii. Zvláštní pozornost byla zaměřena na vliv speciálního typu singularity v průsečíku čela trhliny s volným povrchem. Těžiště disertační práce spočívá v numerickém modelování a stochastické analýze problémů šíření trhlin se složitou geometrií v dvojrozměr

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31

Bude, Jérémie. "Ductile fracture simulation using the strong discontinuity method." Thesis, Compiègne, 2015. http://www.theses.fr/2015COMP2243/document.

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Dans un contexte d’évaluation de la criticité des chargements, les travaux de thèse ont les objectifs suivants : prendre en compte les phénomènes sous-jacents à le rupture ductile : les phénomènes de dissipation volumique (plasticité et endommagement) et surfaciques (fissuration). On s'intéresse également à régulariser la solution vis-à-vis du maillage, à prédire le phénomène de transition de mode de rupture plan vers un mode de propagation oblique observé pour certains essais. La méthode utilisée est basée sur la méthode des discontinuités fortes. Un des enjeux majeurs de ces travaux est d’ét

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32

Van, Der Merwe Carel Wagener. "A peridynamic model for sleeved hydraulic fracture." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/95993.

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Thesis (MEng)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: Current numerical methods in the eld of hydraulic fracturing are based mainly on continuum methods, such as the Finite Element Method (FEM) and the Boundary Element Method (BEM). These methods are governed by Linear Elastic Fracture Mechanics (LEFM) criteria, which su er from the inherent aw of a non-physical stress representation at the fracture tip. In response to this, a non-local method is proposed, namely the peridynamic theory, to model sleeved hydraulic fracture. A 2D implicit quasi-static ordinary state based p

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33

Haswell, Jane V. "A fracture mechanics methodology for the assessment of fatigue cracks in tubular joints : (based on the finite element method)." Thesis, Teesside University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.290767.

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Fixed jacket offshore structures. which react environmental wave loading. are generally constructed using tubular steel members. When subject to load. severe surface and through-thickness stress gradients occur due to local bending of the tubular wall. The cyclic nature of the environmental wave loading results in high stress concentration at the joints. which can lead to fatigue cracking. British Gas currently operates twelve fixed offshore structures. two of which. the Rough A-Complex structures. are now ageing and showing signs of fatigue cracking. The objective of the work described in thi

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34

Gigliotti, Luigi. "Assessment of the applicability of XFEM in Abaqus for modeling crack growth in rubber." Thesis, KTH, Hållfasthetslära (Inst.), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-103919.

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The eXtended Finite Element Method is a partition of unity based method, particularly suitable for modelling crack propagation phenomena, without knowing a priori the crack path. Its numerical implementation is mostly achieved with stand-alone codes. The implementation of the eXtended Finite Element Method in commercial FEA softwares is still limited, and the most famous one including such capabilities is Abaqus TM. However, due to its relatively recent intro-duction, XFEM technique in Abaqus has been proved to provide trustable results only in few simple benchmark problems involving linear el

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35

Zhao, Lv. "On the fracture of solar grade crystalline silicon wafer." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEI134/document.

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La rentabilité des cellules à base de silicium est un point essentiel pour le marché photovoltaïque et cela passe notamment par l'amélioration du rendement électrique, la baisse des coûts de production ainsi que le renforcement de la fiabilité/durabilité des wafers. Des procédés innovants émergent, qui permettent d'obtenir des wafers ultra minces avec moins de perte de matière première. Cependant il est nécessaire de mettre en place des méthodes de caractérisation afin d’analyser la rigidité et la tenue mécanique de ces matériaux. Dans ce travail, des essais de flexion ont été effectués pour c

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36

Peng, Daren 1957. "Methods for failure assessment of structures and applications to shape optimisation." Monash University, Dept. of Mechanical Engineering, 2002. http://arrow.monash.edu.au/hdl/1959.1/7682.

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37

Kirugulige, Madhusudhana S. "A study of mixed-mode dynamic fracture in advanced particulate composites by optical interferometry, digital image correlation and finite element methods." Auburn, Ala., 2007. http://repo.lib.auburn.edu/07M%20Dissertations/KIRUGULIGE_MADHUSUDHANA_29.pdf.

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38

Makhecha, Dhaval Pravin. "Dynamic Fracture of Adhesively Bonded Composite Structures Using Cohesive Zone Models." Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/29631.

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Using experimental data obtained from standard fracture test configurations, theoretical and numerical tools are developed to mathematically describe non-self-similar progression of cracks without specifying an initial crack. A cohesive-decohesive zone model, similar to the cohesive zone model known in the fracture mechanics literature as the Dugdale-Barenblatt model, is adopted to represent the degradation of the material ahead of the crack tip. This model unifies strength-based crack initiation and fracture-mechanics-based crack progression. The cohesive-decohesive zone model is implemente

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39

Treifi, Muhammad. "Fractal-like finite element method and strain energy approach for computational modelling and analysis of geometrically V-notched plates." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/fractallike-finite-element-method-and-strain-energy-approach-for-computational-modelling-and-analysisof-geometrically-vnotched-plates(93e63366-8eef-4a29-88a4-0c89cf13ec1f).html.

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The fractal-like finite element method (FFEM) is developed to compute stress intensity factors (SIFs) for isotropic homogeneous and bi-material V-notched plates. The method is semi-analytical, because analytical expressions of the displacement fields are used as global interpolation functions (GIFs) to carry out a transformation of the nodal displacements within a singular region to a small set of generalised coordinates. The concept of the GIFs in reducing the number of unknowns is similar to the concept of the local interpolation functions of a finite element. Therefore, the singularity at a

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40

QUINAN, MARCO A. D. "Uma metodologia para determinação do fator de intensidade de tensões causado por tensões térmicas utilizando a fotoelasticidade." reponame:Repositório Institucional do IPEN, 2005. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11270.

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Blandford, Robert. "Characterization of fatigue crack propagation in AA 7075-T651." Master's thesis, Mississippi State : Mississippi State University, 2001. http://library.msstate.edu/etd/show.asp?etd=etd-04092001-152127.

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42

Findley, Kip Owen. "Physically-based models for elevated temperature low cycle fatigue crack initiation and growth in Rene." Diss., Available online, Georgia Institute of Technology, 2005, 2005. http://etd.gatech.edu/theses/available/etd-04292005-092902/.

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Thesis (Ph. D.)--Materials Science and Engineering, Georgia Institute of Technology, 2006.<br>McDowell, David, Committee Member ; Gokhale, Arun, Committee Member ; Saxena, Ashok, Committee Chair ; Johnson, Steven, Committee Member ; Sanders, Thomas, Committee Member.

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Dubravec, Kristián. "Elastoplastická analýza napětí a deformace a stanovení lomových parametrů při tahovém namáhání těles s koncentrátory napětí." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-443729.

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The aim of this thesis is the construction of a diagram of fracture strain for high strength steel OCHN3MFA and its application for the estimation of fracture toughness of this material. The first part of the thesis contains the necessary theoretical framework for numerical modelling of tensile tests of various specimens - smooth specimen, specimen with a notch and specimen with a circumferential crack, it describes the influence of triaxiality on the fracture of bodies and the possibilities of construction of the diagram of fracture strain. Subsequently, a numerical model of these specimens i

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Rizzatti, Luciano. "Analise dinamica, numerica e experimental de uma viga trincada." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263231.

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Orientador: Jose Maria Campos dos Santos<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica<br>Made available in DSpace on 2018-08-04T03:08:11Z (GMT). No. of bitstreams: 1 Rizzatti_Luciano_M.pdf: 4568270 bytes, checksum: 355f300e3ff2990b56197b32d323e5eb (MD5) Previous issue date: 2005<br>Resumo: Neste trabalho apresenta-se um elemento finito contendo uma trinca na região central, o qual permite simular o comportamento dinâmico para qualquer comprimento de trinca. O elemento simula o comportamento de uma viga de seção retangular sujeita a esforços

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Bargos, Fabiano Fernandes 1984. "Aspects of the discretized peridynamic theory and the finite element method for concurrent multiscale simulation = Aspectos da teoria peridinâmica discretizada e do método dos elementos finitos para simulação em múltiplas escalas concorrentes." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263447.

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Orientador: Marco Lucio Bittencourt<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica<br>Made available in DSpace on 2018-08-22T02:31:27Z (GMT). No. of bitstreams: 1 Bargos_FabianoFernandes_M.pdf: 142755072 bytes, checksum: b7dcee861f8864c85cd32b66447f6d26 (MD5) Previous issue date: 2009<br>Resumo: Nesse trabalho, considera-se a simulação em múltiplas escalas concorrentes, usando a teoria peridinâmica e a elasticidade clássica, para a simulação de problemas de engenharia. Primeiramente a teoria peridinâmica em uma dimensão é estudada em detalhes

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Leach, Austin M. "A NEW CONSTRAINT BASED FRACTURE PREDICTION METHODOLOGY FOR DUCTILE MATERIALS CONTAINING SURFACE CRACKS [FLAWS]." Master's thesis, Mississippi State : Mississippi State University, 2004. http://library.msstate.edu/etd/show.asp?etd=etd-07122004-155332.

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47

Patel, Nirdesh D. "Efficient prediction of bite fracture force for hard food items." Amherst, Mass. : University of Massachusetts Amherst, 2009. http://scholarworks.umass.edu/theses/228/.

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48

Navrátil, Petr. "Šíření trhliny v železničním kole za provozních podmínek." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-234022.

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This doctoral thesis was written under supervision of my supervisor Prof. Ing. Přemysl Janicek, DrSc. and under supervision of my specialist supervisor Ing. Petr Skalka, Ph.D. The thesis deals with the influence of various operating conditions on crack behaviour in in a wheel rim and/or tire. The dissertation topic was motivated by cooperation with Pardubice University, Faculty of Jan Perner. The first part of the thesis presents a literature search, which provides a current state-of-art in the field of contact loading, crack propagation behaviour under mixed-mode and thermal field generated d

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Ahmed, Lamis. "Models for analysis of young cast and sprayed concrete subjected to impact-type loads." Doctoral thesis, KTH, Betongbyggnad, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-168211.

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The strive for a time-efficient construction process naturally put focus on the possibility of reducing the time of waiting between stages of construction, thereby minimizing the construction cost. If recently placed concrete, cast or sprayed, is exposed to impact vibrations at an early age while still in the process of hardening, damage that threatens the function of the hard concrete may occur. A waiting time when the concrete remains undisturbed, or a safe distance to the vibration source, is therefore needed. However, there is little, or no, fully proven knowledge of the length of this dis

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Silvestri, Chiara. "Development and validation of a knee-thigh-hip LSDYNA model of a 50th percentile male." Worcester, Mass. : Worcester Polytechnic Institute, 2008. http://www.wpi.edu/Pubs/ETD/Available/etd-042908-144927/.

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Dissertation (Ph.D.)--Worcester Polytechnic Institute.<br>Keywords: active muscles, out-of-position, fracture mechanisms, impacts, KTH, dynamic ligament failure model. Includes bibliographical references (leaves 353-365).

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