The 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.

1 Basic relations in theories of elastic plates.- I Isotropic rectangular plates.- 2 Differential equations of the component theory.- 3 The Reissner plate theory.- 4 Refined theory of Hencky.- 5 Refined theory of Kromm.- 6 Generalized theory.- 7 Boundary conditions.- 8 Bending of long rectangular plates to a cylindrical surface.- 9 Solution of the boundary value problem for a rectangular plate.- 10 Plate with two opposite edges simply supported.- 11 Free rectangular plate.- 12 Simply supported plate subjected to boundary bending moments.- 13 Completely simply supported plate under distributed loading.- 14 Completely built-in plate under distributed loading.- 15 Plate with two opposite edges simply supported and the other two edges free under a continuous load.- 16 Plate with two opposite edges simply supported and the other two edges built-in under a continuous load.- II Orthotropic rectangular plates.- 17 Differential equations of the component theory. Case H= (KxKy)¿.- 18 Generalized theory.- 19 Refined theory developed by K. Girkmann and R. Beer.- 20 General solution of the boundary value problem according to the component theory.- 21 Orthotropic rectangular plate under a continuous load.- III Isotropic circular plates.- 22 Differential equations of the component theory in cylindrical coordinates.- 23 Generalized theory of circular plates.- 24 Rotationally symmetrical bending.- 25 Circular plates under rotationally symmetrical loads.- 26 Annular plates under rotationally symmetrical loads.- 27 General solution of governing equations of the component theory for loads distributed according to the law p?(?) sin n ?.- 28 Antisymmetrical bending of a circular plate under the load ?? sin ?.- IV Circular plates on elastic foundation under rotationally symmetricalloads.- 29 Governing equations of the component theory.- 30 Auxiliary formulae for Bessel functions.- 31 Functions expressing the general solution of the homogeneous problem.- 32 Fundamental solution.- 33 Compensating solution.- 34 Numerical example.- Author index.