Corner singularities and regularity results for the Reissner/Mindlin plate model

Journal of Elasticity

Volumn 103, Issue 2, 2011, Pages 113-135

  Rössle, Andreas ^a   Sändig, Anna Margarete ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Corner singularities; Elliptic boundary value problem for systems; Regularity results in polygons; Reissner Mindlin plate

Indexed keywords

CORNER SINGULARITY; ELLIPTIC BOUNDARY VALUE PROBLEM; ELLIPTIC BOUNDARY VALUE PROBLEM FOR SYSTEMS; ELLIPTIC SYSTEM; MATERIAL PARAMETER; POLYGONAL DOMAIN; REAL NUMBER; REGULARITY RESULTS IN POLYGONS; REISSNER-MINDLIN PLATE; STRESS POTENTIAL; WEAK SOLUTION;

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; GEOMETRY; ORDINARY DIFFERENTIAL EQUATIONS; SOBOLEV SPACES;

MINDLIN PLATES;

EID: 79952195182     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-010-9258-5     Document Type: Article

References (25)

1. M.S. Agranovic M.I. Vishik 1964 Elliptic problems with a parameter and parabolic problems of general type Russ. Math. Surv. 19 53 157 10.1070/RM1964v019n03ABEH001149
2. S. Agmon A. Douglis L. Nirenberg 1959 Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I Comm. Pure Appl. Math. 12 623 727 0093.10401 10.1002/cpa. 3160120405 125307
3. S. Agmon A. Douglis L. Nirenberg 1964 Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II Comm. Pure Appl. Math. 17 35 92 0123.28706 10.1002/cpa.3160170104 162050
4. I. Babuška L. Li 1991 Hierarchic modelling o (Pubitemid 21664208)
5. I. Babuška L. Li 1992 The problem of plate modeling: Theoretical and computational results Comput. Methods Appl. Mech. Eng. 100 249 273 0764.73040 10.1016/0045-7825(92)90185-M (Pubitemid 23570567)
6. H. Blum R. Rannacher 1980 On the boundary value problem of the biharmonic operator on domains with angular corners Math. Methods Appl. Sci. 2 556 581 0445.35023 10.1002/mma.1670020416 595625 1980MMAS....2..556B
7. W.S. Burton G.B. Sinclair 1986 On the singularities in Reissner's theory for the bending of elastic plates J. Appl. Mech. 53 220 222 10.1115/1.3171716 (Pubitemid 16537012)
8. P. Grisvard 1989 Singularités en elasticité Arch. Ration. Mech. Anal. 107 157 180 0706.73013 10.1007/BF00286498 996909
9. Lagnese, J.E.: Boundary stabilization of thin plates. SIAM Stud. Appl. Math., vol. 10. SIAM, Philadelphia (1989)
10. V.A. Kondrat'ev 1967 Boundary value problems for elliptic equations in domains with conical or angular points Trans. Mosc. Math. Soc. 16 227 312 0194.13405
11. Kozlov, V.A., Maz'ya, V.G., Rossmann, J.: Elliptic Boundary Value Problems in Domains with Point Singularities. American Mathematical Society, Providence (1997)
12. Kozlov, V.A., Maz'ya, V.G., Rossmann, J.: Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations. American Mathematical Society, Providence (2001)
13. H. Melzer R. Rannacher 1980 Spannungskonzentrationen in Eckpunkten der Kirchhoffschen Platte Bauingenieur 55 181 184
14. R.D. Mindlin 1951 Influence of rotary inertia and shear on flexural motions of elastic plates Trans. ASME Ser. E 18 31 38 0044.40101
15. Morozov, N.F.: Matematicheskye voprosy teorii treshchin (Mathematical Methods in the Theory of Cracks). Nauka, Moscow (1984), in Russian
16. E. Reissner 1944 On the theory of bending of elastic plates J. Math. Phys. 23 184 191 0061.42501 11647
17. A. Rössle 2000 Corner singularities and regularity of weak solutions for the two-dimensional Lamé equations on domains with angular corners J. Elast. 60 57 75 0976.74019 10.1023/A:1007639413619 (Pubitemid 32409067)
18. Rössle, A., Sändig, A.-M.: Corner singularities and regularity results for the Reissner/Mindlin plate model. Report 2001/04 of the SFB 404 at the University Stuttgart (2001)
19. A. Rössle M. Bischoff W. Wendland E. Ramm 1999 On the mathematical foundation of the (1,1,2)-plate model Int. J. Solids Struct. 36 2143 2168 0962.74036 10.1016/S0020-7683(98)00071-7
20. A.-M. Sändig U. Richter R. Sändig 1989 The regularity of boundary value problems for the Lamé equations in a polygonal domain Rostock. Math. Kolloqui. Heft 36 21 50 0674.35024
21. Schwab, C.: Hierarchic models of elliptic boundary value problems on thin domains-a-posteriori error estimation and Fourier analysis. Habilitation thesis, University of Stuttgart, Mathematical Institute A (1995)
22. C. Schwab 1996 A-posteriori modeling error estimation for hierarchic plate models Num. Math. 74 221 259 0856.73031 10.1007/s002110050215 1403898 (Pubitemid 126108501)
23. C. Schwab S. Wright 1995 Boundary layers of hierarchical beam and plate models J. Elast. 38 1 40 0834.73040 10.1007/BF00121462 1323554
24. Wloka, J.T., Rowley, B., Lawruk, B.: Boundary Value Problems for Elliptic Systems. Cambridge University Press, Cambridge (1995)
25. D.H.Y. Yen M. Zhou 1989 On the corner singularities in Reissner's theory for the bending of elastic plates J. Appl. Mech. 56 726 729 0723.73053 10.1115/1.3176159 (Pubitemid 20655183)