Coupled deformations of elastic curves and surfaces

International Journal of Solids and Structures

Volumn 35, Issue 16, 1998, Pages 1915-1952

  Atai, A A ^a   Steigmann, D J ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY VALUE PROBLEMS; COMPRESSIVE STRESS; FINITE DIFFERENCE METHOD; RELAXATION PROCESSES; STRESS CONCENTRATION; SURFACES; TWO DIMENSIONAL;

COUPLED DEFORMATIONS; ELASTIC CURVES;

DEFORMATION;

EID: 0032083912     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(97)00130-3     Document Type: Article

References (47)

1. Acerbi, E. and Fusco, N. (1984) Semicontinuity problems in the calculus of variations. Archive for Rational Mechanics and Analysis 86, 125-145.
2. Atai, A. and Steigmann, D. J. (1997) On the nonlinear mechanics of discrete networks. Archive of Applied Mechanics 67, 303-119.
3. Ball, J. M. (1977) Convexity conditions and existence theorems in nonlinear elasticity. Archive for Rational Mechanics and Analysis 63, 337-403.
4. Bliss, G. A. (1946) Lectures on the Calculus of Variations. University of Chicago Press.
5. Bufler, H. and Schneider, H. (1994) Large strain analysis of rubber-like membranes under dead weight, gas pressure, and hydrostatic loading. Computational Mechanics 14, 165-188.
6. Cannarozzi. M. (1985) Stationary and extremum variational formulations for the elastostatics of cable networks. Meccanica 20, 136-143.
7. Carroll, M. M. (1988) Finite strain solutions in compressible elasticity. Journal of Elasticity 20, 65-92.
8. Como, M. and Grimaldi, A. (1995) Theory of Stability of Continuous Elastic Structures. CRC Press, Boca Raton, FL.
9. Dacarogna, B. (1989) Direct Methods in the Calculus of Variations. Springer, Berlin.
10. Fisher, D. (1988) Configuration dependent pressure potentials. Journal of Elasticity 19, 77-84.
11. Flanagan, D. P. and Belytschko, T. (1981) A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. International Journal for Numerical Methods in Engineering 17, 679-706.
12. Gao, D. Y. (1992) Global extremum criteria for finite elasticity. ZAMP 43, 924-937.
13. Gao, Y. and Strang, G. (1989) Geometric nonlinearity: potential energy, complementary energy, and the gap function. Quarterly of Applied Mathematics XLVII, 487-504.
14. Haseganu, E. M. and Steigmann, D. J. (1994a) Analysis of partly wrinkled membranes by the method of dynamic relaxation. Computational Mechanics 14, 596-614.
15. Haseganu, E. M. and Steigmann, D. J. (1994b) Theoretical flexural response of a pressurized cylindrical membrane. International Journal of Solids and Structures 31, 27-50.
16. Haseganu, E. M. and Steigmann, D. J. (1996) Equilibrium analysis of finitely deformed elastic networks. Computational Mechanics 17, 359-373.
17. Herrmann, W. and Bertholf, L. D. (1983) Explicit Lagrangian finite-difference methods. Computational Methods for Transient Analysis, eds T. Belytschko and T. J. R. Hughes, pp. 361-416. Elsevier, Amsterdam.
18. Klouček, P. and Luskin, M. (1994) The computation of the dynamics of the martensitic transformation. Continuum Mechanics and Thermodynamics 6, 209-240.
19. Knops, R. J. and Wilkes, E. W. (1973) Theory of elastic stability. Handbuch der Physik, Vol. VIa/3, ed. S. Flügge, p. 125. Springer, Berlin.
20. Kohn, R. V. and Strang, G. (1986) Optimal design and relaxation of variational problems. Communications on Pure and Applied Mathematics 39, 1-25 (Part I), 139-182 (Part II) and 353-377 (Part III).
21. Kohn, R. V. and Strang, G. (1986) Optimal design and relaxation of variational problems. Communications on Pure and Applied Mathematics 39, 1-25 (Part I), 139-182 (Part II) and 353-377 (Part III).
22. Kohn, R. V. and Strang, G. (1986) Optimal design and relaxation of variational problems. Communications on Pure and Applied Mathematics 39, 1-25 (Part I), 139-182 (Part II) and 353-377 (Part III).
23. Li, X. and Steigmann, D. J. (1995) Point loads on a hemispherical elastic membrane. International Journal of NonLinear Mechanics 30, 569-581.
24. Libai, A. and Simmonds, J. G. (1997) The Nonlinear Theory of Elastic Shells, 2nd edn. Cambridge University Press. In press.
25. Mansfield, E. (1953) Neutral holes in plane sheet-reinforced holes which are elastically equivalent to the uncut sheet. Quarterly Journal of Mechanics and Applied Mathematics 6, 370-378.
26. Naghdi, P. M. and Tang, P. Y. (1977) Large deformation possible in every isotropic elastic membrane. Philosophical Transactions of the Royal Society of London A287, 145-187.
27. Odgen, R. W. (1984) Non-linear Elastic Deformations. Ellis-Horwood, Chichester.
28. Papadrakakis, M. (1981) A method for the automatic evaluation of dynamic relaxation parameters. Computational Methods in Applied Mechanics and Engineering 25, 35-48.
29. Pipkin, A. C. (1986) The relaxed energy density for isotropic elastic membranes. IMA Journal of Applied Mathematics 36, 85-99.
30. Pipkin, A. C. (1994) Relaxed energy densities for large deformations of membranes. IMA Journal of Applied Mathematics 52, 297-308.
31. Podio-Guidugli, P. (1988) A variational approach for live loadings in finite elasticity. Journal of Elasticity 19, 25-36.
32. Rybka, P. (1992) Dynamical modeling of phase transitions by means of viscoelasticity in many dimensions. Proceedings of the Royal Society of Edinburgh 121A, 101-138.
33. Silling, S. A. (1987) Incompressibility in dynamic relaxation. ASME Journal of Applied Mechanics 54, 539-544.
34. Silling, S. A. (1988a) Numerical studies of loss of ellipticity near singularities in an elastic material. Journal of Elasticity 19, 213-239.
35. Silling, S. A. (1988b) Finite difference modelling of phase changes and localization in elasticity. Computational Methods in Applied Mechanics and Engineering 70, 251-273.
36. Silling, S. A. (1989) Phase changes induced by deformation in isothermal elastic crystals. Journal of the Mechanics and Physics of Solids 37, 293-316.
37. Steigmann, D. J. (1986) Proof of a conjecture in elastic membrane theory. ASME Journal of Applied Mechanics 53, 595-596.
38. Steigmann, D. J. (1991) A note on pressure potentials. Journal of Elasticity 26, 87-93.
39. Steigmann, D. J. and Li, D. (1995) Energy-minimizing states of capillary systems with bulk, surface, and line phases. IMA Journal of Applied Mathematics 55, 1-17.
40. Steigmann, D. J. and Ogden, R. W. (1997) Plane deformations of elastic solids with intrinsic boundary elasticity. Proceedings of the Royal Society of London A453, 853-877.
41. Swart, P. J. and Holmes, P. J. (1992) Energy minimization and the formation of microstructure in dynamic antiplane shear. Archive for Rational Mechanics and Analysis 121, 37-85.
42. Tabarrok, B. and Qin, Z. (1992) Nonlinear analysis of tension structures. Computers and Structures 45, 973-984.
43. Underwood, P. (1983) Dynamic relaxation. Computational Methods for Transient Analysis, eds T. Belytschko and T. J. R. Hughes, pp. 245-265. Elsevier, Amsterdam.
44. van Tiel, J. (1984) Convex Analysis. Wiley, New York.
45. Varga, O. H. (1966) Stress Strain Behavior of Elastic Materials. Wiley, New York.
46. Varley, E. and Cumberbatch, E. (1980) Finite deformations of elastic materials surrounding cylindrical holes. Journal of Elasticity 10, 341-405.
47. Wu, C.-H. (1979) Large finite strain membrane problems. Quarterly of Applied Mathematics 347-359.