Optimal strategies for problems of simultaneous attack against an area defense without impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker. The defense has no impact-point prediction; that is, it has no knowledge of any attacker's destination prior to allocation of area interceptors. For a given attack, the defense wishes to allocate its interceptors to maximize the total expected survival value of the targets. For a given attack size, the offense seeks a strategy to minimize total expected surviving value against best defense. We determine an optimal defensive strategy directly and develop an algorithm to determine an optimal attack and the optimal value of the min-max problem. A dynamic programming technique is used to obtain integer solutions, and illustrative computational results are provided.     

Linear search with bounded resources

A point is placed at random on the real line according to some known distribution F, and a search is made for this point, beginning at some starting points s on the line, and moving along the line according to some function x(t). The objective of this article is to maximize the probability of finding the point while traveling at most d units. Characterizations of simple optimal searches are found for arbitrary distributions, for continuous distributions with continuous density everywhere (e.g., normal, Cauchy, triangular), and for continuous distributions with density which is continuous on its support (e.g., exponential, uniform). These optimal searches are also shown to be optimal for maximization of the expected number of points found if the points are placed on the line independently from a known distribution F.     

Rectilinear m-Center problem

In this article we consider the unweighted m-center problem with rectilinear distance. We preent an O(n^m–2 log n) algorithm for the m-center problem where m ≥ 4.     

The discrete evasion game with three-move lag

The discrete evasion game with three-move lag, formulated over 30 years ago, was one of the earliest games with time-lag complications. This game remains unsolved even though it is well known that the game has a value. In this article we obtain an upper bound for the value by constructing a strategy which consists of 400 conditional probabilities for the minimizing player. This is believed to be the best upper bound known.     

A model for critical crack size estimation in fatigue failure of gun barrels

With repeated firing, fatigue cracks are produced in a gun barrel, and the barrel is no longer useful when a crack reaches a critical size. The initial crack size and the critical crack size, as well as the number of firings producing the critical crack size, may be considered as random variables. Assuming a proportional damage model for crack growth, a method for estimating the critical crack size distribution is presented. From these results, an estimate of the barrel life, or the residual barrel life once a crack of a given size is measured, can be obtained.     

An efficient SPH methodology for modelling mechanical characteristics of particulate composites

Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical, automobile, aerospace including defence technology. Variety of modelling techniques have been adopted in the past to model mechanical behaviour of particulate composites. Due to their favourable properties, particle-based methods provide a convenient platform to model failure or fracture of these composites. Smooth particle hydrodynamics (SPH) is one of such methods which demonstrate excellent potential for modelling failure or fracture of particulate composites in a Lagrangian setting. One of the major challenges in using SPH method for modelling composite materials depends on accurate and efficient way to treat interface and boundary conditions. In this paper, a master-slave method based multi-freedom constraints is proposed to impose essential boundary conditions and interfacial displacement constraints in modelling mechanical behaviour of composite materials using SPH method. The proposed methodology enforces the above constraints more accurately and requires only smaller condition number for system stiffness matrix than the procedures based on typical penalty function approach. A minimum cut-off value-based error criteria is employed to improve the compu-tational efficiency of the proposed methodology. In addition, the proposed method is further enhanced by adopting a modified numerical interpolation scheme along the boundary to increase the accuracy and computational efficiency. The numerical examples demonstrate that the proposed master-slave approach yields better accuracy in enforcing displacement constraints and requires approximately the same computational time as that of penalty method.     

On vibration analysis of functionally graded carbon nanotube reinforced magneto-electro-elastic plates with different electro-magnetic conditions using higher order finite element methods

This article deals with evaluating the frequency response of functionally graded carbon nanotube rein-forced magneto-electro-elastic (FG-CNTMEE) plates subjected to open and closed electro-magnetic cir-cuit conditions. In this regard finite element formulation has been derived. The plate kinematics adjudged via higher order shear deformation theory (HSDT) is considered for evaluation. The equations of motion are obtained with the help of Hamilton's principle and solved using condensation technique. It is found that the convergence and accuracy of the present FE formulation is very good to address the vibration problem of FG-CNTMEE plate. For the first time, frequency response analysis of FG-CNTMEE plates considering the effect of various circuit conditions associated with parameters such as CNT dis-tributions, volume fraction, skew angle, aspect ratio, length-to-thickness ratio and coupling fields has been carried out. The results of this article can serve as benchmark for future development and analysis of smart structures.     

Relative performance of novel blast wave mitigation system to conventional system based on mitigation percent criteria

Recent researches focused on developing robust blast load mitigation systems due to the threats of terrorist attacks. One of the main embraced strategies is the structural systems that use mitigation techniques. They are developed from a combination of structural elements and described herein as conventional systems. Among the promising techniques is that redirect the waves propagation through hollow tubes. The blast wave propagation through tubes provides an efficient system since it combines many blast wave phenomena, such as reflection, diffraction, and interaction. In this research, a novel blast load mitigation system, employed as a protection fence, is developed using a technique similar to the technique of the bent tube in manipulating the shock-wave. The relative performance of the novel system to the conventional system is evaluated based on mitigation percent criteria. Performances of both systems are calculated through numerical simulation. The proposed novel system proved to satisfy high performance in mitigating the generated blast waves from charges weight up to 500 kg TNT at relatively small standoff distances (5 m and 8 m). It mitigates at least 94％ of the blast waves, which means that only 6％ of that blast impulse is considered as the applied load on the targeted structure.