SOME DECAY AND OTHER ESTIMATES IN TWO-DIMENSIONAL LINEAR ELASTOSTATICS
James N. Flavin, Robin John Knops · The Quarterly Journal of Mechanics and Applied Mathematics · 1988
A displacement boundary-value problem is considered for a two-dimensional, simply-connected region consisting of homogeneous, isotropic, linear elastic material. The region is bounded by two straight edges (one of which may be degenerate to a point, however) parallel to the x1-coordinate axis. The straight edges are subject to specified displacements while the other (lateral) boundaries are subject to zero displacement. Explicit upper bounds in terms of the data are obtained for a certain cross-sectional mean-square measure of the first-order displacement derivatives, and it is shown how pointwise bounds on the displacement may be deduced therefrom. For a certain subclass of the problems considered, the estimates obtained are of the exponential decay type which have come to be associated with Saint-Venant's principle.