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**Thermoelastic stability.**
*(English)*
Zbl 0718.73011

Thermal stresses III, Mech. Math. Methods, 2. Ser., Therm. Stresses 3, 107-189 (1989).

[For the entire collection see Zbl 0706.00026.]

In the context of this article thermoelastic stability of heated thin elastic and viscoelastic structures is considered from an engineering point of view. Using simple structures and employing Hooke’s law we show similarities of thermal and deadload buckling with respect to critical stress and bifurcation of the state of equilibrium. We also consider the effects on effective stiffness with respect to resistance to deadweight loadings, and discuss the thermal stability problem in comparison to the force-loading problem in the narrow post-buckling range of deformations. The shallow two-bar Von Mises truss serves as a simple structure which exhibits a snap-through-type of instability which may be absent under thermal loading conditions with deformation control. Bifurcation and snapping are studied for plates and thin shells of simple geometry. Berger’s approximation is used in the narrow postbuckling range and for consideration of geometric imperfections.

In Section 4 we discuss analytical and seminumerical approaches which have been extensively computerized. A review on finite difference and finite element methods is presented. Numerical results for shell buckling and stability of a “pipeline” are outlined in considerable detail. The final Section 5 gives a short introduction into lifetime problems where an increase of temperature or temperature fluctuations accelerate the creep process. Thus, a change of temperature strongly affects the creep parameter and may cause failure of shallow thin-walled structures by subsequent (elastic) snap-through buckling.

The list of references at the end of the paper is far from complete but presents the material needed for further detailed studies of the fascinating field of thermal stability.

In the context of this article thermoelastic stability of heated thin elastic and viscoelastic structures is considered from an engineering point of view. Using simple structures and employing Hooke’s law we show similarities of thermal and deadload buckling with respect to critical stress and bifurcation of the state of equilibrium. We also consider the effects on effective stiffness with respect to resistance to deadweight loadings, and discuss the thermal stability problem in comparison to the force-loading problem in the narrow post-buckling range of deformations. The shallow two-bar Von Mises truss serves as a simple structure which exhibits a snap-through-type of instability which may be absent under thermal loading conditions with deformation control. Bifurcation and snapping are studied for plates and thin shells of simple geometry. Berger’s approximation is used in the narrow postbuckling range and for consideration of geometric imperfections.

In Section 4 we discuss analytical and seminumerical approaches which have been extensively computerized. A review on finite difference and finite element methods is presented. Numerical results for shell buckling and stability of a “pipeline” are outlined in considerable detail. The final Section 5 gives a short introduction into lifetime problems where an increase of temperature or temperature fluctuations accelerate the creep process. Thus, a change of temperature strongly affects the creep parameter and may cause failure of shallow thin-walled structures by subsequent (elastic) snap-through buckling.

The list of references at the end of the paper is far from complete but presents the material needed for further detailed studies of the fascinating field of thermal stability.