Matches in SemOpenAlex for { <https://semopenalex.org/work/W2102771906> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W2102771906 abstract "If a thin elastic circular plate B : ∣ z ∣ < 1 is clamped (simply supported, respectively) along its edge ∣ z ∣ = 1, its deflection at z ∈ B under a point load at ζ ∈ B , measured positively in the direction of the gravitational pull, is the biharmonic Green's function β( z , ζ) of the clamped plate (γ( z , ζ) of the simply supported plate, respectively). We ask: how do β( z , ζ) and γ( z , ζ) compare with the corresponding deflections β 0 ( z , ζ) and γ 0 ( z , ζ) of the punctured circular plate B 0 : 0 < ∣ z ∣ < 1 that is “clamped” or “simply supported”, respectively, also at the origin? We shall show that γ( z , ζ) is not affected by the puncturing, that is, γ(·, ζ) = γ 0 (·, ζ), whereas β(·, ζ) is: on B 0 × B 0 . Moreover, while β((·, ζ) is of constant sign, β 0 (·, ζ) is not. This gives a simple counterexmple to the conjecture of Hadamard [6] that the deflection of a clampled thin elastic plate be always of constant sign: The biharmonic Gree's function of a clampled concentric circular annulus is not of constant sign if the radius of the inner boundary circle is sufficiently small . Earlier counterexamples to Hadamard's conjecture were given by Duffin [2], Garabedian [4], Loewner [7], and Szegö [9]. Interest in the problem was recently revived by the invited address of Duffin [3] before the Annual Meeting of the American Mathematical Society in 1974. The drawback of the counterexample we will present is that, whereas the classical examples are all simply connected, ours is not. In the simplicity of the proof, however, there is no comparison." @default.
- W2102771906 created "2016-06-24" @default.
- W2102771906 creator A5015619807 @default.
- W2102771906 creator A5062118211 @default.
- W2102771906 date "1977-12-01" @default.
- W2102771906 modified "2023-09-23" @default.
- W2102771906 title "Green's function of the clamped punctured disk" @default.
- W2102771906 cites W1982789125 @default.
- W2102771906 cites W2046557222 @default.
- W2102771906 cites W2099050224 @default.
- W2102771906 cites W2141069455 @default.
- W2102771906 cites W2319012751 @default.
- W2102771906 cites W2335044413 @default.
- W2102771906 doi "https://doi.org/10.1017/s0334270000001557" @default.
- W2102771906 hasPublicationYear "1977" @default.
- W2102771906 type Work @default.
- W2102771906 sameAs 2102771906 @default.
- W2102771906 citedByCount "4" @default.
- W2102771906 countsByYear W21027719062013 @default.
- W2102771906 countsByYear W21027719062015 @default.
- W2102771906 crossrefType "journal-article" @default.
- W2102771906 hasAuthorship W2102771906A5015619807 @default.
- W2102771906 hasAuthorship W2102771906A5062118211 @default.
- W2102771906 hasBestOaLocation W21027719061 @default.
- W2102771906 hasConcept C114614502 @default.
- W2102771906 hasConcept C121332964 @default.
- W2102771906 hasConcept C134306372 @default.
- W2102771906 hasConcept C139676723 @default.
- W2102771906 hasConcept C145784156 @default.
- W2102771906 hasConcept C162838799 @default.
- W2102771906 hasConcept C182310444 @default.
- W2102771906 hasConcept C199360897 @default.
- W2102771906 hasConcept C2524010 @default.
- W2102771906 hasConcept C2777027219 @default.
- W2102771906 hasConcept C2780990831 @default.
- W2102771906 hasConcept C2781355719 @default.
- W2102771906 hasConcept C33923547 @default.
- W2102771906 hasConcept C41008148 @default.
- W2102771906 hasConcept C60292330 @default.
- W2102771906 hasConcept C62520636 @default.
- W2102771906 hasConcept C90296322 @default.
- W2102771906 hasConceptScore W2102771906C114614502 @default.
- W2102771906 hasConceptScore W2102771906C121332964 @default.
- W2102771906 hasConceptScore W2102771906C134306372 @default.
- W2102771906 hasConceptScore W2102771906C139676723 @default.
- W2102771906 hasConceptScore W2102771906C145784156 @default.
- W2102771906 hasConceptScore W2102771906C162838799 @default.
- W2102771906 hasConceptScore W2102771906C182310444 @default.
- W2102771906 hasConceptScore W2102771906C199360897 @default.
- W2102771906 hasConceptScore W2102771906C2524010 @default.
- W2102771906 hasConceptScore W2102771906C2777027219 @default.
- W2102771906 hasConceptScore W2102771906C2780990831 @default.
- W2102771906 hasConceptScore W2102771906C2781355719 @default.
- W2102771906 hasConceptScore W2102771906C33923547 @default.
- W2102771906 hasConceptScore W2102771906C41008148 @default.
- W2102771906 hasConceptScore W2102771906C60292330 @default.
- W2102771906 hasConceptScore W2102771906C62520636 @default.
- W2102771906 hasConceptScore W2102771906C90296322 @default.
- W2102771906 hasLocation W21027719061 @default.
- W2102771906 hasOpenAccess W2102771906 @default.
- W2102771906 hasPrimaryLocation W21027719061 @default.
- W2102771906 hasRelatedWork W126594179 @default.
- W2102771906 hasRelatedWork W1552449299 @default.
- W2102771906 hasRelatedWork W1554952955 @default.
- W2102771906 hasRelatedWork W1999624841 @default.
- W2102771906 hasRelatedWork W2069624256 @default.
- W2102771906 hasRelatedWork W2119687747 @default.
- W2102771906 hasRelatedWork W2130616910 @default.
- W2102771906 hasRelatedWork W2224059946 @default.
- W2102771906 hasRelatedWork W2253383015 @default.
- W2102771906 hasRelatedWork W2255992453 @default.
- W2102771906 hasRelatedWork W2270048742 @default.
- W2102771906 hasRelatedWork W2284557637 @default.
- W2102771906 hasRelatedWork W2319771370 @default.
- W2102771906 hasRelatedWork W2323443721 @default.
- W2102771906 hasRelatedWork W2409382102 @default.
- W2102771906 hasRelatedWork W251048310 @default.
- W2102771906 hasRelatedWork W2906921889 @default.
- W2102771906 hasRelatedWork W2953120335 @default.
- W2102771906 hasRelatedWork W2963757881 @default.
- W2102771906 hasRelatedWork W2970414351 @default.
- W2102771906 isParatext "false" @default.
- W2102771906 isRetracted "false" @default.
- W2102771906 magId "2102771906" @default.
- W2102771906 workType "article" @default.