Vol. 12 ( ) Mirifusus Evolution of Radiolarian Mirifusus (Marine Plankton) and Mechanical Optimization of Frame Structure Structual Mechanichal

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1 Vol. (009 8 ) Mirifusus Evolution of Radiolarian Mirifusus (Marine Plankton) and Mechanical Optimization of Frame Structure Structual Mechanichal Verification of Succession of Its Skeleton Shape Takashi YOSHINO, Naoto ISHIDA, Naoko KISHIMOTO, Atsushi MATSUOKA, Toshiyuki KURIHARA, Katsunori KIMOTO, and Shu MATSUURA We discussed the evolution of the skeleton of radiolaria (marine plankton) from a viewpoint of optimization process of frame structure. The genus Mirifusus, a group of Mesozoic radiolaria, has a character of detailed and geometric frame between segments. The geometric framework was evolved from combination of pentagon and rhombus to triangle through pentagon. We treated such frameworks as two dimensional rigid frames with periodic boundary condition. We obtained normalized displacement of upper-side under the condition of compress or tortional force for each framework. The results show that the triangle structure is most effective if the -D frame is applied both of compress and torsional forces in most cases. Such a structure corresponds to final frame structure of genus Mirifusus during its evolution process. Key Words : radiolaria, genus Mirifusus, frame structure, structural mechanics, evolution. µm µm ) ) SiO 3). Mirifusus Mirifusus Mirifusus ) Mirifusus dianae baileyi

2 Mirifusus - Type - - Type - - Type 3 - L H Mirifusus unit cell L/n y x Mirifusus.. Mirifusus Type Mirifusus guadalupensis Type Mirifusus dianae dianae Type 3 Type 3 Mirifusus dianae baileyi Type Type Mirifusus Type Type Type 3 3 Mirifusus y x x L H α = H/L n a = nh/l x n

3 H Mirifusus P P/n n y x Mirifusus Mirifusus xy Mirifusus Nassellaria ). E A I P/EH = Mirifusus x r V β V = βh 3 r = βh3 () nπl l H α n H r = r/h l = l/h r = β nπl () i j ij K ij K ij = AE k ij H Ka ij(θ ij ) + EI (k ij H) 3 Kb ij(θ ij, k ij ) (3) K a ij Kb ij k ij H ij θ ij x ij ( ) K ij = EH πr kij 3 Kij(θ a ij ) + k ij r Kb ij(θ ij, k ij ) () () () 3. Type 3. Type θ 3 x 3 Mirifusus 3 3 H a θ θ

4 P/n 3 P/n Unit Cell θ L/n 3 H β = 0.5 β = Β 0.5 Β Β Β 3 Type β = β = 3 Type Type 3 Type 3 Type 3 ( H tan θ ) a 3 3 H a cos θ l l = a cos θ + tan θ a (5) P/n y P/n x α n θ β n 3 tan θ nα (6) Type 3 n θ 3 r < L/n (7) 5 Type θ β θ n tan θ α < n < γα + (γ cos θ) + γ( sin θ) α cos θ γ = π α 3 β 3. (8) α n β θ θ 0 θ π/ (6) 0 θ arctan(nα) (9) θ θ n β θ 5 α = 0., n = 0 β = 0.5,,, 3 θ β 5 θ θ Type

5 n 5 n 0 n 30 n n 5 n 0 n 30 n 50 n = 5 n = 5 n = 0 n = 0 n = 30 n = 30 n = 50 n = 50 6 Type n θ n θ 7 Type n θ n θ, α = 0. β = 0. (8) n 6 n n θ θ π/3 n π/3 n a y n n α = 0. β = 0. n 7 θ n θ 3 y P/n 5 3 P/n Unit Cell θ 3 H 5 L/n 8 Type. Type. 8 Type Type y Type Type Type θ

6 Type Type Type 3 Type Type Type Type l ( l = a cos θ + tan θ ) (0) a n Type tan θ α < n < γ α + (γ cos θ) + γ ( sin θ) α cos θ (). γ = π α 3 β Type α n β θ Type θ 0 θ arctan(nα) () θ θ, α = 0. β = 0. Type n 9 Type θ θ 9 0 θ θ n θ θ Type Type n = 5 n = 0 n = 30 n = n 5 n 0 n 30 n 50 9 Type n θ n θ n = 5 n = 0 n = 30 n = n 5 n 0 n 30 n 50 0 Type n θ n θ α 0. n β Type Type Type Type β 0., 0., 0.5,, n n 0 n 00 β

7 Displacement Ratio Displacement Ratio Number of Division, n Number of Division, n b=0. b=0. b=0.5 b= b= b=0. b=0. b=0.5 b= b= Type Type Type β Type β Type β 0.5 Type n Type 5. Type Type 3 Mirifusus Type Mirifusus n n Type 3 Type Type Type Type 3 Type θ Type Type 5 Type Type Type Type Type 3 Type Type 3 Type Type Type 6. Mirifusus Type Type 3 Type Type 3 Type Type Type Type

8 ) Matsuoka, A.: Living radiolarian feeding mechanisms: new light on past marine ecosystems, Swiss J. Geosci., Vol. 00, pp , 007. ) Vol. pp ) 973 ) Baumgartner, P.O., O Dogherty, L., Gorican, S., Urquhart, E., Pillevuit, A., and De Wever, P.: Middle Jurassic to Lower Cretaceous Radiolaria of Tethys: Occurrences, Systematics, Biochronology, Mémoires de Géologie (Lausanne), No. 3, 995. (009 9 )

Ł\”ƒ-2005

$Ł\”ƒ-2005$