TY - JOUR
T1 - Some decay and other estimates in two-dimensional linear elastostatics
AU - Flavin, J. N.
AU - Knops, R. J.
PY - 1988/5
Y1 - 1988/5
N2 - 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. © 1988 Oxford University Press.
AB - 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. © 1988 Oxford University Press.
UR - http://www.scopus.com/inward/record.url?scp=0009284251&partnerID=8YFLogxK
U2 - 10.1093/qjmam/41.2.223
DO - 10.1093/qjmam/41.2.223
M3 - Article
SN - 0033-5614
VL - 41
SP - 223
EP - 238
JO - Quarterly Journal of Mechanics and Applied Mathematics
JF - Quarterly Journal of Mechanics and Applied Mathematics
IS - 2
ER -