| Автор | Pan, Feixia |
| Автор | Beatty, Millard, F. |
| Дата выпуска | 1997 |
| dc.description | The instability of a cylindrical tube of uniform crosssection, made of a homogeneous, isotropic Bell constrained material and subjected to end thrust parallel to its axis, is examined. The theory of small deformations superimposed on an assigned finite homogeneous deformation is applied to derive equations for the stability analysis. The solution presented by Wilkes for the incompressible case is extended to study the system of equations for the infinitesimal superimposed displacements. In contrast to Wilkes, the roots of the characteristic equation are examined for three possible situations in which these roots may be real, pure imaginary, or complex conjugate. The solutions of the system of ordinary differential equations corresponding to these cases are discussed. The buckling equation is thus derived, and conditions imposed by the nature of the characteristic roots are presented. |
| Издатель | Sage Publications |
| Название | Instability of a Bell Constrained Cylindrical Tube Under end Thrust-Part 1: Theoretical Development |
| Тип | Journal Article |
| DOI | 10.1177/108128659700200301 |
| Print ISSN | 1081-2865 |
| Журнал | Mathematics and Mechanics of Solids |
| Том | 2 |
| Первая страница | 243 |
| Последняя страница | 273 |
| Аффилиация | Beatty, Millard, F., Department of Engineering Mechanics, University of Nebraska Lincoln, Lincoln, NE 685880347 |
| Выпуск | 3 |
| Библиографическая ссылка | [1] Beatty, M. F. and Pan, F.: Stability of an internally constrained, hyperelastic slab. Forthcoming. |
| Библиографическая ссылка | [2] Wilkes, E. W.: On the stability of a circular tube under end thrust. Quarterly Journal of Mechanics and Applied Mathematics, 8, 89-100 (1955). |
| Библиографическая ссылка | [3] Pan, F. and Beatty, M. F.: Remarks on the instability of an incompressible and isotropic, hyperelastic thickwalled cylindrical tube. J. Elasticity: Forthcoming. |
| Библиографическая ссылка | [4] Beatty, M. F. and Hayes, M. A.: Deformations of an elastic, internally constrained material: Part I. Homogeneous deformations. Journal of Elasticity, 29, 1-84 (1992). |
| Библиографическая ссылка | [5] Bell, J. F.: Contemporary perspectives in finite strain plasticity. International Journal of Plasticity, 1, 3-27 (1985). |
| Библиографическая ссылка | [6] Bell, J. F.: Material objectivity in an experimentally based incremental theory of large finite plastic strain. International Journal of Plasticity, 6, 293-314 (1990). |
| Библиографическая ссылка | [7] Southwell, R. V.: On the general theory of elastic stability. Philosophical Transactions of the Royal Society A, 213, 187-244 (1914). |
| Библиографическая ссылка | [8] Dean, W. R.: On the theory of elastic stability. Proceedings of the Royal Society of London, 107A, 734-760 (1925). |
| Библиографическая ссылка | [9] Beatty, M. F.: Instability of a fiberreinforced thick slab under axial loading. International Journal of Non Linear Mechanics, 25, 343-362 (1990). |
| Библиографическая ссылка | [10] Beatty, M. F. and Hayes, M. A.: Deformations of an elastic, internally constrained material: Part III. Small superimposed deformations and waves. Zeitschriftfir angewandte Mathematik und Physik (ZAMP), 46(Special Issue), S72-S106 (1995). |
| Библиографическая ссылка | [11] Guo, Z. H.: Rates of stretch tensors. Journal of Elasticity, 14, 263-267 (1984). |
| Библиографическая ссылка | [12] Beatty, M. F. and Hayes, M. A.: Deformations of an elastic, internally constrained material: Part II. Nonhomogeneous deformations. Quarterly Journal of Mechanics and Applied Mathematics, 45, 663-709 (1992). |
| Библиографическая ссылка | [13] Relton, F. E.: Applied Bessel Functions, Blackie & Son Limited, London & Glasgow, 1946. |
| Библиографическая ссылка | [14] McLachlan, N. W.: Bessel Functions for Engineers, Clarendon Press, Oxford, UK, 1953. |
| Библиографическая ссылка | [15] Beatty, M. F. and Pan, F.: On determinants having complex conjugate columns or rows. J. Elasticity: Forthcoming. |
| Библиографическая ссылка | [16] Beatty, M. F.: Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues with examples. Applied Mechanics Reviews, 40(Pt. 1), 1699-1734 (1987). (See also [17].) |
| Библиографическая ссылка | [17] Beatty, M. F.: Introduction to nonlinear elasticity, in Nonlinear Effects in Fluids and Solids, pp. 13-112, ed., M. M. Carroll & M. A. Hayes, Plenum, New York, 1996. |
| Библиографическая ссылка | [18] Beatty, M. F.: Elastic stability of rubber bodies in compression. Finite Elasticity, Ed. R.S. Rivlin, ASME Applied Mechanics Division Volume, 27, 125-150 (1977). |
