C. Schwab, "A-posteriori modeling error estimation for hierarchic plate models", Num. Math. 74(1996) 221-259. Home/Search Document Details and Download
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Asymptotics of Arbitrary Order for a Thin Elastic Clamped.. - Dauge, Gruais (1995) (2 citations) (Correct)
....ijkl , satisfies the usual symmetry relations A ijkl = A jikl = A ijlk = A klij and is supposed to be uniformly positive definite, namely: 8x 2 Omega ; 8(t ij ) 2 R 9 s.t. t ij = t ji ; A ijkl (x ) t kl t ij c t 2 ij (1.2) where c 0 is a positive constant. Moreover, as in [16] [38] we assume that 8 : A fffifl3 = 0 8ff; fi; fl 2 f1; 2g A ff333 = 0 8ff 2 f1; 2g: 1.3) The relations (1.3) are satisfied for any isotropic material, and also for an orthotropic material whose orthotropy axes are either normal or tangent to the plane containing . Property (1.3) is referred ....
....assume that 8 : A fffifl3 = 0 8ff; fi; fl 2 f1; 2g A ff333 = 0 8ff 2 f1; 2g: 1.3) The relations (1.3) are satisfied for any isotropic material, and also for an orthotropic material whose orthotropy axes are either normal or tangent to the plane containing . Property (1. 3) is referred in [38] as the characterization of monoclinic materials, and it is noted there that this is the weakest assumption so that the system of elasticity can be uncoupled into a bending and a membrane problems. To simplify our forthcoming analysis, we moreover assume at this stage that the coefficients of A do ....
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C. Schwab. A-posteriori modeling error estimation for hierarchic plate models. Preprint, University of Maryland, Baltimore, Maryland 1994.
Asymptotics of Arbitrary Order for a Thin Elastic Clamped.. - Dauge, Gruais (1995) (2 citations) (Correct)
.... ; 8(t ij ) 2 R 9 s.t. t ij = t ji ; A ijkl (x ) t kl t ij c t 2 ij (1.2) where c 0 is a positive constant. Moreover, we assume that the coefficients of A do not depend on the vertical coordinate x 3 and smoothly depend on the in plane variables (x 1 ; x 2 ) and, as in [12] [24] that 8 : A fffifl3 = 0 8ff; fi; fl 2 f1; 2g A ff333 = 0 8ff 2 f1; 2g: 1.3) The relations (1.3) are satisfied for any isotropic material, and allow the uncoupling of the system of elasticity into bending and membrane problems. Problem (1.1) is studied with the help of a scaling in order to ....
C. Schwab. A-posteriori modeling error estimation for hierarchic plate models. Preprint, University of Maryland, Baltimore, Maryland 1994.
Analysis of membrane locking in hp FEM for a cylindrical shell - Gerdes, Matache, Schwab Self-citation (Schwab) (Correct)
....three dimensional and two dimensional linearly elastic models (see [4] and the references there) much work needs to be done on the computable a posteriori estimation of the shell modeling error. Any such estimate requires, however, an accurate numerical solution of the shell model itself (see [13] for an analysis of the plate case) Here, the hp FEM seems to be an attractive alternative to other, more classical approaches, or to approaches tailored specifically to bending dominated shells. A Appendix Theorem A.1 The roots of the characteristic polynomial P ( t; 3t 4 10 ....
C. Schwab, "A-posteriori modeling error estimation for hierarchic plate models", Num. Math. 74(1996) 221-259.
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