薄肉球殼の座屈に関する一考察

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タイトル別名
  • A STUDY ON THE BUCKLING OF SIN SPHERICAL SHELLS BY EXTERNAL PRESSURE
  • 薄肉球殻の座屈する一考察
  • ウスニク キュウカラ ノ ザクッスル イチ コウサツ

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The critical stress for an ideal spherical shell under uniform external pressure is given by the formula [numerical formula]. It is almost four times greater than the experimental value. In putting forward their explanation of the discrepancy between experiment and the classical theory, Th. Von Karman and others made the assumption that a "jamp" or "snap" into the buckled state is possible if the shape of the shell is imperfect or if the applied pressure is pulsating. However, these theorys did not suceed in giving a satisfactory solution to the problem of determining the minimum pressure in a non-linear state. In the exposition of this question we shall follow our energy method. Intreducing the notations II_0: Total energy in the first form of equilikrium. II_1: Total energy in the additional condition of equilibrium. y: Unit additional displacement. We set up the expression △II=II_1-II_0, if u_1 and w_1 is the symmetrical additional displacement for the axis, and taking expressions for the conditions with the stable and unstable states of equilibrium merge into one state, namly setting: (2:11). Besides, we set up the expression (5:11) that the additional functions ξ(φ) and η(φ) satisfying the equation (2:11). Results of calculations carried out for values of σ_<ck>, we also found the value: [numerical formula] Secondly, we setting (5:11), and we obtain: [numerical formula].

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