Theories of elastic platesThe present monograph deals with refined theories of elastic plates in which both bending and transverse shear effects are taken into account and with some of their applications. Generally these more exact theories result in inte gration problems of the sixth order; consequently, three mutually independent boundary conditions at each edge of the plate are required. This is in perfect agreement with the conclusions of the theory of elasticity. The expressions for shearing forces following from refined theories are then valid for the whole investigated region including its boundary where the corresponding boundary conditions for these shearing forces can be prescribed. Quite different seems to be the situation in the classical Kirchhoff-Love's theory in which the influence of transverse shearing strains is neglected. Owing to this simplification the governing differential equation developed by the classical theory is of the fourth order only; consequently, the number of boundary conditions appurtenant to the applied mode of support appears now to be in disagreement with the order of the valid governing equation. Then, limiting the validity of the expressions for shearing forces to the open region of the middle plane and introducing the notion of the so called fictitious Kirchhoff's shearing forces for the boundary of the plate, three actual boundary conditions at each edge of the plate have to be replaced by two approximate conditions transformed in the Kirchhoff's sense. |
Contents
I | xiii |
II | 1 |
IV | 11 |
V | 13 |
VII | 34 |
IX | 42 |
XI | 54 |
XIII | 88 |
XXXIII | 414 |
XXXV | 429 |
XXXVII | 440 |
XXXVIII | 452 |
XL | 473 |
XLI | 475 |
XLII | 497 |
XLIV | 506 |
XV | 97 |
XVII | 118 |
XIX | 197 |
XX | 207 |
XXII | 262 |
XXIV | 304 |
XXV | 324 |
XXVI | 357 |
XXVIII | 375 |
XXIX | 384 |
XXX | 391 |
XXXI | 393 |
XLVI | 517 |
XLVIII | 535 |
L | 549 |
LI | 572 |
LII | 579 |
LIII | 581 |
LV | 592 |
LVII | 600 |
LVIII | 613 |
LX | 644 |
LXII | 655 |
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Common terms and phrases
A₁ a²w according to Eqs amBn ax² B₁ B₂ B₂n bending moments Bessel functions boundary bending boundary bending moments boundary conditions C₁ C₂ ch² circular plate classical theory component theory constants of integration corresponding D₁ defined by Eqs deflection denote dx² elastic equilibrium conditions expressions extr factor formulae governing equations k,ßx k₁ kmam kmamb Kromm lateral load notations obtain Pa² particular solution quantities refined theories relations respect sh kay sh ẞx shamy shearing forces shearing strains shearing stresses simply supported ß² ẞny stress components Substituting Table transverse shearing strains twisting moments v₁(e values vo(e w₁ yield ηπ ΜΠ ΣΣ Впа др дх ду მთ