Erratum to "An iterative method for shakedown analysis" [Comput. Methods Appl. Mech. Engrg. 191 (2002) 5761-5792] (DOI:10.1016/S0045-7825(02)00496-6) (original) (raw)

Theorems of restricted dynamic shakedown

International Journal of Mechanical Sciences, 1993

Dynamic shakedown for a rate-independent material with internal variables is addressed in the hypothesis that the load values are restricted to those of a specified load history of finite or even infinite duration, thus ruling out the possibility-typical of classical shakedown theory-of indefinite load repetitions.

Concept of the limit yield condition in shakedown theory

International Journal of Solids and Structures, 1997

The concept of the limit yield condition is introduced which makes possible the extension of both the static (Melan) shakedown conditions, and the necessary kinematic (Koiter) one to a class of classical constitutive material models with internal variables. This class includes material models with both bounded and unbounded nonlinear isotropic strain-hardening. It is assumed that the yield conditions are convex with respect to stresses for all admissible values of the internal variables, but convexity in the internal variables is not assumed. Connections are established between the response of elastic perfectly plastic bodies to cyclic loading and that of bodies with internal variables. A method for estimating the limit yield condition is developed, and an example of this application is given.

A correction note on "Three-step iterative methods for nonlinear equations'' and generalization of method

Journal of Modern Methods in Numerical Mathematics, 2013

In the paper [Muhammad Aslam Noor, Khalida Inayat Noor, Threestep iterative methods for nonlinear equations, Applied Mathematics and Computation, 183 (2006), pp. 322-327], Authors presented an algorithm (Algorithm 2.3) and stated a theorem (Theorem 2.3) to prove the cubic order of convergence but the given proof does not show cubic order of convergence. Actually, the mathematical derivation steps to develop the Algorithm 2.3 are wrong. In this note, we present the correct mathematical developments and finally provide computational order of convergence in the favor of our claim and provide the generalization of the method.