THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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CHAPTER 4: Finite element model of locomotor stress in the metatarsus of INTRODUCTION Gorgosaurus Iibfatus (Tyrannosauridae) The third metatarsal (MT III) of tyrannosaurids is triangular in distal cross section. The tensile keystone hypothesis (Chapter 3) proposes that under high impulse Ioadings, with the metatarsus acutely angled to the substrate, the distal portion of MT III is displaœd anterodorsally. Ligaments arrest this displacement, and draw metatarsals II and IV towards the planta centerline of MT Ill. These loadings therefore unify the structure distally. The metatarsals are less subject individually to torsion and shear, and their collective strength is thereby increased. A prerequisite to the tensile keystone hypothesis is the structural integnty of the proximal splint of MT III. Using beam theory equations, Holtz (1 994a) found that the splint could not support body weight in large tyrannosaurids, but did not investigate the combined effects of locomotory stresses on the splint and the rest of the metatarsus, This chapter incorporates morphology, biological material properties, and loading environments of the metatarsals into a finite element stress analysis. Finite element analysis (FEA) elucidates stress and strain within constitutive bones of the arctometatarsus, and reveals the potential role of ligaments on intemietatarsal kinematics. Finite element modeling: background and applicabil@f to biological questions Finite element analysis determines stresses and strains within a structure by subdividing it into a finite number of shapes (elements) connected at points
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THE UNIVERSITY OF CALGARY Functiona
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Many figures in this thesis use col
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ACKNOWLEûGEM ENTS Many friends and
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Approval page Acknowledgements Tabi
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CONCLUDING COMMENTS Figures for Cha
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CHAPTER 5: Mechanical and phylogene
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LIST OF FIGURES Figure 1 .l. Phylog
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Figure 3.6. Osteological correlates
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AMNH GI HMN IVPP MOR NMC OMNH PIN P
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and constructional morphology revea
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1985, Bryant and Seymour 1990). If
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surfaces of a Tyrannosaurus rex spe
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3. Troodontidae (Figure 1.2): Trwdo
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Hypothesized functions of the tyran
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1. Atomization (Chapters 2 and 3).
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Figure 1.1. P hylogenetic diagram o
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Figure 1.2. Phylogenetic diagram of
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Figure 1 .S. Skeletal restorations
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did not quantify the degree of prox
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qualitative debate over arctometata
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This hypothesis focuses on tyrannos
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Table 2.1. Theropod and Plafeosauru
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specimens in the figures reflects a
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were not attempted. While this limi
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Chapter 3). 1 now address variation
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- Ç6'P 1 68'€tr 1 L'OC 99'66 L'9
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Table 2.3: Log-transformed values f
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experiences a sharp laterally indin
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ecause it can be cursorily dassifie
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arctometatarsalian specimens, the l
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) Shaf€ and region of proximal ar
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a) Ginglymus. Figure 2.14 shows the
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) Shaft and region of proximal arti
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measurements of width pV2S%TU-DE an
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Table 2.4b Variancelmeasurement eac
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the largest sum of linear measureme
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Table 2.5: Specimen statistics Herr
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and Sinraptor dongi specimens. With
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In addition, a hook like proximal a
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oth physical narrowing and elongati
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1s the MT 111 shape segregation fun
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tyrannosaurids, ornithomimid, and t
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proximal constriction, white EImisa
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Figure 2.2. Tyrannosaurid, trwdonti
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Figure 2.4. Dromaeosaurid and carno
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- Anterior (flexor) surface medial
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Figure 2.7. Left MT III of Tyrannos
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Figure 2.8. Left MT III of Gorgosau
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Figure 2.9. Left MT III of an omith
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Figure 2.10. Left metatarsus of Tmd
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Figure 2.1 1. Left MT III of Elmisa
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Figure 2.12. Right MT III of Deinon
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Figure 2.13. Left MT III of Allosau
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Figure 2.14. Left metatarsus of Sin
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Figure 2.15. Plots of MT Ill specir
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Figure 2.16. Plot of third metatars
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tv . ... . Ri. . . .
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Figure 2.19. Plot of third metatars
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CHAPTER 3: Tensile keystone model o
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dynamically transmitted Iommotor fo
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Table 3.1 . Metatarsi examined in t
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interrnetatarsal dynamics in these
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compelled analysis of movement evid
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Once prepared, TMP 94.1 2.602 and i
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Page 147 and 148: Table 3.2. Surface areas of intemet
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Page 151 and 152: 4) Forces from anterior displacerne
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Page 159: Figure 3.1. Schematic representatio
Page 163: Figure 3.3. CT reconstruction of ri
Page 167: Figure 3.5. MT II (left element) an
Page 171: Figure 3.7. Osteological correlates
Page 175: Figure 3.9. Osteological correlates
Page 179: Figure 3.1 1 ae. The metatarsal rec
Page 187: Figure 3.13. Ligament contribution
Page 191 and 192: Figure 3.15. Anatorny of the equid
Page 193: Figure 3.16. Cornparison of loading
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Page 199 and 200: Material and Ioading regimes of fhe
Page 201 and 202: Two analyses were fun in order to t
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Page 205 and 206: This quantity approximates the vert
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Page 211 and 212: Table 4.1. Material properties of b
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Page 217 and 218: 1) Informative strain results versu
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Page 221 and 222: Specifically, osteological correlat
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Page 226: Figure 4.2. Initial loads and bound
Page 230: Figure 4.4. Simplified representati
Page 234: Figure 4.6. Strain distribution in
Page 237 and 238: The analyses of the Gorgosaurus Iib
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tenable from the available evidence
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equivalent horsepower, 15 economy c
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Other aptations refiect multiple fu
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This and other systernatically info
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(Russell 1975, McGregor 2000). Meta
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was the default developmental patte
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Arnong dromaeosaurids and birds, th
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hypothesis. Fossil evidence of basa
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suggestive of grasping ability. Neo
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available evidence without propriet
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Figure 5.1. Phylogeny of the Therop
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LITERTURE ClTED Alexander R.M. 1977
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Carter D.R., Fyhrie, D.P., and Whal
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Galton P.M. 1982. Elaphrosaurus, an
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Hutchinson J.R., Stidham T.A., Sniv
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Novas F.E. 1993. New information on
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Stein B.R. and Casinos 1997. What i
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APPENDIX Principal Components Analy
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highest degree, and so on. Specimen
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THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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