There are many sources of risk affecting the Network elements may lead to Network failure, so planners need to consider them in the Network design. One of the most important strategies for disruption risk management is the static resilience. In this strategy, the Network functionality is maintained after the disruption event by the prevention and Hardening actions. In this paper, a resilient capacitated fixed-charge location-allocation model is proposed. Both facility Hardening and equipping of the Network to backup facilities for disrupted elements are considered together to avoid supply Network failure due to random disruption. Facilities are decided to be hardened in multiple levels before disruption events. The problem is formulated as a non-linear integer programming model, then its equivalent linear form is presented. A Lagrangian decomposition algorithm (LDA) is developed to solve large-scale instances. Computational results confirm the efficacy of the proposed solution approach comparing to classical solution approaches in large-scale problems. Moreover, the superiority of the proposed model is confirmed by comparing to the classical models.

Transient thermal field in laser surface Hardening treatment of medium carbon steel was analyzed by employing both three-dimensional analytical model and finite element model. In finite element model the laser beam was considered as a moving plane heat flux to establish the temperature rise distribution in the work-piece, while in analytical model laser beam was considered as an internal heat source. The numerical results were compared with the analytical results. In laser heat treatment of steel some methods are used to produce a wider and nearly uniform average irradiance profile. It may be achieved by rotating the beam optically, thereby producing an overlapping spiral track, or by dithering the beam (rocking the lens or mirror) perpendicular to the track, thus producing a zigzag pattern. In this paper, these models are used to cover the two mentioned patterns for laser Hardening with Gaussian distribution, and to compare the results with the hardened region of bimodal and uniform distribution. The results show that dithering beam and rotating beam are useful for obtaining a uniform heat intensity distribution, if the parameters of dithering beam or rotating beam are properly chosen with the aid of these models. The diffusion process being a time dependent phenomenon, an interaction time of 15 ms was taken as a basis to determine the hardened region.

In this paper, a corotational constitutive model for rigid plastic isotropic and kinematic Hardening materials obeying von Mises yield criterion is introduced. This constitutive model relates the corotational rate of the back stress tensor to the corotational rate of the logarithmic strain tensor. It is illustrated that use of Jaumann and Zaremba corotational rates in the constitutive model yields the same results for a given problem. Applying the proposed constitutive model to the simple shear problem, the effects of nonlinear isotropic and kinematic Hardenings on the stress components are studied.