Biodynamic response of shipboard crew to underwater shock is of a major concern to navies. An underwater shock can produce very high accelerations, resulting in severe human injuries aboard a battleship. Protection of human bodies from underwater shock is implemented by installing onboard isolators. In this paper, the optimal underwater shock isolation to protect human bodies is studied. A simple shock-structure-isolator-human interaction model is first constructed. The model incorporates the effect of fluid-structure interaction, biodynamic response of human body, isolator influence. Based on this model, the optimum shock isolation is then formulated. The performance index and estriction are defined. Thirdly, GA (genetic algorithm) is employed to solve the formulated optimization problem. GA is a powerful evolutionary optimization scheme suitable for large-scale and multi-variable optimization problems that are otherwise hard to be solved by conventional methods. Abrief introduction to GA is given in the paper. Finally, the method is applied to an example problem and the limiting performance characteristic is obtained.

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 in uenced by statistical uctuations, the combination coe-cients (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 con-structed. By combining the sample information (likelihood function) and the smoothness information (smooth prior distribution) in the Bayes' theorem, the in uence of statistical uctuations 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

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.

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.

For nonlinear problems, it is shown that the accuracy and stability of superconvergent patch recovery (SPR) method can be remarkably improved through the modi!cations introduced in this paper. These modi!cations 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 modi!ed SPR procedure, a new scheme for submodeling !nite element analysis is developed. Comparison of the numerical results obtained from this new scheme and traditional method shows encouraging improvements.

Lagrange interpolation is extended to the complex plane in this paper. It turns out to be composed of two parts: polynomial and rational interpolations of an analytical function. Based on Lagrange interpolation in the complex plane, a complex variable boundary collocation approach is constructed. The method is truly meshless and singularity free. It features high accuracy obtained by use of a small number of nodes as well as dimensionality advantage, that is, a two-dimensional problem is educed to a one-dimensional one. The method is applied to twodimensional problems in the theory of plane elasticity. Numerical examples are in very good agreement with analytical ones. The method is easy to be implemented and capable to be able to give the stress states at any point within the solution domain.

Differential Quadrature (DQ) is a numerical technique of high accuracy, but it is sensitive to grid distribution and requires that the number of grid points cannot be too large. These two requirements greatly restrict wider applications of DQ method. Through a simplified stability analysis in this paper, it is concluded that these two limitations are due to stability requirements. This analysis leads us to propose to localize differential quadrature to a small neighbourhood so as to keep the balance of accuracy and stability. The derivatives at a grid point are approximated by a weighted sum of the points in its neighbourhood rather than of all grid points. The method is applied to the one-and two-dimensional wave equations. Numerical examples show the present method produces very accurate results while maintaining good stability. The proposed method enables us to solve more complicated problems and enhance DQ's flexibility significantly.

Dynamic plastic response of a submarine oil pipeline to an underwater explosion bubble is studied in this paper. A detailed fluid-structure analysis is given to find the fluid forces acting on the pipeline. Assuming the pipeline is made from rigid, perfectly plastic material, we obtain the hydroplastic equation governing the dynamic plastic deflection of such a pipeline. The equation is analytically solved. Three examples are given to discuss the features of the dynamic plastic response and the applicability range of the present analysis. The relation between the half pipe length and maximum permanent plastic deflection is also given.

The dynamic plastic response of a submerged free-free beam to an underwater explosion bubble is studied in this paper. A fluid-structure analysis is given to find the fluid force acting on the beam. Assuming that the beam is made from rigid, perfectly plastic material, we obtain the hydroplastic equation governing the dynamic plastic deflection of such a beam. The equation is analytically solved. Examples are given to discuss the features of the dynamic plastic response. It is observed that longer beams sustain larger plastic deformations than shorter beams, but shorter beams undergo larger rigid body motion than longer beams. Most of energy is consumed on plastic deformation rather than on rigid body motion. It is impossible, however, for more than three hinges to form on the beam.