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| Content Provider | Springer Nature Link |
|---|---|
| Author | Berezhi, D. V. Paimushin, V. N. Shalashilin, V. I. |
| Copyright Year | 2009 |
| Abstract | Earlier it was shown in [1, 2] that the equations of classical nonlinear elasticity constructed for the case of small strains and arbitrary displacements are ill posed, because their use in specific problems may result in the appearance of “spurious” bifurcation points. A detailed analysis of these equations and the construction, in their stead, of consistent equations of geometrically nonlinear theory of elasticity can be found in [3]. Certain steps in this direction were also made in [4, 5]. In [3], it was also stated that the methods and applied program packages (APPs) based on the use of the classical relations of nonlinear elasticity require some revision and correction. In the present paper, this conclusion is justified and confirmed by numerical finite-element solutions of several three-dimensional geometrically nonlinear deformation problems and linearized problems on the stability of equilibrium of a rectilinear beam. These solutions were obtained by using two APPs developed by the authors and the well-known APP “ANSYS.” It is shown that the classical equations of the geometrically nonlinear theory of elasticity, which underly the first of the developed APP and the well-known APP “ANSYS,” often lead to overestimated buckling loads for structural members as compared with the consistent equations proposed in [1–3]. |
| Starting Page | 837 |
| Ending Page | 851 |
| Page Count | 15 |
| File Format | |
| ISSN | 00256544 |
| Journal | Mechanics of Solids |
| Volume Number | 44 |
| Issue Number | 6 |
| e-ISSN | 19347936 |
| Language | English |
| Publisher | Allerton Press, Inc. |
| Publisher Date | 2010-01-14 |
| Publisher Place | Heidelberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | geometric nonlinearity small strains large displacements Mechanics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Physics and Astronomy Mechanics of Materials |
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