Some static and dynamic problems concerning non-linear behavior of plates and shallow shells with discontinuous boundary conditions

Abstract

Berger's field equations are generalized to dynamic phenomena in anisotropic plates and shallow shells the anisotropy being either of a cylindrically orthotropic or rectilinearly orthotropic type. Under the assumption that the rim of the structure is prevented from inplane motions explicit equations for the coupling parameter are given. Method of solution in the dynamic case is illustrated by an example involving isotropy and original axial symmetry of the structure. It is shown that for the non-linear oscillations of built-in circular plates a close agreement is reached with the results obtained by means of the Von Kármán field equations and a different coordinate function. The procedure suggested for solution of dynamic problems associated with the discontinuities of the boundary conditions is discussed and illustrated on an isotropic case involving a circular plate partially simply supported and partially clamped at the periphery. A numerical example is given concerning static behavior of an infinite isotropic strip uniformly loaded and simply supported along the edges except for two symmetrically situated built-in segments. The dependence of the average moment of clamping on the width of the built-in segments as well as on the load intensity for a fixed width of the segments is displayed on graphs.