Application of piece‐wise linear weight functions for 2D 8‐node quadrilateral element in contact problems

The present study is a continuation of our previous work with the aim to reduce problems caused by standard higher order elements in contact problems. The difficulties can be attributed to the inherent property of the Galerkin method which gives uneven distributions of nodal forces resulting in oscillating contact pressures. The proposed remedy is use of piece‐wise linear weight functions. The methods to establish stiffness and/or mass matrix for 8‐node quadrilateral element in 2D are presented, i.e. the condensing and direct procedures. The energy and nodal displacement error norms are also checked to establish the convergence ratio. Interpretation of calculated contact pressures is discussed. Two new 2D 8‐node quadrilateral elements, QUAD8C and QUAD8D, are derived and tested in many examples, which show their good performance in contact problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Constitutive modelling and numerical simulation of multivariant phase transformation in superelastic shape‐memory alloys

This work concerns the micromechanical constitutive modelling, algorithmic implementation and numerical simulation of polycrystalline superelastic alloys under multiaxial loading. The model is formulated in finite deformations and incorporates the effect of texture. The numerical implementation is based on the constrained minimization of the Helmholtz free energy with dissipation. Simulations are conducted for thin tubes of Nitinol under tension–torsion, as well as for a simplified model of a biomedical stent. Copyright © 2004 John Wiley & Sons, Ltd.     

Crushing behaviour of the energy absorbing 'tensor skin' panels

ABSTRACT Research results concerning the simulation of the crushing behaviour of composite systems with energy absorption characteristics are presented in the present work. The study is focused on the ‘tensor skin’ concept, an energy absorbing composite system that was originally developed to improve the crashworthiness of helicopters under water impact and which is promising for utilization in the construction of the lower part of composite fuselage aircraft. The ‘tensor skin’ concept comprises a folded or corrugated composite construction, which upon loading unfolds by forming ‘plastic hinges’, leading to an increase in the load bearing capability of the structure. The numerical modelling issues and the critical aspects of the simulation are discussed. Verification of the numerical simulation procedure is performed by experimental work. The experimental results utilized to assess and validate the numerical procedure were derived within the European Research Project ‘Design for Crash Survivability – CRASURV’ (BRITE – Aeronautics Area). The results of the simulations are generally in good agreement with experimental data.     

Understanding and Modeling the Effect of Surfactants in Enhanced Particle Removal from Surfaces in Aqueous Media

The removal of particulate contamination is a critical issue for many manufacturing processes. It is particularly critical to the electronics industry in which small pieces of microscopic debris remaining after chemical mechanical planarization (cmp) using submicron polishing particles can cause device failure. One way to enhance particle removal following the cmp process is to utilize surfactants. Recent research has shown ways to model the effect of surfactants on enhanced particle removal. However, previous research has not demonstrated the effect of ionic strength on enhanced particle removal associated with surfactant use. Past research has also not shown the combined effects of ionic strength and surfactant concentration on enhanced particle removal using surfactants. This article summarizes the parameters affecting particle removal, and it provides data and analysis on the effect of ionic strength as well as the combined effects of ionic strength and surfactant concentration on particle removal following cmp processing.     

Adaptive Edge Detectors for Piecewise Smooth Data Based on the minmod Limiter

We are concerned with the detection of edges—the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our previous work [Gelb and Tadmor, Appl. Comp. Harmonic Anal., 7, 101–135 (1999)] and realized in the dual Fourier space, is based on concentration factors; with a proper choice of concentration factors one can achieve higher-orders—in fact in [Gelb and Tadmor, SIAM J. Numer. Anal., 38, 1389–1408 (2001)] we constructed exponentially accurate edge detectors. Since the stencil of these highly-accurate detectors is global, an outside threshold parameter is required to avoid oscillations in the immediate neighborhood of discontinuities. In this paper we introduce an adaptive edge detection procedure based on a cross-breading between the local and global detectors. This is achieved by using the minmod limiter to suppress spurious oscillations near discontinuities while retaining high-order accuracy away from the jumps. The resulting method provides a family of robust, parameter-free edge-detectors for piecewise smooth data. We conclude with a series of one- and two-dimensional simulations.To David Gottlieb, on his 60th birthday, with friendship and appreciation.     

Stabilization Methods for Spectral Element Computations of Incompressible Flows

A stabilization method for the spectral element computation of incompressible flow problems is investigated. It is based on a filtering procedure which consists in filtering the velocity field by a spectral vanishing Helmholtz-type operator at each time step. Relationship between this filtering procedure and SVV-stabilization method, introduced recently in [JCP, 2004, 196(2), p680], is established. A number of numerical examples are presented to show the accuracy and stabilization capability of the method.     

Fatigue Behavior and Retrofit Investigation of Distortion-Induced Web Gap Cracking

This paper studies a Kansas Department of Transportation welded plate girder bridge that developed fatigue cracks at small web gaps close to the girder top flange. Repair had been previously performed by softening the connection plate end with a slot retrofit, but cracks were recently found to have reinitiated at some of the repaired details and are again propagating. A comprehensive finite-element method study was performed to investigate the cracking behavior observed in the bridge and to recommend appropriate measures for future bridge retrofit. The analytical results show that stresses developed at the top flange web gaps could exceed yielding under the loading of an HS15 fatigue truck. The current slot repair used in the bridge was found to have introduced higher magnitude fatigue stresses in the web gap. To achieve a permanent repair of the bridge, it is recommended that a welded connection plate to flange attachment be used during future bridge retrofit. The web gap details should be able to withstand unlimited number of load cycles once this additional repair is performed.     

Measurement of the Timoshenko Shear Stiffness. II: Effect of Transverse Compressibility

This is the second of two papers devoted to the issue of measuring the Timoshenko shear stiffness of thin-walled composite beams. In the first paper, the effect of warping on the effective Timoshenko shear stiffness, as measured through bending tests, was studied. The bending test was simulated using finite-element analysis, and the results indicated that the warping effect was minimal. On the other hand, the evidence suggests that transverse flexibility may have a significant influence on the effective Timoshenko shear stiffness, decreasing the effective shear stiffness at shorter test spans. The purpose of the present study is to further investigate this effect and to explore the use of a sandwich theory to predict the measurement error. A higher-order sandwich theory, which captures the transverse strain at concentrated loads and supports, is applied to a commercially available thin-walled composite beam. The results indicate that the sandwich model does capture the decrease in the effective shear stiffness at short spans, and the dependence of the shear stiffness on span-to-depth ratio is similar to that calculated in the first paper, using the finite-element method.     

Significance of the elastic peak stress evaluated by FE analyses at the point of singularity of sharp V-notched components

The paper presents an expression useful to estimate the notch stress intensity factor (NSIF) from finite element analyses carried out by using a mesh pattern with a constant element size. The evaluation of the NSIF from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the presented expression is that (i) only the elastic peak stress numerically evaluated at the V‐notch tip is needed and no longer the whole stress–distance set of data; (ii) the adopted meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. The proposed expression needs the evaluation of a virtual V‐notch tip radius, i.e. the radius which would produce the same elastic peak stress than that calculated by FEM at the sharp V‐notch tip by means of a given mesh pattern. Once such a radius has been theoretically determined for a given geometry, the expression can be applied in a wide range of notch depths and opening angles.