THERMAL DEFORMATIONS AND STRESSES IN CIRCULARLY CURVED THIN BEAMS AND RINGS
Titel:
THERMAL DEFORMATIONS AND STRESSES IN CIRCULARLY CURVED THIN BEAMS AND RINGS
Auteur:
Fettahlioglu, Omer A. Steele, Theodore K.
Verschenen in:
Journal of thermal stresses
Paginering:
Jaargang 11 (1988) nr. 3 pagina's 233-255
Jaar:
1988
Inhoud:
A consistent treatment of the combined effects of extensional, flexural, and shearing deformations of thin, circularly curved beams and rings subjected to thermal loads of arbitrary variation, and general distributed and concentrated in-plane loads is presented. The present treatment, which deals with the problem in its general form, has been developed from variational considerations using Hamilton's principle to derive the exact Euler equations of motion and consistent boundary conditions for thin rings and curved beams in terms of the radial and tangential midsurface displacements and the rotation of the normal that, concomitantly, include the effects of extensional and shearing deformations. Discontinuity conditions corresponding to discrete application of generalized forces and consistent conditions on the time axis are also obtained. For static analysis, the coupled Euler equations of motion are transformed into three uncoupled differential equations, sixth-order in radial and tangential displacements, respectively, and fourth-order in rotation. Complete solutions of the governing equations are derived in exact form for general thermal and static load distributions. The particular solutions are then specialized for linear temperature variation through the thickness with uniform temperature over the outer and inner faces of the ring as well as with nonuniform temperature of trigonometric variation over the faces. The effects of the radial and tangential components of the distributed static loads are also incorporated into the particular solutions. The results confirm that the extensional and shearing deformations can play a significant role in the bending of curved beams with restrained edges subjected to nonuniform heating.
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