Drifting response of hysteretic oscillators to stochastic excitation

Under a zero-mean, broad-band, stationary-random load, the symmetric elastic perfectly plastic oscillator and many similar hysteretic systems exhibit a Brownian-like displacement response: asymptotically, the displacement mean vanishes and the displacement variance linearly increases with time. This diverging behavior, often referred to as the drift, is observed even when the excitation power spectrum vanishes at zero frequency, an instance so far lacking a satisfactory modeling within the framework of statistical linearization. The paper presents a linearization-based method which captures the drift in such an instance without requiring any simulation-calibrated parameter. The method combines statistical linearization with stochastic averaging and a generalized van der Pol transformation comprising terms introduced to make allowance for the drift. Model predictions are compared with Monte Carlo estimates for an excitation whose power spectrum vanishes at zero frequency. Good agreement is found for a wide range of excitation levels despite the extremeness of the non-linearity.     

Anisotropic mesh adaptation: towards user‐independent,mesh‐independent and solver‐independent CFD. Part I: general principles

The present paper is the lead article in a three‐part series on anisotropic mesh adaptation and its applications to structured and unstructured meshes. A flexible approach is proposed and tested on two‐dimensional, inviscid and viscous, finite volume and finite element flow solvers, over a wide range of speeds. The directional properties of an interpolation‐based error estimate, extracted from the Hessian of the solution, are used to control the size and orientation of mesh edges. The approach is encapsulated into an edge‐based anisotropic mesh optimization methodology (MOM), which uses a judicious sequence of four local operations: refinement, coarsening, edge swapping and point movement, to equi‐distribute the error estimate along all edges, without any recourse to remeshing. The mesh adaptation convergence of the MOM loop is carefully studied for a wide variety of test cases. The mesh optimization generic coupling of MOM with finite volume and finite element flow solvers is shown to yield the same final mesh no matter what the starting point is. It is also shown that on such optimized meshes, the need for computational fluid dynamics (CFD) stabilization artifices, such as upwinding or artificial viscosity, are drastically reduced, if not altogether eliminated, in most well‐posed formulations. These two conclusions can be considered significant steps towards mesh‐independent and solver‐independent CFD. The structure of the three‐part series is thus, 1, general principles; 2, methodology and applications to structured and unstructured grids; 3, applications to three‐dimensional flows. Copyright © 2000 John Wiley & Sons, Ltd.     

Screening of spherical moulds manufactured isotropically in plasma etching conditions

Micro-moulding is a critical rapid prototyping process chain used for a wide range of applications. This study demonstrates that it is possible to manufacture mould at low excitation frequency plasma (380 kHz), on a silicon substrate using fluorinated chemistry. According to the mask aperture designed and process time, the cavities profile characteristics, depending on the plasma chemistry, were analysed to predict the degree of anisotropy and the curvature. We show the possibility of creating curvature shapes with a desirable conic constant k of 1.25. In particular, we highlighted the smallest aperture sizes are more attractive for replicating optical micro-lens arrays using silicon moulds. Otherwise, the largest aperture sizes gain more attention for optoelectronics, microsystems, and microfluidics applications.     

On thermodynamic potentials in thermoelasticity under small strain and finite thermal perturbation assumptions

Expressions for thermodynamic potentials (internal energy, Helmholtz energy, Gibbs energy and enthalpy) of a thermoelastic material are developed under the assumption of small strains and finite changes in the thermal variable (temperature or entropy). The literature provides expressions for the Helmholtz energy in terms of strain and temperature, most often as expansions to the second order in strain and to a higher order in temperature changes, which ensures an affine stress–strain relation and a certain temperature dependence of the moduli of the material. Expressions are here developed for the four potentials in terms of all four possible pairs of independent variables. First, an expression is obtained for each potential as a quadratic function of its natural mechanical variable with coefficients depending on its natural thermal variable that are identified in terms of the moduli of the material. The form of the coefficients’ dependence on the thermal variable is not specified beforehand so as to obtain the most general expressions compatible with an affine stress–strain relation. Then, from each potential expressed in terms of its natural variables, expressions are derived for the other three potentials in terms of these same variables using the Gibbs–Helmholtz equations. The paper provides a thermodynamic framework for the constitutive modeling of thermoelastic materials undergoing small strains but finite changes in the thermal variables, the properties of which are liable to depend on the thermal variables.     

Prototropic tautomerism and microsolvation in antitumor drug imexon: a DFT study

Density functional theory method, at the B3LYP/6–311+G(d, p) level has been used to explore the geometries, relative energies, and electronic properties of all hypothetically possible prototropic tautomers of imexon. The specific interactions of the tautomeric forms of imexon with one and two solvating water molecules have been investigated. The relative stability order of the complexes remains unchanged upon interaction with one water molecule. The addition of a second water molecule, however, stabilizes the oxo-amino form more than the oxo-imino structure. The bulk water environment has been simulated by a combination of microhydration and the conductor-like polarizable continuum model. The energy profile corresponding to the prototopic tautomerisms connecting oxo-imino form with oxo-amino, hydroxyl-amino, and one rare tautomer has been studied. We found that the tautomerism activation barriers are high enough as to conclude that only the oxo-imino tautomer should be found in the gas phase. Our results present clear evidence that microhydration with one and two solvating water molecules considerably lower these barriers by a concerted multiple proton transfer mechanism.

     

Anisotropic mesh adaptation: towards user‐independent,mesh‐independent and solver‐independent CFD. Part II. Structured grids

The present paper is the second article in a three‐part series on anisotropic mesh adaptation and its application to (2‐D) structured and unstructured meshes. In the first article, the theory was presented, the methodology detailed and brief examples given of the application of the method to both types of grids. The second part details the application of the mesh adaptation method to structured grids. The adaptation operations are restricted to mesh movement in order to avoid the creation of hanging nodes. Being based on a spring analogy with no restrictive orthogonality constraint, a wide grid motion is allowed. The adaptation process is first validated on analytical test cases and its high efficiency is shown on relevant transonic and supersonic benchmarks. These latter test cases are also solved on adapted unstructured grids to provide a reference for comparison studies. The third part of the series will demonstrate the capability of the methodology on 2‐D unstructured test cases. Copyright © 2002 John Wiley & Sons, Ltd.