An approach to modeling blast and fragment risks from improvised explosive devices

In this paper, we develop numerical methods for modeling blast and fragments generated from explosive detonation and apply them to scenarios representing improvised explosive devices in confined spaces. The detonation of condensed phase explosives is modeled with a programmed burn method in a three-dimensional multimaterial flow solver. This solver has been coupled with a Lagrangian particle solver to model the acceleration of explosive-driven fragments. We first simulate an explosion in a long cylindrical tube to validate the fluid solver for a partially-confined blast. We then simulate explosions on a subway train platform for 10 kg and 30 kg C4 charges. The maximum shock overpressure and impulse are used to predict the risk of common blast injuries. To represent improvised explosive threats, we model C4 charges with spherical, cylindrical, and disk shapes that are surrounded by a layer of spherical fragments. We find that the explosive charge shape plays an important role in the acceleration of the spherical fragments. Finally, a realistic scenario of an improvised explosive detonation near a bomb technician is investigated to assess fragment trajectory and blast loads in the near field.     

Numerical Study of the Stressed-Deformed State of Rock during Explosive Fracture

The dynamic loading of a rock mass during explosion of a borehole explosive is studied using a continuum mechanics approach in two-dimensional plane and axially symmetric formulations with the aid of a modified finite element method [1, 2]. This numerical technique makes it possible to study wave processes in a rock mass owing to explosions of single charges as well as those of systems of borehole explosives under different conditions. These include varying the site at which the charge is initiated and accounting for the propagation velocity of detonations in the explosive, so it is possible to calculate the shape of the stress field created by a charge with a given design. Numerical simulation of the explosion process for multiple borehole explosive charges with delays relative to one another can be used to obtain the optimum delay time for initiation and the distances between the charges. These results can also extend our concepts of the processes taking place in a rock mass during explosive fracture.     

计入气穴的水下爆炸作用下结构流固耦合三维数值模拟

水下爆炸在结构物面附近产生的气穴现象,严重影响水下爆炸作用下的流固耦合动响应,是舰船水下爆炸领域的难点,传统的边界元方法、有限元方法(FEM)难以解决水下爆炸气穴现象这类强非线性问题．针对此问题,计及流体中的气穴现象,考虑流体的可压缩型,忽略流体粘性,建立水下爆炸瞬态强非线性流固耦合三维数值模型,采用流体谱单元方法(SEM)和结构有限元方法求解该模型．计算结果表明:相对有限元法,谱单元法具有更高的计算精度,且谱单元解与解析解、试验值吻合良好．在此基础上,结合ABAQUS软件,分别探讨三维球壳、船体板架在水下爆炸作用下的瞬态流固耦合机理,给出气穴区域及其对水中结构物动响应的影响特征,旨在为舰船水下爆炸瞬态流固耦合问题的相关研究提供参考．     

泡沫覆盖层对水下爆炸气泡射流防护机理缩比试验研究

水下爆炸会对水中结构物造成严重威胁。柔性覆盖层或夹层板能够降低水中结构物水下爆炸冲击响应，因此成为研究的热点。以往的研究多集中于覆盖层对冲击波的防护机理，适用于较远距离的水下爆炸情况。近距离水下爆炸除了冲击波外，爆炸气泡溃灭时产生的朝向结构物的高速水射流更为致命。该文针对这种情况，基于量纲原理，推导缩比相似关系，通过缩比模型水下爆炸试验发现了覆盖层表面空化微气泡群对爆炸气泡形成高速水射流过程产生干扰，提出了泡沫覆盖层钢板水下爆炸气泡射流防护机理。     

Nonlinear finite element reliability analysis of Concrete-Faced Rockfill (CFR) dams under static effects

The response of concrete slab on Concrete-Faced Rockfill (CFR) dams is very important. This study investigates the reliability of the concrete slab on a CFR dam by the improved Rackwitz–Fiessler method under static loads. For this purpose, ANSYS finite element analysis software and FERUM reliability analysis program are combined with direct coupled method and response surface method. Reliability index and probability of failure of the concrete are computed in the all critical points of the concrete slab by dam height. This study is also expanded for the reliability of CFR dams including different concrete slab thickness. In addition to the linear behavior, geometrically and materially non-linear responses of the dam are considered in the finite element analysis which is performed with reliability analysis. The Drucker–Prager method and the multi linear kinematic hardening method are, respectively, used for concrete slab and for rockfill and foundation rock. Finite element model used in the analyses includes dam–reservoir–foundation interaction. Reservoir water is modeled by the Lagrangian approach. Welded and friction contact based on the Coulomb’s friction law are considered in the joints of the dam. One-dimensional two noded contact elements are used to define friction. The self-weight of the dam and the hydrostatic pressure of the reservoir water are considered in the numerical solutions. According to this study, hydrostatic pressure, nonlinear response of the rockfill and the decrease in the concrete slab thickness reduce the reliability of the concrete slab of the CFR dam. Besides, the CFR dam models including friction are safer than the models including welded contact in the joints.     

A mathematical-model approach to human population explosions caused by migration

If the human population density becomes extremely high in a small area, then we say that a population explosion occurs in the area. Geographical movements of human population can form a regional overconcentration of population. If such an overconcentration becomes excessive, then it often forms a population explosion. In this paper, by taking a mathematical-model approach to human population explosions caused by migration, we obtain a sufficient condition for population to explode. It is known in sociodynamics that geographical population movements are described by a nonlinear integro-partial differential equation whose unknown function denotes the population density. This equation is called the master equation, and has its origin in statistical physics. We express a population explosion as a blow-up solution to the initial-value problem for this equation. We will study a population explosion as an interdisciplinary subject among human population dynamics, statistical physics, and the theory of nonlinear functional equations. The principal result is as follows: if a human population migrates within a sufficiently small domain, if the gradient of initial population density is sufficiently large, if the population gravitates strongly toward densely populated areas, and if a cost incurred in moving is sufficiently small, then a population explosion occurs.     

Dynamic inversion method for the material parameters of a high arch dam and its foundation

The overall mechanical behavior of the structure of an arch dam is comprehensively reflected by the vibration modal information included in measured vibration response. Hence, the results obtained from inverting material parameters based on measured vibration data are often superior to those based on static monitoring data. In this study, a dynamic inversion method for the material parameters of a high arch dam and its foundation is proposed on the basis of the measured vibration response. First, an arch dam prototype test is conducted to obtain the measured dynamic displacement response as input. Then, a stochastic subspace identification method based on singular entropy is formulated to determine the modal parameters. Second, a dynamic elastic modulus (DEM) with a great influence on the modal parameters is selected as the material parameter to be inverted. Then, a response surface model (RSM), which reflects the nonlinear relationship between the material and modal parameters of each zone, is constructed. Latin hypercube sampling is used to generate the sample library of the DEM. The RSM is fitted by modal parameters calculated on the basis of the arch dam finite element model (FEM) and is applied to replace the FEM. Finally, the optimization mathematical model of the inversion of the DEM is established. Then, the objective function is optimized through a genetic algorithm, and the optimal combination of the DEM in each zone is inverted. The modal parameters of the arch dam calculated by inversion results are consistent with those measured by variation law and values. Therefore, the inversion results are reasonable and reliable. This method provides a new idea for determining the material parameters of a high arch dam and its foundation during the operation period.     

Numerical investigation of interactions of multiple spherical shock waves between themselves and with the underlying surface

Within the investigation of various aspects of asteroid and comet danger and, in particular, the explosion of several fragments of meteoroids in the atmosphere above the Earth surface, the toy problem about four point explosions in the case of their special arrangement above the underlying surface is numerically solved. Complex interactions of primary and secondary shock waves between themselves, with the hard surface, and with tangential discontinuities are examined. The structure of flow inside gas regions disturbed by the explosions—the occurrence of eddy structures in them and the influence of reflected shocks waves on them—are investigated. The tendency of the external wave fronts of each explosion to form a unified front and the tendency of their internal hot domains to merge into a joined configuration (where the second process proceeds a little later than the first one) is revealed. This unified front and joined configuration are qualitatively identical to the external internal structure for the solitary explosion. The specially arranged explosions are chosen because the effects of multiple diffraction, interference, and, the main thing, cumulation of spherical waves are manifested more clearly in this caseTwo variants with different altitude of the explosions above the surface are calculated.     

Advances in concrete arch dams shape optimization

This paper presents an efficient methodology to find the optimum shape of arch dams. In order to create the geometry of arch dams a new algorithm based on Hermit Splines is proposed. A finite element based shape sensitivity analysis for design-dependent loadings involving body force, hydrostatic pressure and earthquake loadings is implemented. The sensitivity analysis is performed using the concept of mesh design velocity. In order to consider the practical requirements in the optimization model such as construction stages, many geometrical and behavioral constrains are included in the model in comparison with previous researches. The optimization problem is solved via the sequential quadratic programming (SQP) method. The proposed methods are applied successfully to an Iranian arch dam, and good results are achieved. By using such methodology, efficient software for shape optimization of concrete arch dams for practical and reliable design now is available.     

The radiation of non-stationary spherical pressure waves by a moving and partially permeable boundary

The radiation (generation) of pressure waves by a spherical cavity is investigated using the non-linear time-transformation method in wave initial-boundary-value problems with specified Neumann-type boundary conditions on a moving and partially permeable boundary [1, 2]. The results obtained reflect the hydrodynamic processes which accompany underwater explosions of different physical kinds and of limited power.     

水下爆炸气泡融合动态特性研究

在自然界中,气泡融合是一种重要的物理现象．基于势流理论,采用边界积分法,对水下爆炸气泡融合进行数值模拟研究．依据已有的数值研究成果和实验数据,建立气泡融合三维动力学数值模型,数值模拟结果与实验值吻合良好．应用该文开发的三维计算程序,分析距离、水深等特征参数对气泡融合动态特性的影响,得到了一些规律性的曲线和结论,旨在为水下爆炸气泡融合机理和动态特性研究提供理论参考．     

Shape optimal design of arch dams using an adaptive neuro-fuzzy inference system and improved particle swarm optimization

An efficient methodology is proposed to find the optimal shape of arch dams including fluid–structure interaction subject to earthquake ground motion. In order to reduce the computational cost of optimization process, an adaptive neuro-fuzzy inference system (ANFIS) is built to predict the dam effective response instead of directly evaluating it by a time-consuming finite element analysis (FEA). The presented ANFIS is compared with a widespread neural network termed back propagation neural network (BPNN) and it appears a better performance generality for estimating the dam response. The optimization task is implemented using an improved version of particle swarm optimization (PSO) named here as IPSO. In order to assess the effectiveness of the proposed methodology, the optimization of a real world arch dam is performed via both IPSO–ANFIS and PSO–BPNN approaches. The numerical results demonstrate the computational advantages of the proposed IPSO–ANFIS for optimal design of arch dams when compared with the PSO–BPNN approach.     

Conservation Laws,Hamiltonian Structure,Modulational Instability Properties and Solitary Wave Solutions for a Higher‐Order Model Describing Nonlinear Internal Waves

Recent theoretical advances in connecting the wave‐induced mean flow with the conserved pseudomomentum per unit mass has permitted the first rational derivation of a model that describes the weakly nonlinear propagation of internal gravity plane waves in a continuously stratified fluid. Depending on the particular parameter regime examined the new model corresponds to an extended bright or dark derivative nonlinear Schrödinger equation or an extended complex‐valued modified Korteweg‐de Vries or Sasa–Satsuma equation. Mass, momentum, and energy conservation laws are derived. A noncanonical infinite‐dimensional Hamiltonian formulation of the model is introduced. The modulational stability characteristics associated with the Stokes wave solution of the model are described. The bright and dark solitary wave solutions of the model are obtained.     

Successive Canard Explosions in a Singularly Perturbed Spruce-Budworm Model with Holling-II Functional Response

By combining geometric singular perturbation theory (GSPT) with qualitative method, this paper analyzes the phenomenon of successive canard explosions in a singularly perturbed Spruce-Budworm model with Holling-II functional response. We select suitable parameters such that the critical curve is $S$-shaped, and the full model only admits a unique equilibrium. Then, under the variation of the breaking parameter, it is found that a canard explosion followed by an inverse canard explosion successively occurs in this model. That is, a relaxation oscillation arises via the first canard explosion, which persists for a large interval of parameter until it vanishes via the so-called inverse canard explosion. All these theoretical predictions are verified by numerical simulations.     

A General Cavitation Model for the Highly Nonlinear Mie-Grüneisen Equation of State

A general one-fluid cavitation model is proposed for a family of Mie-Grüneisen equations of state (EOS), which can provide a wide application of cavitation flows, such as liquid-vapour transformation and underwater explosion. An approximate Riemann problem and its approximate solver for the general cavitation model are developed. The approximate solver, which provides the interface pressure and normal velocity by an iterative method, is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian grids. Several numerical examples, including Riemann problems and underwater explosion applications, are presented to validate the cavitation model and the corresponding approximate solver.     

Non-linear seismic response of concrete gravity dams to near-fault ground motions including dam-water-sediment-foundation interaction

This study focuses on non-linear seismic response of a concrete gravity dam subjected to near-fault and far-fault ground motions including dam-water-sediment-foundation rock interaction. The elasto-plastic behavior of the dam concrete is idealized using Drucker–Prager yield criterion based on associated flow rule assumption. Water in the reservoir is represented by 9-noded isoparametric quadrilateral fluid finite elements while the dam, the foundation rock and the sediment layer are modeled by using 8-noded isoparametric quadrilateral solid finite elements. The program NONSAP modified for elasto-plastic analysis of fluid-structure systems using the Lagrangian fluid finite element is employed in the response calculations. The fluid element includes the effects of surface waves and sloshing behavior of fluids. Non-linear seismic analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. The results obtained from linear and non-linear analyses are compared with each other.     

Finite-element modeling of the interaction of reinforcement with concrete matrix

A finite-element model of a reinforced concrete beam with rebars modeled by a 3-D deformable body has been developed. An analysis of the stress-strain state of the beam allowed us to determine the stress distribution on cross sections of the rebars and the location of zones with cracks in concrete. It is found that the break of bond between the reinforcement and concrete goes outside the areas of intensely cracked concrete matrix. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 309–316, May–June, 2008.     

Shape optimal design of arch dams including dam-water–foundation rock interaction using a grading strategy and approximation concepts

Optimal design of arch dams including dam-water–foundation rock interaction is achieved using the soft computing techniques. For this, linear dynamic behavior of arch dam-water–foundation rock system subjected to earthquake ground motion is simulated using the finite element method at first and then, to reduce the computational cost of optimization process, a wavelet back propagation neural network (WBPNN) is designed to predict the arch dam response instead of directly evaluating it by a time-consuming finite-element analysis (FEA). In order to enhance the performance generality of the neural network, a dam grading technique (DGT) is also introduced. To assess the computational efficiency of the proposed methodology for arch dam optimization, an actual arch dam is considered. The optimization is implemented via the simultaneous perturbation stochastic approximation (SPSA) algorithm for the various conditions of the interaction problem. Numerical results show the merits of the suggested techniques for arch dam optimization. It is also found that considering the dam-water–foundation rock interaction has an important role for safely designing an arch dam.     

On efficient numerical methods for an initial-boundary value problem with nonlocal boundary conditions

Many physical phenomena are modeled by nonclassical hyperbolic boundary value problems with nonlocal boundary conditions. In this paper, the problem of solving the one-dimensional wave equation subject to given initial and non-local boundary conditions is considered. These non-local conditions arise mainly when the data on the boundary cannot be measured directly. Several finite difference methods with low order have been proposed in other papers for the numerical solution of this one dimensional non-classic boundary value problem. Here, we derive a new family of efficient three-level algorithms with higher order to solve the wave equation and also use a Simpson formula with higher order to approximate the integral conditions. Additionally, the fourth-order formula is also adapted to nonlinear equations, in particular to the well-known nonlinear Klein–Gordon equations which many physical problems can be modeled with. Numerical results are presented and are compared with some existing methods showing the efficiency of the new algorithms.