Measure-concept in mechanics

Thermal creep stress and strain analysis in non-homogeneous spherical shell

“…For finding thermal creep stresses and strain rates, the transition function is taken through the principal stress difference (see Seth, 1962Seth, , 1966Thakur, 2011Thakur, , 2014Thakur et al, 2016Thakur et al, , 2017 at the transition point P → −1. We define the transition function ψ as…”

“…Seth's transition theory does not acquire any assumptions like the yield condition, incompressibility condition, and thus poses and solves a more general problem from which cases pertaining to the above assumptions can be worked out. This theory utilizes the concept of a generalized strain measure and asymptotic solution at critical points or turning points of differential equations defining the deformed field and has been successfully applied to a large number of problems (Seth, 1962(Seth, , 1966Thakur, 2011Thakur, , 2014Thakur et al, 2016Thakur et al, , 2017. Seth (1962) defined the concept of generalized strain measures as…”

Creep Transition of Spherical Shell Under Internal Pressure

“…In order to calculate the creep stresses, we define the transition function R = ( − ) through the principal stress difference as taken by Seth, Hulsarkar, Gupta [4,5,7].…”

Mathematical model in a thin non-homogeneous rotating disc for isotropic material with rigid shaft by using Seth's transition theory

“…The disc is made of the material having constant density ρ but variable modulus of rigidity ( ) r µ µ = and thickness of disc is assumed sufficiently small so that it is effectively in a state of plane stress, that is, the axial stress zz T is zero. 13 The displacement components in cylindrical polar co-ordinate are given by [6]:…”

“…For finding the plastic stress, the transition function is taken through the principal stress (see SETH [5,6], HULSURKAR [7], GUPTA etl. [4,[10][11][12], SHUKLA [8,9 ] , THAKUR [14 -42]) at the transition point P → ±∞ .…”