Transition Analysis of Collapse of Thick Cylinders

Abstract

Hive einiger ad-hoc-Annahmen wie derjenigen der Inkompressibilitat und einer besonderen Form der FlieJbedingung hat T . Y . T h o m a s theoretische Ergebnisse uber den Zusammenbruch dicker Zylinder erhulten, die mit den experimentellen Ergebnissen von P . W. B r i d g m a n gut iibereinstimmen. Die von B . R . Seth und anderen aufgestellte Ubertragungstheorie liefert bereits diese und noch allgemeinere Ergebnisse, ohne irgendwelche Annahmen machen zu mussen. By making a number of ad-hoc assumptions like that of incompressibility and a particular form of the yield condition T . Y. T h o m a s has obtained theoretical results on the collapse of thick cylinders, which compare well with the experimental results of P . W. B r i d g m a n . The transition theory, developed by B . R. S e t h and others, readily gives all these and more general results without making any assumptiow. C n 0~0 1 4 b m pans ad-hoc-npennocHnoH KaH o HecxmaeMocTH EI 0~0608 4opMbi YCJIOBEI$I TeKy.recm nonyseabi. T. IO. T o Ma c o M TeopeTmecme ~C~O B E I H n n~ pacnana TOJICTHX U~~H H H P O B , Xopomo COBnaxamqtie c ~K C~~P E I M~H T~J I~H M M H p e a y n b~a~a~~ n. B. EpHxxMaHa. kl3 c03nam08 5. P. C B T O M H np. TeopHH nepexona, He HymRamqeZicsx B ~a~nx-nmBo npennocbinHax, BbiTeHamT rcpoMe sbrmenpw BeneHHbtX Cm6 6onee 061IIEIe pe3ynbTaTbI.

Elastic-plastic Transition of Transversely Isotropic Thick-walled Rotating Cylinder under Internal Pressure

“…A thick-walled cylinder is also widely used as a structural component in oil refineries, power industries, atomic power plants, etc. Problems of thickwalled cylinder under internal pressure have been analysed [1][2][3][4] for isotropic homogeneous elastic-plastic states. In their treatment, the following assumptions were made: (i) the incompressibility conditions, (ii) the deformation is small enough to make infinitesimal strain theory applicable,and (iii) the yield criterion, Incompressibility of the material in plasticity is one of the most important assumption that simplifies the problem.…”

“…Infact, in most of the cases, it is not possible to find a solution in closed form without this assumption. Transition theory 4 does not require any of the above assumptions, and thus solves a more general problem. This theory utilizes the concept of generalised strain measure, which not only gives the well-known strain measures, but can also be used to find the stresses in plasticity and creep problems by determining the asymptotic solution at the transition points of the governing differential equations.…”

“…where n is the measure and A ij e is the principal Almansi finite strain components 4 . The displacement components in cylindrical polar coordinates are given by,…”

Creep Deformation of a Thin Rotating Disk of Exponentially Varying Thickness with Inclusion

“…It has been shown that for the uni-axial case a generalized measure, which includes all the known measures of Cauchy, Green, Almansi, Hencky and others, is given by [7]. The generalized principal strain measure is defined as [8] …”

Elastoplastic analysis in functionally graded thick-walled rotating transversely isotropic cylinder under a radial temperature gradient and uniform pressure

“…where n is the strain measure coefficient, e ii A is the Almansi finite strain component, i = 1 , 2 , 3 , and n = − 2 , − 1 , 0 , 1 , 2 , respectively, indicate Green, Cauchy, Hencky, Swainger, and Almansi measures. This theory has been applied to a more general and wider range of problems [19–26]. Using his theory, Seth [25] studied elastic–plastic transition stresses and strains in tubes under pressure.…”