On Saint-Venant's Principle for a Curvilinear Rectangle in Linear Elastostatics  

Oleh:

Flavin, J.N. ; Gleeson, B.

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: Mathematics and Mechanics of Solids vol. 8 no. 4 (Aug. 2003), page 337-348.
Topik: Spatial decay; Saint-venant principle; two-dimensional elastostatics; curvilinear rectangle
Fulltext: 337MMS84.pdf (158.66KB)

Isi artikel

Solutions of the biharmonic equation are considered in the curvilinear rectangular region 0 <, 0 a, a <, r < b in the presence of boundary conditions 0 = 0,. = 0 on the edges r = a, r = b, 0 = 00 = 0 on the edge 0 = a, (r, 0) denoting plane polar coordinates, a, b, a(< 27r) being constants; non-null boundary conditions are envisaged on the other edge 0 = 0, involving the specification of 0, 0a thereon. An energy-like measure E(B) of the solution in the region between arbitrary 0 and 0 = a is defined, and is proven to be positive definite provided that b/a < e°`. It is established that E(B)/E(0) decays (at least) exponentially with respect to 0, under the aforementioned restriction on b/a. Additionally, a principle of the Dirichlet type is established (again provided b/a < e°`), which provides an upper bound for E(0) in terms of data (0 and 0B) prescribed on the edge 0 = 0. When combined with the earlier result we obtain an explicit upper decay estimate for E(B). The estimate can be regarded as a version of Saint-Nbnant's principle for a curvilinear strip, in the context of two-dimensional (homogeneous isotropic) elastostatics, the edge 0 = 0 being subjected to a self-equilibrated (in-plane) load, the remainder of the boundary being traction-fire. The Saint-venant estimate continues to hold, mutatis mutandis, for any simply connected, two-dimensional domain, whose boundary consists of a straight line 0 = 0, carrying a self-equilibrated load, and a smooth (traction-free) curve.

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