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| Titel: |
Initial Postbuckling of Elastic Rods Subjected to Thermal Loads and Resting on an Elastic Foundation |
| Auteur: |
Vaz, M. A. Nascimento, M. S. Solano, R. F. |
| Verschenen in: |
Journal of thermal stresses |
| Paginering: | Jaargang 30 (2007) nr. 4 pagina's 381-393 |
| Jaar: |
2007-04 |
| Inhoud: |
In practical applications encountered in some mechanical systems initially straight slender elements laterally supported by elastic foundations may be prevented from thermal expansion. In such conditions a compressive force is created and a serious equilibrium instability phenomenon may take place when a critical temperature gradient is imparted to the structure. If the temperature is further increased the rod may experience relatively large deflections, and a geometrically non-linear two-point boundary value problem describes this behaviour. However, if finite but moderate deflections are admitted, an approximate solution may be obtained if a classical perturbation expansion method is applied to the non-linear ordinary differential governing equations. This approach renders a set of linear equations which can be sequentially solved. This work proposes an analytical solution for the assessment of the initial post-buckling configuration of slender elastic rods supported on linear elastic foundations and subjected to a uniform temperature gradient. The rod ends are assumed hinged and immovable and the thermal strain-temperature relationship is linear. The governing equations are derived and made non-dimensional so it is seen that two parameters rule the problem: the foundation stiffness modulus and the rod slenderness ratio. Results are presented and discussed for one slenderness ratio and a range of foundation stiffness that corresponds to the fourth buckling mode. Generally an increase in the applied temperature is associated with a decrease in the compressive force, but it is shown particular conditions where an opposite behavior is observed. The initial post-buckling results for unsupported rods are compared with existing full post-buckling solution and show excellent agreement, given that in practical situations the deflections are moderate. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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