Smeared crack approach: back to the original track

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd.     

The optimum control of thruster system for dynamically positioned vessels

An offshore vessel with a dynamic positioning system (DP system) needs fast response to produce thrust to counteract the environmental forces acting on it for the purpose of maintaining its position and heading as close as possible to the working position. Therefore, quick and effective modulation of the thrust is the problem to determine the thrust and the rotation angle of the thruster devices of the ship. This paper presents an effective optimum control for a thruster system, using the sequential quadratic method to achieve economical and effective modulation of the thrust and the direction of the thruster. An optimum control study of a 2280 tons DP coring vessel with five rotary azimuth thruster marine positioning is studied in detail, which can quickly and exactly estimate the thrusts and angles of direction of all the thrusters. The results can provide a valuable thruster system for a dynamically positioned vessel.     

基于GPS的短基线定向测量及精度分析

介绍了利用GPS载波相位测量技术进行短基线定向的基本方法,推导了估计GPS短基线定向的精度公式,得到了对于边长400～700 m的基线可以达到±(1"～2")的方位精度.     

Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

Strength and stability of frictional sliding of gabbro gouge at elevated temperatures

To investigate the strength of frictional sliding and stability of mafic lower crust, we conducted experiments on oven-dried gabbro gouge of 1 mm thick sandwiched between country rock pieces (with gouge inclined 35° to the sample axis) at slip rates of 1.22 × 10^− 3 mm/s and 1.22 × 10^− 4 mm/s and elevated temperatures up to 615 °C. Special attention has been paid to whether transition from velocity weakening to velocity strengthening occurs due to the elevation of temperature.Two series of experiments were conducted with normal stresses of 200 MPa and 300 MPa, respectively. For both normal stresses, the friction strengths are comparable at least up to 510 °C, with no significant weakening effect of increasing temperature. Comparison of our results with Byerlee's rule on a strike slip fault with a specific temperature profile in the Zhangbei region of North China shows that the strength given by experiments are around that given by Byerlee's rule and a little greater in the high temperature range.At 200 MPa normal stress, the steady-state rate dependence a − b shows only positive values, probably still in the “run-in” process where velocity strengthening is a common feature. With a normal stress of 300 MPa, the values of steady-state rate dependence decreases systematically with increasing temperature, and stick-slip occurred at 615 °C. Considering the limited displacement, limited normal stress applied and the effect of normal stress for the temperatures above 420 °C, it is inferred here that velocity weakening may be the typical behaviour at higher normal stress for temperature above 420 °C and at least up to 615 °C, which covers most of the temperature range in the lower crust of geologically stable continental interior. For a dry mafic lower crust in cool continental interiors where frictional sliding prevails over plastic flow, unstable slip nucleation may occur to generate earthquakes.     

Mongolian gerbils and Daurian pikas responded differently to changes in precipitation in the Inner Mongolian grasslands

Mongolian gerbils (Meriones unguiculatus) and Daurian pikas (Ochotona dauurica) are two key small mammal species in the Inner Mongolian grasslands, China. Mongolian gerbils displayed density-dependent population growth, but the time lag of density dependence was short and within season. The spring–autumn population growth rate was inversely related to population density in Mongolian gerbils of the Erdos desert grasslands. The autumn–spring population growth rate of Mongolian gerbils was inversely related to winter precipitation. Precipitation had stronger effects on the population growth of gerbils during the non-breeding season. The monthly population growth rate of Daurian pikas was positively related to the monthly precipitation and was inversely related to population density in central Inner Mongolia. Daurian pikas select habitats with tall plants. Increased precipitation enhances plant production and increases the height of plants in arid and semi-arid regions. This enhancement of plant height might increase the population growth of Daurian pikas. Mongolian gerbils live in short grasslands. Increased winter precipitation might result in higher winter mortality of Mongolia gerbils, or taller plants might supress gerbil population growth in wet years. Therefore, responses of small mammal species to changes in precipitation depend on the life history of small mammals and changes in vegetation induced by climatic changes.     

Estimation of azimuth and slowness of tele-seismic signals recorded by a local seismic network

Introduction The azimuth and slowness are two major features of seismic signals. The accurate estimation of them is quite important for both phase identification and event location. Generally, there are two types of seismic stations, i.e. 3-component stations (3C) and arrays. To estimate the two direc-tional parameters, the polarization analysis (Jurkevics, 1988) is commonly used for 3C stations and the frequency-wavenumber spectrum analysis ( f-k) (Capon, 1969; Kvaerna, Doornbos, 1986) is …