Folded shells: A variational approach. (English) Zbl 0780.73043
Folded shells are characterized by the fact that their regular part is a smooth two-dimensional surface in \(\mathbb{R}^ 3\) and their singular part is a smooth curve in \(\mathbb{R}^ 3\). The theory starts from a three- dimensional elastic body passing to the limit “thickness \(\to 0\)”. The investigation is based on a variational method and results in the physical elucidation of the convergence of the minimizing sequence of the approximating problems to the solution of a limiting minimization problem. The case of a smooth curve in \(\mathbb{R}^ 2\) with a point in \(\mathbb{R}^ 2\) as its singular part is considered also. Two examples are presented.
Reviewer: H.Bufler (Stuttgart)
MSC:
| 74K15 | Membranes |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74P10 | Optimization of other properties in solid mechanics |
References:
| [1] | E. Acerbi - G. Buttazzo - D. Percivale , Thin inclusions in linear elasticity; a variational approach , J. Reine Angew. Math. 300 ( 1988 ), pp. 1 - 16 . MR 936993 | Zbl 0633.73021 · Zbl 0633.73021 · doi:10.1515/crll.1988.386.99 |
| [2] | D. Caillerie , The effect of a thin inclusion of high rigidity in an elastic body , Math. Methods Appl. Sci. 2 ( 1980 ), pp. 251 - 270 . MR 581205 | Zbl 0446.73014 · Zbl 0446.73014 · doi:10.1002/mma.1670020302 |
| [3] | P.G. Ciarlet - P. Destuynder , A justification of the two-dimensional linear plate model , J. Méc. Théor. Appl. 18 ( 1979 ), pp. 315 - 344 . MR 533827 | Zbl 0415.73072 · Zbl 0415.73072 |
| [4] | P.G. Ciarlet - H. Le Dret - R. Nzengwa , Modelisation de la jonction entre un corps élastique tridimensionnel et une plaque , C.R. Acad. Sci. Paris Sér. I Math. 305 ( 1987 ), pp. 55 - 58 . MR 902275 | Zbl 0632.73015 · Zbl 0632.73015 |
| [5] | P.G. Ciarlet - H. Le Dret , Justification de la condition aux limite d’encastrement d’une plaque par une méthode asymptotique , C.R. Acad. Sci. Paris Sér. I Math. 307 ( 1988 ), pp. 1015 - 1018 . MR 978264 | Zbl 0679.73008 · Zbl 0679.73008 |
| [6] | E. De Giorgi - G. Dal Maso , \Gamma -convergence and Calculus of Variations , Lecture Notes in Math. 979 , Springer Verlag . ( 1983 ). Zbl 0511.49007 · Zbl 0511.49007 |
| [7] | M.P. D , Differential geometry of curves and surfaces , Englewood-Cliff. ( 1976 ). Zbl 0326.53001 · Zbl 0326.53001 |
| [8] | I. Ekeland - R. Temam , Convex Analysis and Variational problems , North Holland ( 1976 ). MR 463994 | Zbl 0322.90046 · Zbl 0322.90046 |
| [9] | R.V. Kohn - M. Vogelius , A new model for thin plates with rapidly varying thichness II; a convergence proof , Quart. Appl. Math. 43 ( 1985 ), pp. 1 - 23 . MR 782253 | Zbl 0565.73046 · Zbl 0565.73046 |
| [10] | H. Le Dret , Modelisation d’une plaque pliee , (preprint). |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
