By C. von Westenholz (Eds.)
The target of quantity III is to put down the right kind mathematical foundations of the two-dimensional concept of shells. To this finish, it presents, with none recourse to any a priori assumptions of a geometric or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, via asymptotic tools, with the thickness because the "small" parameter.
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Additional info for Differential Forms in Mathematical Physics
Linearized change of c u r v a t u r e tensor on a surface . 6. Inequalities of K o r n ' s t y p e a n d infinitesimal rigid disp l a c e m e n t l e m m a on a general surface . . . . . 100 I n e q u a l i t y of K o r n ' s t y p e a n d infinitesimal rigid disp l a c e m e n t l e m m a on an elliptic surface . . . . 8 ~. C o m p l e m e n t - Recovery of a surface from its m e t r i c a n d c u r v a t u r e tensor fields . . . . . . . . 7. Exercises Chapter . . . . . . .
2. T h e t h r e e - d i m e n s i o n a l equations over a d o m a i n independent ofe ....................... 3. G e o m e t r i c a l a n d mechanical preliminaries . . . . 4. T h e t w o - d i m e n s i o n a l equations of linearly elastic " m e m b r a n e " a n d "flexural" shells derived by m e a n s of a f o r m a l a s y m p t o t i c analysis . . . . . . . . 5. S u m m a r y of the convergence t h e o r e m s . . . . . 183 Exercises 190 . . . . . . . . . . . .
P - Po U rl" partition of the boundary of ~ with area ro > O. O 9~ C R 3 -+ R 3" injective and smooth enough mapping such that the three vectors 0 i 0 are linearly independent at all points in ~. O ( ~ ) C R 3" reference configuration of an elastic body. AiJkl _ Agijgkl § #(gik gjl § gil gjk). contravariant components of the three-dimensional elasticity tensor. )~ ) 0 and # > 0" Lam~ constants of a homogeneous, isotropic, elastic material, whose reference configuration is a natural state. fi E L2(g2) 9 contravariant components of the applied body force density.