Modeling of laser keyhole welding: Part I. mathematical modeling,numerical methodology,role of recoil pressure,multiple reflections,and free surface evolution

A three-dimensional laser-keyhole welding model is developed, featuring the self-consistent evolution of the liquid/vapor (L/V) interface together with full simulation of fluid flow and heat transfer. Important interfacial phenomena, such as free surface evolution, evaporation, kinetic Knudsen layer, homogeneous boiling, and multiple reflections, are considered and applied to the model. The level set approach is adopted to incorporate the L/V interface boundary conditions in the Navier-Stokes equation and energy equation. Both thermocapillary force and recoil pressure, which are the major driving forces for the melt flow, are incorporated in the formulation. For melting and solidification processes at the solid/liquid (S/L) interface, the mixture continuum model has been employed. The article consists of two parts. This article (Part I) presents the model formulation and discusses the effects of evaporation, free surface evolution, and multiple reflections on a steady molten pool to demonstrate the relevance of these interfacial phenomena. The results of the full keyhole simulation and the experimental verification will be provided in the companion article (Part II).     

Reliability and scale effect in toughness of concrete structures

In the present work, the distribution of the random toughness characteristics (i.e. critical energy release rate, G_1c) has been evaluated on the basis of experimental observations. Fracture test results from three groups of geometrically similar concrete specimens of size (width×total depth×thickness), 420×420×50–1680×1680×200 mm³, made with different maximum aggregate size of 9.5, 19, 38, and 76 mm were analyzed using a recently proposed distribution of extremes. In applications of probability, it is important to use an appropriate distribution type and adequate techniques for estimating the parameters of distribution. In this study, a new type distribution of minima is employed for probability computations. It was noticed that the entropy of distribution increases with the crack length, i.e. the uncertainty of toughness, G_1c, value increases with crack length. A non-linear reduction of the maximum allowable splitting force with the defect size, a, was noticed. For large specimens, the maximum allowable splitting load is more sensitive to the required reliability level than that for small specimens. Reliability increases with aggregate size when all other conditions were constant.     

Efficient mixed Timoshenko–Mindlin shell elements

The precise representation of rigid body motions in the displacement patterns of curved Timoshenko–Mindlin (TM) shell elements is considered. This consideration requires the development of the strain–displacement relationships of the TM shell theory with regard to their consistency with the rigid body motions. For this purpose a refined TM theory of multilayered anisotropic shells is elaborated. The effects of transverse shear deformation and bending‐extension coupling are included. The fundamental unknowns consist of five displacements and eight strains of the face surfaces of the shell, and eight stress resultants. On the basis of this theory the simple and efficient mixed models are developed. The elemental arrays are derived using the Hu–Washizu mixed variational principle. Numerical results are presented to demonstrate the high accuracy and effectiveness of the developed 4‐node shell elements and to compare their performance with other finite elements reported in the literature. Copyright © 2002 John Wiley & Sons, Ltd.     

Constant thrust programming for a multistage rocket flown in vacuum with a given initial/final thrust-to-weight ratio in an arbitrary stage

The burn time and burnout velocity of a multistage rocket flown vertically in vacuum with constant thrust tangential to the flight path and a prescribed initial/final thrust-to-weight ratio in an arbitrary stage have been determined. The present paper also deals with optimal staging under given conditions of flight.     

High-Frequency Variations in the Rotation of the Earth

We report here observational results demonstrating that a three-station network of properly distributed VLBI observatories can routinely determine UT1 with a formal standard error of ±0.05 ms of time, in an observing period of 24 h. We also report the results of a three-month series of daily observing sessions of only 1-h duration with a single interferometer, which produced estimates of UT1 with standard errors of ±0.1 ms. The UT1 values obtained from the 1-h observing sessions track smoothly between the points of the 24-h time series, and the combined time series shows that it is not unusual for UT1 to vary by 1-2 ms in periods of several days. Preliminary results of reprocessing the 24-h observing sessions in 2-h segments suggest that variations of 0.4 ms may occur on time scales of only 6-8 h.     

Flotation machine design: impeller—stator interaction

The separate contributions of impellers and stators to suction are studied by means of interaction models. From these, suction can be predicted when interchangeable components are used in any combination, and in either direction of impeller rotation. Methods are devised by which numerical values of the impeller and stator terms can be simply assigned. The resulting model provides good agreement with experiment. The influence of variability in component geometry is reflected in the model parameters. Possible applications of the model are suggested.