抛物形缓坡方程的数值研究

对2种典型的抛物形缓坡方程进行比较系统的数值研究。通过对4种典型地形上的波浪变形的数值模拟，详细讨论了网格节点数对数值解精度的影响、模型对初始入射角的敏感程度、非线性项对数值结果的影响等。研究结果可为实际应用抛物形缓坡方程研究大区域复杂地形上的波浪传播提供一定的理论指导。     

解梁的平衡方程的混合有限体积元方法

针对梁的平衡方程导出了一类混合有限体积元格式，并用非常直观的方法证明了该格式按离散H^1半模及离散L^2模具有一阶精度。最后，具体算例表明，该算法计算效果良好。     

一种机构可靠性的仿真分析方法

实际工作中,机构的运动规律并非是确定的,而是在允许的偏差范围内离散分布的,是不确定的。文章介绍了一种计算机构可靠性的方法。该方法将计算机概率仿真方法与机构运动学、动力学微分方程结合起来,通过对影响机构可靠性的基本变量进行离散化并定义极限状态,最终得出准确的可靠度指标。从而能影响到对产品的设计,最终达到对产品进行优化的目的。     

Perfectly matched layers for transient elastodynamics of unbounded domains

One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non‐tangential angles‐of‐incidence and of all non‐zero frequencies. In a recent work [Computer Methods in Applied Mechanics and Engineering 2003; 192: 1337–1375], the authors presented, inter alia, time‐harmonic governing equations of PMLs for anti‐plane and for plane‐strain motion of (visco‐) elastic media. This paper presents (a) corresponding time‐domain, displacement‐based governing equations of these PMLs and (b) displacement‐based finite element implementations of these equations, suitable for direct transient analysis. The finite element implementation of the anti‐plane PML is found to be symmetric, whereas that of the plane‐strain PML is not. Numerical results are presented for the anti‐plane motion of a semi‐infinite layer on a rigid base, and for the classical soil–structure interaction problems of a rigid strip‐footing on (i) a half‐plane, (ii) a layer on a half‐plane, and (iii) a layer on a rigid base. These results demonstrate the high accuracy achievable by PML models even with small bounded domains. Copyright © 2004 John Wiley & Sons, Ltd.     

Generation and adaptation of computational surface meshes from discrete anatomical data

Fast and accurate scanning devices are nowadays widely used in many engineering and biomedical fields. The resulting discrete data is usually directly converted into polygonal surface meshes, using ‘brute‐force’ algorithms, often resulting in meshes that may contain several millions of polygons. Simplification is therefore required in order to make storage, computation and display possible if not efficient. In this paper, we present a general scheme for mesh simplification and optimization that allows to control the geometric approximation as well as the element shape and size quality (required for numerical simulations). Several examples ranging from academic to complex biomedical geometries (organs) are presented to illustrate the efficiency and the utility of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Gradient method for inverse heat conduction problem in nanoscale

An inverse heat conduction problem for nanoscale structures was studied. The conduction phenomenon is modelled using the Boltzmann transport equation. Phonon‐mediated heat conduction in one dimension is considered. One boundary, where temperature observation takes place, is subject to a known boundary condition and the other boundary is exposed to an unknown temperature. The gradient method is employed to solve the described inverse problem. The sensitivity, adjoint and gradient equations are derived. Sample results are presented and discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

FEM for evaluation of weight functions for SIF, COD and higher-order coefficients with application to a typical wedge splitting specimen

In the evaluation of accurate weight functions for the coefficients of first few terms of the linear elastic crack tip fields and the crack opening displacement (COD) using the finite element method (FEM), singularities at the crack tip and the loading point need to be properly considered. The crack tip singularity can be well captured by a hybrid crack element (HCE), which directly predicts accurate coefficients of first few terms of the linear elastic crack tip fields. A penalty function technique is introduced to handle the point load. With the use of these methods numerical results of a typical wedge splitting (WS) specimen subjected to wedge forces at arbitrary locations on the crack faces are obtained. With the help of appropriate interpolation techniques, these results can be used as weight functions. The range of validity of the so-called Paris equation, which is widely used in the evaluation of the COD from the stress intensity factors (SIFs), is established.     

Dispersion relations for SH-wave propagation in periodic piezoelectric composite layered structures

Propagation behavior of horizontally polarized shear waves (SH-waves) in a periodic piezoelectric-polymeric layered structure is taken into account. The layered structures are consisted of piezoelectric thin films bonded perfectly with polymeric thin films alternately. The phase velocity equations of SH-waves propagation in the periodic layered piezoelectric structure are obtained for the cases of wave propagation in the direction normal to the interface and along the interface, respectively. Filter effect of this kind of structure and the effects of volume fraction and shear modulus ratio of piezoelectric layer to polymeric layer on the phase velocity are discussed in detail, respectively. One set of piezoelectric thin film--polymeric thin film multilayer system (PZT-5H piezoelectric ceramics--polythene) is chosen to show the numerical simulation, basic properties of SH-waves propagation in this particular structure are revealed.     

新乡地区塑限与液限之线性回归方程研究

中通过对大量试验数据的统计，得出了塑限与液限之间的线性回归方程，并与实测数据进行了对比，结果表明两有良好的一致性．     

一次时滞微分方程零解的全局吸引性

讨论了含有一个滞量的线性、非线性泛函微分方程零解的全局吸引性，对于线性泛函微分方程，x(t)=-a(t)x(t)-6(t)x(t-τ)，构造了Liapunov泛函，利用Liapunov稳定性定理，得到了线性泛函微分方程零解全局吸引的一个充分条件，同时将这一结论应用于非线性方程x(t)=F(t，x(t)，x(t-τ))和立xt)=f(x(t-τ))，证明了在一定条件下它的零解是全局吸引的。