Analytical solution to the bending of a nonlinearly hardening wide curved bar

Arslan, Eray
Eraslan, Ahmet Nedim
An analytical solution to the partially plastic deformation of a nonlinearly hardening wide curved bar is derived. The bar considered has a narrow rectangular cross-section and is under pure bending. The analytical treatment is based on Tresca's yield criterion, its associated flow rule and a Swift-type nonlinear hardening law. Taking numerical limits, the complete solution is verified in comparison to the linear hardening solution available in the literature.


Thermal convection in the presence of a vertical magnetic field
Guray, E.; Tarman, H. I. (Springer Science and Business Media LLC, 2007-11-01)
The interaction between thermal convection and an external uniform magnetic field in the vertical is numerically simulated within a computational domain of a horizontally periodic convective box between upper and lower rigid plates. The numerical technique is based on a spectral element method developed earlier to simulate natural thermal convection. In this work, it is extended to a magnetoconvection problem. Its main features are the use of rescaled Legendre-Lagrangian polynomial interpolants in expanding...
Propagation of waves from a spherical cavity with and without a shell embedment
Akkas, N; Zakout, U; Tupholme, GE (Springer Science and Business Media LLC, 2000-01-01)
A spherical cavity in an infinite, elastic medium with and without a shell embedment is subjected to axisymmetric, non-torsional surface loads in the radial and meridional directions. The so-called Residual Variable Method (RVM) is used to obtain exact, closed-form solutions of the wave propagation problems. Some representative numerical results are presented graphically for the stresses created in two realistic loading situations.
Exact solution of rotating FGM shaft problem in the elastoplastic state of stress
Akis, Tolga; Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2007-10-01)
Plane strain analytical solutions to estimate purely elastic, partially plastic and fully plastic deformation behavior of rotating functionally graded (FGM) hollow shafts are presented. The modulus of elasticity of the shaft material is assumed to vary nonlinearly in the radial direction. Tresca's yield criterion and its associated flow rule are used to formulate three different plastic regions for an ideal plastic material. By considerina different material compositions as well as a wide range of bore radi...
Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp
Dağ, Serkan; YILDIRIM, BORA; Ozatag, A. Cihan (Springer Science and Business Media LLC, 2013-08-01)
This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson's ratio is taken as a constant. Coulomb's dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity probl...
ORCAN, Y; GAMER, U (Springer Science and Business Media LLC, 1991-01-01)
Subject of the investigation is the deformation of a perfectly plastic cylinder with uniform temperature inside its cylindrical core and zero surface temperature. The calculation is based on Tresca's yield condition and the flow rule associated to it. For small radii of the hot core. a plastic region appears at the center and expands towards the surface of the cylinder with increasing core temperature. The other possibility is that, depending on the core radius, two plastic regions form one after the other ...
Citation Formats
E. Arslan and A. N. Eraslan, “Analytical solution to the bending of a nonlinearly hardening wide curved bar,” ACTA MECHANICA, pp. 71–84, 2010, Accessed: 00, 2020. [Online]. Available: