Zusammenfassung
Diese Arbeit befasst sich mit der allgemeinen Behandlung antiklastischer Durchbiegungsprobleme. Von Kármáns Gleichung für grosse Durchbiegungen und antiklastische Deformation wurden mit Hilfe der Frobeniusschen Methode gelöst. Für Platten, deren Dicke proportional einer beliebigen Potenz des Abstandes vom Plattenrand ist, wurden Lösungen in Form allgemeiner hypergeometrischer Funktionen ausgearbeitet. Numerische Resultate für antiklastische Deformation werden für verschiedene Plattendicken präsentiert.
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Abbreviations
- A i :
-
integration constants
- a ir :
-
coefficients of the series
- b :
-
halfwidth of plate
- b i :
-
characteristic numbers, functions ofn, defined by Equation (11)
- c ij :
-
=b j −b i +1
- p F q :
-
generalized hypergeometric function, defined by Equation (18)
- H :
-
harmonic sum, defined by Equation (23)
- n :
-
thickness variation parameter
- R :
-
longitudinal radius of curvature
- s i :
-
roots of indicial equation
- t :
-
thickness of plate
- t o :
-
thickness of plate aty=0
- u :
-
=Y y1
- w(y) :
-
transverse deflection of a bent strip atx=0
- w c :
-
complementary part of solutionw
- w p :
-
particular part of solutionw
- w (oy) :
-
initial deviation of middle surface of strip fromx-y plane atx=0
- x, y, z :
-
rectangular Cartesian coordinates, defined in Figure 1
- y 1 :
-
=1-y/b
- γ:
-
=4-2n
- δ:
-
=y 1 d/dy 1
- δ u :
-
=u d/du
- λ:
-
\( = b[3(1 - \mu ^2 )]^{1/4} /\sqrt {R t_0 } \)
- μ:
-
Poisson's ratio
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Pao, Y.C., Wang, H.C. Hypergeometric series solutions of some anticlastic deformation problems. Journal of Applied Mathematics and Physics (ZAMP) 18, 889–899 (1967). https://doi.org/10.1007/BF01602726
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DOI: https://doi.org/10.1007/BF01602726