On the Galerkin formulation of the smoothed particle hydrodynamics method

In this paper, we propose a Galerkin‐based smoothed particle hydrodynamics (SPH) formulation with moving least‐squares meshless approximation, applied to free surface flows. The Galerkin scheme provides a clear framework to analyse several procedures widely used in the classical SPH literature, suggesting that some of them should be reformulated in order to develop consistent algorithms. The performance of the methodology proposed is tested through various dynamic simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena. Copyright © 2004 John Wiley & Sons, Ltd.     

Three‐dimensional finite element computations for frictional contact problems with non‐associated sliding rule

This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non‐associated.The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non‐associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi‐axes ratio. The frictional contact law and its inverse are derived from a single non‐differentiable scalar‐valued function, called a bi‐potential. The convexity properties of the bi‐potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time‐integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor–corrector step addresses all cases (sticking, sliding, no‐contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour. Copyright 2004 John Wiley & Sons, Ltd.     

Exact static element stiffness matrices of non‐symmetric thin‐walled curved beams

An evaluation procedure of exact static stiffness matrices for curved beams with non‐symmetric thin‐walled cross section are rigorously presented for the static analysis. Higher‐order differential equations for a uniform curved beam element are first transformed into a set of the first‐order simultaneous ordinary differential equations by introducing 14 displacement parameters where displacement modes corresponding to zero eigenvalues are suitably taken into account. This numerical technique is then accomplished via a generalized linear eigenvalue problem with non‐symmetric matrices. Next, the displacement functions of displacement parameters are exactly calculated by determining general solutions of simultaneous non‐homogeneous differential equations. Finally an exact stiffness matrix is evaluated using force–deformation relationships. In order to demonstrate the validity and effectiveness of this method, displacements and normal stresses of cantilever thin‐walled curved beams subjected to tip loads are evaluated and compared with those by thin‐walled curved beam elements as well as shell elements. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical solution of second‐order,two‐point boundary value problems using continuous genetic algorithms

Second‐order, two‐point boundary‐value problems are encountered in many engineering applications including the study of beam deflections, heat flow, and various dynamic systems. Two classical numerical techniques are widely used in the engineering community for the solution of such problems; the shooting method and finite difference method. These methods are suited for linear problems. However, when solving the non‐linear problems, these methods require some major modifications that include the use of some root‐finding technique. Furthermore, they require the use of other basic numerical techniques in order to obtain the solution. In this paper, the author introduces a novel method based on continuous genetic algorithms for numerically approximating a solution to this problem. The new method has the following characteristics; first, it does not require any modification while switching from the linear to the non‐linear case; as a result, it is of versatile nature. Second, this approach does not resort to more advanced mathematical tools and is thus easily accepted in the engineering application field. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. However, being a variant of the finite difference scheme with truncation error of the order O(h²), the method provides solutions with moderate accuracy. Numerical examples presented in the paper illustrate the applicability and generality of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.     

Higher‐order extensions of a discontinuous Galerkin method for mid‐frequency Helmholtz problems

Recently, a discontinuous Galerkin method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution of Helmholtz problems in the mid‐frequency regime. In this paper, this method is extended to higher‐order elements. Performance results obtained for various two‐dimensional problems highlight the advantages of these elements over classical higher‐order Galerkin elements such as Q₂ and Q₄ for the discretization of interior and exterior Helmholtz problems. Copyright © 2004 John Wiley & Sons, Ltd.     

A Note on Weighted Least‐squares Estimation of the Shape Parameter of the Weibull Distribution

This study proposes an alternative to the weighted least‐squares (WLS) procedure for estimating the shape parameter of the Weibull distribution. Bergman (Journal of Materials Science Letters 1986; 5:611–614), Faucher and Tyson (F&T) (Journal of Materials Science Letters 1988; 7:1199–1203) suggested using different WLS approaches for Weibull parameters. However, the simulation results show that the novel approach is better than that of Bergman, and is not significantly different from that of F&T. Furthermore, the novel approach is also simpler and easier to comprehend. Copyright © 2004 John Wiley & Sons, Ltd.     

Statistical Inference about the Shape Parameter of the New Two‐parameter Bathtub‐shaped Lifetime Distribution

This paper proposes a simple and exact method for conducting a statistical test about the shape parameter of the new two‐parameter lifetime distribution with a bathtub‐shaped or increasing failure rate function, as well as an exact confidence interval for the same parameter. The necessary critical values of the test are given. The method provided in this paper can be used for type II right censored data. Moreover, Monte Carlo simulation and an example are used to compare this new method to the existing approach of Chen (Statistics and Probability Letters 2000; 49:155–161). Copyright © 2004 John Wiley & Sons, Ltd.     

Influence of Powder Morphology and Chemical Composition on Metallic Foams produced by SlipReactionFoamSintering (SRFS)‐ Process

The SlipReactionFoamSintering (SRFS)‐ process is a metallurgical method to produce open‐cell metallic foams of iron based materials, steels and nickel based materials. In this process several chemical reactions take place. Through the most influential parameter, the morphology of the metallic powder, different properties of the foam can be adjusted, such as the viscosity of the slip, the cell structure and the mechanical properties. Several examples are presented in this paper. Moreover, the thermal conductivity of three foams is measured with the transient‐heat‐source‐technique.     

Semi‐Solid Processing of Metal Alloys

Semi‐solid metal casting is an innovative technology for the production of near‐net‐shape parts with demanding mechanical properties. The paper describes different processing routes and materials for semi‐solid‐metal casting (SSM), which have been investigated and also partially developed at the Foundry‐Institute of Aachen University. The standard thixocasting process for aluminium, highly reactive magnesium alloys and steel alloys with high melting points was investigated under variation of a wide range of process parameters. Specially adapted pre‐material production and reheating methods were developed for different materials and their application and future potential is pointed out. The thixocasting experiments were executed on a modified high pressure die‐casting machine with a specially designed “step‐die” providing wall thicknesses from 0.5 to 25 mm. The mechanical properties were tested in dependence of the wall thickness and the metal velocity. The results of these examination show high tensile strength values in combination with very good elongations. The rheocasting process is a new SSM‐forming method with liquid melt as feed‐stock and a high recycling potential. The research results of RCP‐technology (Rheo‐Container‐Process) invented at the Foundry‐Institute and of the Cooling‐Channel‐Process for aluminium and magnesium alloys are promising and are presented in this paper. Studies on semi‐solid processing of magnesium alloys and mixtures of them were conducted by Thixomolding^TM. To establish the most adequate process parameters, the temperature and the mixture relations were varied. Using a mould for tensile test specimens, the mechanical properties and the microstructure evolution could be evaluated. The chemical composition of the different phases was determined using SEM and EDX technologies. Evaluations of the flowing properties were conducted using a spiral mould with a total length of 2m and a cross section of 20mm x 1.5mm.     

Assuring Microstructural Homegeniety in Dual Phase and Trip Steels

The presence of ferrite/pearlite bands in dual phase and TRIP assisted steels is a consequence of microchemical segregation which causes mechanical properties anisotropy. Such inhomogeneous phase distribution produces a lowering of the mechanical properties such as fracture behaviour. This anisotropy is commonly not accounted in micromechanics computations which often assume a random distribution of phases in the solid. The present paper deals with an integral model for this undesirable band formation accounting for the solute segregation caused by solidification, microcomponent diffusion present in the austenitisation process, and the nucleation of the transformed phase in segregated regions. In the present work, the model was applied to two industrial grade dual phase steels and two TRIP assisted steels. The influence of such parameters on band formation is summarised in a number of “band prevention plots”, which are aimed at providing the optimum processing conditions for ferrite/pearlite band prevention.