Umbrella spherical integration: a stable meshless method for non‐linear solids

A stable meshless method for studying the finite deformation of non‐linear three‐dimensional (3D) solids is presented. The method is based on a variational framework with the necessary integrals evaluated through nodal integration. The method is truly meshless, requiring no 3D meshing or tessellation of any form. A local least‐squares approximation about each node is used to obtain necessary deformation gradients. The use of a local field approximation makes automatic grid refinement and the application of boundary conditions straightforward. Stabilization is achieved through the use of special ‘umbrella’ shape functions that have discontinuous derivatives at the nodes. Novel efficient algorithms for constructing the nodal stars and computing the nodal volumes are presented. The method is applied to four test problems: uniaxial tension, simple shear and bending of a bar, and cylindrical indentation. Convergence studies at infinitesimal strain show that the method is well‐behaved and converges with the number of nodes for both uniform and non‐uniform grids. Typical of meshless methods employing nodal integration, the total energy can be underestimated due to the approximate integration. At finite deformation the method reproduces known exact solutions. The bending example demonstrates an interesting example of torsional buckling resulting from the bending. Copyright © 2006 John Wiley & Sons, Ltd.     

The Quasicontinuum Method: Overview, applications and current directions

The Quasicontinuum (QC) Method, originally conceived and developed by Tadmor, Ortiz and Phillips [1] in 1996, has since seen a great deal of development and application by a number of researchers. The idea of the method is a relatively simple one. With the goal of modeling an atomistic system without explicitly treating every atom in the problem, the QC provides a framework whereby degrees of freedom are judiciously eliminated and force/energy calculations are expedited. This is combined with adaptive model refinement to ensure that full atomistic detail is retained in regions of the problem where it is required while continuum assumptions reduce the computational demand elsewhere. This article provides a review of the method, from its original motivations and formulation to recent improvements and developments. A summary of the important mechanics of materials results that have been obtained using the QC approach is presented. Finally, several related modeling techniques from the literature are briefly discussed. As an accompaniment to this paper, a website designed to serve as a clearinghouse for information on the QC method has been established at www.qcmethod.com. The site includes information on QC research, links to researchers, downloadable QC code and documentation. This revised version was published online in June 2006 with corrections to the Cover Date.     

On torque ripple reduction in current-fed switched reluctancemotors

This paper addresses a basic control issue in switched reluctance motor (SRM) drives-the production of a ripple-free torque. Simple and largely model-independent conventional supply waveforms are not able to satisfy this requirement. The goal of this paper is to improve SRM dynamical performance by compensating for motor nonlinearities, while maintaining the robustness of conventional methods. The method is based on a complete parameterization of position-dependent voltage and current profiles in ripple-free operation, and on a waveform optimization to minimize power supply requirements. Furthermore, model uncertainties are included to show that the proposed strategy consistently outperforms the conventional policy. Experimental data verifying the analytical approach are included     

Robust control in the gap: a state-space solution in the presenceof a single input delay

A solution is provided to the problem of (sub)optimal robust design in the gap for a system with a single input lag. The problem is shown to reduce to two matrix algebraic Riccati equations that solve an allied linear-quadratic-Gaussian/H₂ problem and a parameterized differential matrix Riccati equation. The analysis intertwines finite-dimensional delay equations and distributed abstract evolution models. The parameterized family of suboptimal compensators is presented in terms of a neutral equation model     

A melting model for reciprocating screw injection-molding machines

A theoretical model for melting in reciprocating screw injection molding machines is proposed. The model permits the calculation of the solid bed profile as a function of time during the injection cycle. It consists of a dynamic extrusion melting model for the rotation period, a transient heat conduction model with a phase transition for the screw rest period, and a proposed model for the drifting of the beginning of melting during the injection cycle.     

Mixing and residence time distribution in melt screw extruders

The residence time distribution (RTD) functions were derived for screw extruders, based on the “parallel plate” and curved channel flow models. The results indicate a relatively narrow distribution, and they explain several characteristics of screw extruders. The strain distribution in the fluid across the channel was also derived. With the aid of these two functions an average strain of the fluid leaving the extruder was defined. The resulting weighted-average total strain (WATS) provides a quantitative criterion to the “goodness of mixing” in extruders.     

On the reduction of certain frequency-shaped linear quadraticdissipative design problems to an H∞ formulation

This paper concerns a concept of frequency-based quadratic dissipativity and its reduction to an equivalent H_∞ (or μ) condition. The paper is motivated by the observation that a strictly proper system cannot be strictly passive; hence, results on the synthesis of positive real systems using the Cayley transform directly cannot be applied in most physical situations     

H/sup /spl infin// control and estimation with preview-part I: matrix ARE solutions in continuous time

Preview control and fixed-lag smoothing allow a noncausal component in the controller/estimator. Time domain variational analysis is used in a reduction to an open loop differential game, leading to a complete, necessary and sufficient characterization of suboptimal values and an explicit state space design, in terms of a parameterized (nonstandard) algebraic matrix Riccati equation in a general continuous time linear system setting. The solution offers insight into the appropriate structure of the associated Hamiltonian, where the state and co-state are not the usual state of the original dynamic system and that of its adjoint. Rather, the state and co-state are selected to capture the respective lumped effects of initial data and future input selection in the allied game.     

Atmospheric aerosols over two sites in a southeastern region of Texas

Speciated samples of PM_2.5 were collected at the Bayland Park and Orange sites in Southeastern Texas by US EPA (Environmental Protection Agency) from July 2003 to August 2005. A total of 256 samples for the Bayland Park site and 293 samples for the Orange site with 52 species were measured; however, 22 species were excluded because of too many below‐detection‐limit data. Among the 22 species excluded, 19 species are common to both sites. The two data sets were analyzed by positive matrix factorization (PMF) to infer the sources of PM observed at the two sites. The analysis identified ten common source‐related factors: sulphate‐rich secondary aerosol I, sulphate‐rich secondary aerosol II, cement/carbon‐rich, wood smoke, motor vehicle/road dust, nitrate‐rich secondary aerosol, metal processing, soil, sea salt, and chloride‐depleted marine aerosol. sulphate and nitrate mainly exist as ammonium salts. The two sulphate‐rich secondary aerosols account for about 59% and 54% of the PM_2.5 mass concentration at the two sites, respectively. The factor containing highest concentrations of Cl and Na was attributed to sea salt due to the proximity of the monitoring sites to the Gulf of Mexico. The chloride‐depleted marine aerosol was related to the sea salt aerosol but was identified separately due to the chlorine replacement reactions. Basically, the factor of sulphate, nitrate, and soil at the two sites showed similar chemical composition profiles and seasonal variation that reflect the regional characteristics of these sources. The regional factors showed predominantly low frequency variations, however, the area‐related and local factors showed both high and low frequency variations. Motor vehicle/road dust, sea salt, and chloride‐depleted marine aerosol were likely to be area‐related factors. Cement/carbon‐rich, wood smoke, and metal processing factor were likely to be the local sources.