Theories of elastic plates

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)½.- 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.