Excerpt from On the Numerical Determination of Shrinkage Stresses A thin rectangular elastic plate is heated uniformly and then an edge is bonded to a rigid half-space. In this paper we present a numerical method to determine the shrinkage stresses which develop when the plate cools. We assume that the deformations of the plate are adequately described by the theory of plane stress. Thus we must solve a mixed boundary value problem, which we call Problem S, for the two dimensional displacement equations of equilibrium. It ...
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Excerpt from On the Numerical Determination of Shrinkage Stresses A thin rectangular elastic plate is heated uniformly and then an edge is bonded to a rigid half-space. In this paper we present a numerical method to determine the shrinkage stresses which develop when the plate cools. We assume that the deformations of the plate are adequately described by the theory of plane stress. Thus we must solve a mixed boundary value problem, which we call Problem S, for the two dimensional displacement equations of equilibrium. It is solved by a previously developed [1] accelerated iteration method.* Each iterate is the solution of a mixed boundary value problem for Poisson's equation. The iterates are numerically determined by approximating this boundary value problem by difference equations. The resulting system of linear algebraic equations is of quasi tridiagonal form. It is solved by a direct factorization method The procedure is suitable for use with a digital computer. It is applicable to other shrinkage problems with more complicated geometries. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This 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.
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