NEAR-BOUNDARY EXPANSION OF GREEN'S FUNCTION ASSOCIATED WITH CLAMPED PLATES

• Published in: Quarterly of applied mathematics 1976-04, Vol.34 (1), p.39-45
• Main Author: WU, CHIEN-HENG
• Format: Article
• Language: English
• Subjects: Boundary conditions; Coefficients; Greens function; Mathematical functions; Sine function
• ISSN: 0033-569X; 1552-4485
• DOI: 10.1090/qam/455712

The Green's function G(P, P') associated with a clamped plate of arbitrary shape is considered, when P' is at a distance 0(∊) from a regular point O of the boundary. First an outer expansion of G is described, valid when P is not near P'. Then an inner expansion of G is constructed when both P and P' are near 0. The leading term of the inner expansion is just the Green's function Gs for the halfplane bounded by the tangent to the boundary at O, and ∊⁻² Gs differs from ∊⁻²Gs by O(∊). The first two terms of inner expansion agree with the first two terms of the expansion of Gc, the Green's function for the interior of the osculating circle of the boundary at 0, if the boundary is convex at O. If it is concave, Gc is the Green's function for the exterior of the osculating circle. Moreover, ∊⁻²G differs from ∊⁻² Gc by O(∊²). A two-term inner expansion is explicitly given.