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By Pierre Ladeveze

Neighborhood results within the research of buildings

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L ) z = -h r = 0, z = h. 3) (2) Now i n ( 1 1 . 3, σ·-|j·} e t c . 2) while the exact s o l u t i o n may be replaced (with e x p o n_e n t i a l l__ y small e r r o r as h-*0) by the bending p a r t of the i n t e r i o r s o l u t i o n { u . , σ . · } , derived from ( 5 . 1 ) . (The I I extensional p a r t of { u . , σ . ) J On making these s u b s t i t u t i o n s , we o b t a i n a f t e r some s i m p l i - ' j f i c a t i o n that B = - ϋτ^τ1 h2A · (n·4» Now it easily follows from the overall equilibrium of the region |z| s h that A = -P/S-nd Kirchhoff theory.

L , "Energy i n e q u a l i t i e s and e r r o r estimates f o r t o r s i o n of e l a s t i c s h e l l s o f r e v o l u t i o n " , ZAMP, V o l . 2 1 , 1970, p. 352377. J . L , "Les inéquations en mécanique e t en physique", 22 Gol'Denveizer "Theory of e l a s t i c t h i n s h e l l s " , Pergamon Press, 1961. 23 Maisonneuve 1971. T, and Horgan C O , "A two-dimensional Saint-Venant P r i n c i p l e f o r second order l i n e a r e l l i p t i c e q u a t i o n s " , Quart. Appl. M a t h .

Here 9Z sequel, hole by will denote the set define the of all holes. 5) (y- ,y„ ,y~), y_ = 0 rectangles considered J-) + -— 9 x "perturbed" problem. a plane, where the plane into the holes") section space = — (2 9 x . e. the holes. e. : ε 8 σ.. 0ue) n. 3. 8) ASYMPTOTIC EXPANSION Coming back to figure 1, it is clear that some sort of layer holds in the vicinity of Σ. According to the classical techniques of inner and outer expansions (cf. 1) in order to dilate the layer, and we shall search for two different asymptotic expansions out of the layer (outer expansion) and in the layer (inner expansion).

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