The axisymmetric deformation of a thin, or moderately thick, elastic spherical cap

Studies in Applied Mathematics

Volumn 100, Issue 1, 1998, Pages 67-94

  Gregory, R Douglas ^b   Milac, Thomas I ^a   Wan, Frederic Y M ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; SHELLS (STRUCTURES); SPHERES;

ASYMPTOTIC THEORIES; AXISYMMETRIC DEFORMATION; FULL THREE-DIMENSIONAL; MODERATELY THICK; REFINED THEORY; SHELL THEORY; SHELL THICKNESS; SPHERICAL CAPS; THIN SHELL THEORY; THREE-DIMENSIONAL THEORY;

BOUNDARY CONDITIONS;

EID: 0039525540     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.00070     Document Type: Article

References (19)

1. R. D. GREGORY and F. Y. M. WAN, Correct asymptotic theories for the axisymmetric deformation of thin and moderately thick cylindrical shells, Internat. J. Solids Struct. 30: 1957-1981 (1993).
2. R. D. GREGORY and F. Y. M. WAN, Decaying states of plane strain in a semi-infinite strip and the boundary conditions for plate theory, J. Elasticity 14: 27-64 (1984).
3. R. D. GREGORY and F. Y. M. WAN, On plate theories and Saint-Venant's principle. Internat. J. Solids Struct. 21: 1005-1024 (1985).
4. R. D. GREGORY and F. Y. M. WAN, Edge effects in the stretching of plates, in Local Effects in the Analysis of Structures (P. Ladevéze, Ed.), pp. 35-54. Elsevier, Amsterdam, (1985).
5. R. D. GREGORY and F. Y. M. WAN, The interior solution for linear problems of elastic plates, J. Appl. Mech. 55: 551-559 (1988).
6. A. I. LUR'E, Equilibrium of an elastic symmetrically loaded spherical shell, PMM 7: 393-404 (1943). [In Russian.]
7. T. I. MILAC, The linear clastostatics of spherical shells. Ph.D. Thesis, University of Washington, Seattle, WA, (1995).
8. Y. H. LIN and F. Y. M. WAN, First integrals and the interior solution for orthotropic plates in plane strain or axisymmetric deformations, Stud. Appl. Math. 79, 93-125 (1988).
9. M. A. GOLDBERG, V. L. SALERNO, and M. A. SADOWSKI, Stress distribution in a rotating spherical shell of arbitrary thickness, J. Appl. Mech. 28: 127-131 (1961).
10. T. V. VILENSKAIA and I. I. VOROVICH, Asymptotic behavior of the solution of the problem of elasticity for a thin spherical shell, PMM 30: 278-295 (1965).
11. R. A. EUBANKS and E. STERNBERG, On the completeness of the Boussinesq-Papkovich stress functions, J. Rational Mech. Anal. 5: 735-746 (1956).
12. H. S. LEVINE and J. M. KLOSNER, Axisymmetric elasticity solutions of spherical shell segments, J. Appl. Mech. 38: 197-208 (1971).
13. H. S. LEVINE and J. M. KLOSNER, Axisymmetric elasticity solutions of spherical shell segments, in PIBAL Report No. 68-12, Polytechnic Institute of Brooklyn, Brooklyn, New York (1968).
14. S. WOLFRAM, Mathematica: A System for Doing Mathematics by Computer, 2nd ed., Addison-Wesley, New York (1991).
15. yy(0, y) are prescribed, J. Elasticity 10: 57-80 (1980).
16. R. D. GREGORY, The traction boundary value problem for the elastostatic semi-infinite strip; existence of solution, and completeness of the Papkovich-Fadle eigenfunctions. J. Elasticity 10: 295-327 (1980).
17. E. REISSNER and F. Y. M. WAN, Rotationally symmetric stress and strain in shells of revolution. Stud. Appl. Math. 48: 1-17 (1969).
18. M. ABRAMOWITZ and I. A. STEGUN, Handbook of Mathematical Functions, Dover, New York (1965).
19. A. I. LUR'E, Three-Dimensional Problems of the Theory of Elasticity, Interscience, New York, (1964).