Z. Zong

Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology

Abstract In this paper, the smoothed particle hydrodynamics (SPH) is applied to simulate the high explosive (HE) explosion which consists of detonation and dispersion process. The combination of meshless and Lagrangian nature inherent in the SPH methodology avoids the disadvantages of traditional numerical methods in treating large deformations, large inhomogeneities and tracing free surfaces in the extremely transient explosion process. Four numerical examples are presented with comparisons from different sources. The presented numerical examples involve in various HE explosion scenarios of arbitrary charge shape and different detonation orientations. The simulation results show that the presented SPH methodology can give good prediction for both the magnitude and form of the detonation wave as well as the pressure transient in the explosion process. Major physics of the HE explosion can be well captured in the simulation.

AN OVERVIEW ON SMOOTHED PARTICLE HYDRODYNAMICS

This paper presents an overview on smoothed particle hydrodynamics (SPH), which is a meshfree, particle method of Lagrangian nature. In theory, the interpolation and approximations of the SPH method and the corresponding numerical errors are analyzed. The inherent particle inconsistency has been discussed in detail. It has been demonstrated that the particle inconsistency originates from the discrete particle approximation process and is the fundamental cause for poor approximation accuracy. Some particle consistency restoring approaches have been reviewed. In application, SPH modeling of general fluid dynamics and hyperdynamics with material strength have been reviewed with emphases on (1) microfluidics and microdrop dynamics, (2) coast hydrodynamics and offshore engineering, (3) environmental and geophysical flows, (4) high-explosive detonation and explosions, (5) underwater explosions, and (6) hydrodynamics with material strength including hypervelocity impact and penetration.

Biodynamic response of shipboard sitting subject to ship shock motion.

Underwater shock can produce very high accelerations, resulting in severe human injuries. In this paper, a shock-structure-human interaction model is proposed to study the biodynamic response of a shipboard sitting subject to ship motion induced by underwater shock (ship shock motion) wherein, the human body is modeled using a lumped parameter system with the parameters obtained from dynamic tensile tests. The results obtained from the human model used in this paper and living human drop test are also compared. Numerical results have revealed the characteristics of human response to ship shock motion. The part in direct contact with the structure (like the pelvis) is much more vulnerable than other parts (like the head). The influences of structural damping and stiffness on the peak loads acting on the human body are investigated. Both damping and stiffness have important influences on the pelvis, but have much less influences on other parts. Injury criteria in the literature are also summarized to facilitate injury assessment.

Estimation of complicated distributions using B-spline functions

The distributions of some of random variables are quite complicated and difficult to determine using ordinary statistical models. A method is presented in this paper which gives satisfactory estimation of the complicated distribution of a continuous random variable. There are two key steps in the method: one being that the probability density function (p.d.f.) of a random variable is approximated by a linear combination of B-splines and the other being that the best model is determined by entropy analysis. Extensive numerical experiments have made it clear that the proposed method is useful to determine the p.d.f. directly from a set of sample points without using any prior knowledge of the distribution form.

Dynamic response of a laminated pipeline on the seabed subjected to underwater shock

Abstract The dynamic response of a simply supported underwater laminated pipeline lying on the seabed subjected to underwater explosion shock is studied. A fluid–structure interaction model is given. An approximate approach is introduced to estimate the explosion shock loading. The pipeline is modeled as a simply supported laminated moderately thick cylindrical shell. A modal analysis technique is employed to obtain the dynamic response of the pipeline subjected to underwater explosion shock. From results obtained in this paper, it can be found that the dynamic response of the pipe is local deformation. Compared with the strengths in the circumferential and the longitudinal directions, the strength of the radial direction for the pipe is weaker. Therefore, the response of the radial direction is larger than those of other directions. Some parametric studies including the charge weight, the stand-off distance and the length of the pipe were also considered.

A modified superconvergent patch recovery method and its application to large deformation problems

For nonlinear problems, it is shown that the accuracy and stability of superconvergent patch recovery (SPR) method can be remarkably improved through the modifications introduced in this paper. These modifications are (1) use of integration points as sampling points, (2) weighted average procedure and (3) introduction of additional nodes. They are validated through numerical investigations of several large deformation problems. Based on the modified SPR procedure, a new scheme for submodeling finite element analysis is developed. Comparison of the numerical results obtained from this new scheme and traditional method shows encouraging improvements.

A variable order approach to improve differential quadrature accuracy in dynamic analysis

Differential quadrature (DQ) is a numerical technique which can produce highly accurate results by using a considerably small number of grid points. When it is applied to dynamic equations, however, DQ may exhibit dynamic numerical instability. The present paper analyzed the sources of dynamic numerical instability through a simple example, and the main finding is that dynamic stability is dominated by the grid points near and on boundaries. Based on this, we propose a variable order approach which is characterized by applying different DQ schemes to the grid points near boundaries and grid points far away from boundaries. Numerical examples of both linear and non-linear dynamic equations show that the variable order approach presented in this paper may greatly improve dynamic stability, producing convincing results.

Bayesian estimation of complicated distributions

Abstract In a previous paper (Zong Z, Lam KY. Estimation of complicated disributions using B-spline functions. Structural safety 1998; 20(4): 323–32), we used a linear combination of B-spline functions to approximate complicated distributions. The method works well for large samples. In this paper, we extend the method to small samples. We still use a linear combination of B-spline functions to approximate a complicated probability density function (p.d.f). Strongly influenced by statistical fluctuations, the combination coefficients (unknown parameters) estimated from a small sample are highly irregular. Useful information is, however, still contained in these irregularities, and likelihood function is used to pool the information. We then introduce smoothness restriction, based on which the so-called smooth prior distribution is constructed. By combining the sample information (likelihood function) and the smoothness information (smooth prior distribution) in the Bayes theorem, the influence of statistical fluctuations is effectively removed, and greatly improved estimation, which is close to the true distribution, can be obtained by maximizing the posterior probability. Moreover, an entropy analysis is employed to find the most suitable prior distribution in an “objective” way. Numerical experiments have shown that the proposed method is useful to identify an appropriate p.d.f. for a continuous random variable directly from a sample without using any prior knowledge of the distribution form. Especially, the method applies to large or small samples.

Hydrodynamic influence on ship-hull vibration close to water bottom

The problem of a uniform ship-hull girder vibrating vertically close to water bottom is studied. A simple formula for the added mass is found by use of the method of matched asymptotic expansions. Results obtained from the present method and BEM are compared. They are in good agreement in the range considered here. The obtained added mass is used to predict the natural vibrations of a uniform beam vibrating close to water bottom. Numerical values show that the effects of shallow water are significant. The first- and second-order frequencies of the ship hull studied in this paper in deep water are about 1·4–3 times higher than those in shallow water.

Complex differential quadrature method for two-dimensional potential and plane elastic problems

Abstract In this article, complex differential quadrature method based on differential quadrature method in the real domain is proposed for potential and plane elastic problems. By use of Lagrange interpolation in the complex plane instead of boundary integral formulation, the method is free of singularity. The use of collocation ensures that the boundary conditions are exactly satisfied on the boundary. The method is applied to some potential and plane elastic problems. Numerical results obtained by the present method are in good agreement with either analytical solutions or finite element results.