著者

藤井 文夫 Kuo Mo HSIAO 小林 卓哉 井上 吉弘 新田 高洋

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

vol.82, no.836, pp.15-00623, 2016 (Released:2016-04-25)

参考文献数

9

被引用文献数

1

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The popular sports entertainment, billiards, is rich in mechanical issues such as 3D finite rotation, collision, contact and friction, evoking a research interest in rigid-body dynamics, nonlinear CAE and computational mechanics. However, the 3D nonlinear behavior of a rigid ball has so far hardly received the attention of scholars to exercise the mechanical modeling skill. The represent study focuses, therefore, on 3D nonlinear billiard dynamics and attempts to precisely predict the ball behavior in finite rotational motion with collision, contact and slip friction. In dependence upon ball situations, 4 different models are proposed. They are namely, rotation model, strike model, collision model and reflection mode. The rotation model is an elementary model and describes the 3D ball motion after a cue strike and subject to table friction only. The strike model is useful to study the effects of cue striking. For simplicity, the strike points are limited to the ball center, 12, 3, 6 and 9 o'clock' in the ball projection. The collision model ignores the ball-to-ball friction and the law of conservation of momentum holds to predict the velocities of two balls after collision. The reflection model simulates the ball-to-cushion contact in bank shots. Incidence angle, translational and rotational velocities, cushion elasticity and frictional properties may be variable in a parameter study. In all these 4 models, the ball is assumed to be in contact to the table surface. Masse or jump shots are excluded in modeling. The equations of ball motion are time-integrated by forward Euler method. The models are verified and validated in numerical examples including optimization and parameter studies. All computed results well agree with the hustler’s experiences in game practice. The present research work will contribute to develop a skill-up program of professional hustlers.

著者

藤井 文夫 井上 吉弘 新田 高洋

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集C編 (ISSN:18848354)

巻号頁・発行日

vol.78, no.788, pp.1133-1142, 2012 (Released:2012-04-25)

参考文献数

11

被引用文献数

3 6

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Domino is a popular entertainment to enjoy the pleasing wave propagation in a row of solid pieces. This play game may be, however, a tough research subject of dynamic contact mechanics, because finite rotation, contact and friction are included in toy mechanics and these nonlinear effects are all of scientific interest. The major concern of this paper is to develop a computational model to study the domino wave propagation in a long straight row. More specifically, a total of N dominoes are modeled to rectangular rigid-body solids in shape of D (width) x H (height) x B (breadth). Equally spaced dominoes in a long straight row (L=492cm) are assumed to simply rotate around the front bottom edge. To trigger the wave propagation, the first domino is slowly inclined till its side diagonal slightly goes beyond the plumb line. The successive collision mechanism between individual toppling dominoes is investigated as a 2D problem in contact mechanics and we obtain an excellent agreement between the model prediction and experimental result.

著者

小林 卓哉 三原 康子 西脇 剛史 藤井 文夫

出版者

公益社団法人 土木学会

雑誌

土木学会論文集A2(応用力学) (ISSN:21854661)

巻号頁・発行日

vol.70, no.2, pp.I_419-I_428, 2014 (Released:2015-02-20)

参考文献数

13

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局所的な構造不安定の問題,たとえば薄肉構造の局所座屈に代表されるような問題では,部分的な変形が隣接する部分の変形を促し,それらの間でひずみエネルギの授受を伴いながら構造全体の不安定性が増大したり,あるいは解消する挙動が現れる.構造全体の挙動を一つのパラメータによって制御する手法,例えば弧長法によってこの種の問題を安定に解くことは難しく,慣性力あるいは粘性力の効果を導入し,ひずみエネルギの局所的な消散を適正に表現する必要がある.これまで適用例が多い動的陽解法は,その一つの便法である.本研究では最近の汎用FEMを使用し,人工的な粘性を与えることによって局所的な構造不安定に起因する解析の困難を克服した.圧縮を受ける完全円筒に近い弾性円筒シェルを手始めに,材料に起因する不安定現象を含め,全自動かつシームレスの解析によって深い後座屈の領域までをトレースすることが可能になったので報告する.