Failure of an infinitely compressible composite containing a finite cylindrical crack in axial compression

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of the Ukraine. Translated from Prikladnaya Mekhanika, Vol. 31, No. 9, pp. 15–23, September, 1995.     

Three-dimensional linearized stability theory for stratified rock (continuum theory and model of a piecewise-homogeneous medium)

Conclusions Thus, the probability of applying rigorous three-dimensional linearized stability theory to stability problems of stratified rock has been demonstrated in the present work. New qualitative and quantative results have been obtained.This is the complete text of a paper presented at the International Conference on the Mechanical Instability of Rock and Tectonics (Montpelier, France, September 5, 1991 and at the First European Conference on the Mechanics of Deformable Solids (Munich, Germany, 1991). Only the abstract of this article was published in the conference proceedings, not the complete text.Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 1, pp. 3–18, January, 1993.     

Region of applicability of applied theories in problems of the stability of bars and plates with low shear stiffness subjected to uniaxial compression

The question of the region of applicability of applied theories of bending of bars and plates in stability problems is discussed in relation to the case of uniaxial compression. The critical loads given by these theories are compared with the recently obtained solution [4, 5, 7–10] based on the three-dimensional linearized equations of the theory of elasticity [6]. It is established that for the problems in question the Timoshenko and Ambartsumyan theories are accurate enough for engineering purposes over the entire practical region of variation of the geometric and physical parameters of the bar (plate), whereas the use of the Euler-Bernoulli and Kirchhoff-Love theories may lead to unacceptable errors.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev; Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga; Lvov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1124–1126, November–December, 1969.