A Kirchhoff Thin Shell Theory (Classic Reprint)

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Excerpt from A Kirchhoff Thin Shell TheoryThis paper presents a mathematical theory for the deforma tions of isotropic shells under the applications of edge forces. The theory is obtained by imposing the principal of virtual work on the class of deformations which satisfy the Kirchhoff hypothesis, i.e. Those deformations which carry normals to the undeformed middle surface into normals to the deformed middle surface with no change in length along normals. It is not assumed that displacements, strains, or slopes are small. Although in the derivation of the model it is not assumed that the shell is thin, we do not expect the theory to be physically realistic unless the shell is in fact thin.Imposing the principal of virtual work yields a system of differential equations for the three components of position of the deformed middle surface and six relations between the applied edge forces and the deformed middle surface. It will be shown that the system of differential equations can be expressed as a tenth order system. The six relations between edge forces and deformed middle surface contain two arbitrary functions and hence represent four boundary constraints on the deformed middle surface when the edge forces are prescribed.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.