Abstract
The purpose of this paper is to establish the mathematical model on the elastic-plastic transitions occurring in the rotating spherical shells based on compressibility of materials. The paper investigates the elastic-plastic stresses and angular speed required to start yielding in rotating shells for compressible and incompressible materials. The paper is based on the non-linear transition theory of elastic-plastic shells given by B.R. Seth. The elastic-plastic transition obtained is treated as an asymptotic phenomenon at critical points & the solution obtained at these points generates stresses. The solution obtained does not require the use of semi-empirical yield condition like Tresca or Von Mises or other certain laws. Results are obtained numerically and depicted graphically. It has been observed that Rotating shells made of the incompressible material are on the safer side of the design as compared to rotating shells made of compressible material. The effect of density variation has been discussed numerically on the stresses. With the effect of density variation parameter, rotating spherical shells start yielding at the internal surface with the lower values of the angular speed for incompressible/compressible materials.
Highlights
Rotating shell structures have many engineering applications like aviation, rocketry, missiles, electric motors and locomotive engines
EBERLEIN, WRIGGERS, CIVALEK, GÜRSES have done elastic-plastic calculations in shells by using the various theoretical and numerical approaches based on finite element method, shear deformation theory, discrete convolution technique (SCHMIDT and WEICHERT, 1989; SIMO et al.,1990; EBERLEIN and WRIGGERS, 1999; CIVALEK and GÜRSES, 2009)
The distribution of stresses and yielding in an elastic-plastic rotating shell has been calculated by using the concept of generalized strain measures and the generalized Hooke's law at the critical points of the non-linear differential equation defining the equilibrium stage
Summary
Rotating shell structures have many engineering applications like aviation, rocketry, missiles, electric motors and locomotive engines. The elasticplastic problem of rotating spherical shells based on the different degree of compressibility has been solved by using the concept of generalized strain measures and transition theory. The distribution of stresses and yielding in an elastic-plastic rotating shell has been calculated by using the concept of generalized strain measures and the generalized Hooke's law at the critical points of the non-linear differential equation defining the equilibrium stage. The transition theory of elastic-plastic of shells do not use the ad-hoc assumptions like incompressibility, yield conditions those of Tresca, Von Mises and creep-strain laws like those of Norton, ODQVIST (1964). We analyze the non-linear transition problem of thin rotating spherical shell by using the generalized strain measures and Seth's transition theory for different values of the compressibility. The effect of density variation parameter has been discussed numerically and depicted graphically
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