Damage modeling of ballistic penetration and impact behavior of concrete panel under low and high velocities

This work presents a numerical simulation of ballistic penetration and high velocity impact behavior of plain and reinforced concrete panels. This paper is divided into two parts. The first part consists of numerical modeling of reinforced concrete panel penetrated with a spherical projectile using concrete damage plasticity (CDP) model, while the second part focuses on the comparison of CDP model and Johnson-Holmquist-2 (JH-2) damage model and their ability to describe the behavior of concrete panel under impact loads. The first and second concrete panels have dimensions of 1500 mm × 1500 mm × 150 mm and 675 mm × 675 mm × 200 mm, respectively, and are meshed using 8-node hexahedron solid elements. The impact object used in the first part is a spherical projectile of 150 mm diameter, while in the second part steel projectile of a length of 152 mm is modeled as rigid element. Failure and scabbing characteristics are studied in the first part. In the second part, the com-parison results are presented as damage contours, kinetic energy of projectile and internal energy of the concrete. The results revealed a severe fracture of the panel and high kinetic energy of the projectile using CDP model comparing to the JH-2 model. In addition, the internal energy of concrete using CDP model was found to be less comparing to the JH-2 model.     

A note on optimal inventory management under inflation

This paper develops a discounted-cost model that is similar to the classical economic order quantity model but includes inflation rates as parameters of the inventory system. A numerical problem is solved to illustrate the effects.     

Evergreening and operational risk under price competition

“Evergreening” is a strategy wherein an innovative pharmaceutical firm introduces an upgrade of its current product when the patent on this product expires. The upgrade is introduced with a new patent and is designed to counter competition from generic manufacturers that seek to imitate the firm's existing product. However, this process is fraught with uncertainty because the upgrade is subject to stringent guidelines and faces approval risk. Thus, an incumbent firm has to make an upfront production capacity investment without clarity on whether the upgrade will reach the market. This uncertainty may also affect the capacity investment of a competing manufacturer who introduces a generic version of the incumbent's existing product but whose market demand depends on the success or failure of the upgrade. We analyze a game where capacity investment occurs before uncertainty resolution and firms compete on prices thereafter. Capacity considerations that arise due to demand uncertainty introduce new factors into the evergreening decision. Equilibrium analysis reveals that the upgrade's estimated approval probability needs to exceed a threshold for the incumbent to invest in evergreening. This threshold for evergreening increases as the intensity of competition in the generic market increases. If evergreening is optimal, the incumbent's capacity investment is either decreasing or nonmonotonic with respect to low end market competition depending on whether the level of product improvement in the upgrade is low or high. If the entrant faces a capacity constraint, then the probability threshold for evergreening is higher than the case where the entrant is not capacity constrained. Finally, by incorporating the risk‐return trade‐off that the incumbent faces in terms of the level of product improvement versus the upgrade success probability, we can characterize policy for a regulator. We show that the introduction of capacity considerations may maximize market coverage and/or social surplus at incremental levels of product improvement in the upgrade. This is contrary to the prevalent view of regulators who seek to curtail evergreening involving incremental product improvement. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 71–89, 2016