Computational performance of Free Mesh Method applied to continuum mechanics problems

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics.     

Spectral compact difference hybrid computation of passive scalar in isotropic turbulence

An accurate and efficient hybrid numerical method is developed for direct numerical simulation of passive scalar in homogeneous turbulence for the Schmidt number 1 and 50. The hybrid method uses the standard Fourier spectral method for the incompressible Navier–Stokes equation and the combined compact difference scheme for the passive scalar transport equation. Accuracy of the method is carefully examined by comparing with the full spectral method regarding the spectra, probability density function, field structure of the passive scalar, and is found to be very satisfactory. The computational time for the hybrid method is decreased by 26% for the Schmidt number 1 when compared to the full spectral method, and by 77% for the Schmidt number 50 when the number of grid points for the velocity field is reduced under the scale separation.     

A class of plastic constitutive equations with vertex effect—IV. Applications to prediction of forming limit strains of metal sheets under nonproportional loadings

The new plastic (elastoplastic) constitutive equation with vertex effect which was proposed and developed in the previous papers is applied to prediction of the forming limit strains of metal sheets which are subjected to various nonproportional loading without unloading and to proportional loading after another proportional loading with or without unloading. It is demonstrated that the constitutive equation is very effective, that appropriately curved strain-paths give much larger limiting strains than the corresponding straight paths do, that abrupt change in stress- or strain-path very often induces a catastrophic breakage at the instant of the path-change, and that very useful secondary FLDs (forming limit diagrams) can be drawn.     

Brittle fracture and spinnability of viscous materials

Conclusion In both cases, brittle fracture and dropping breakdown, only very little deformation or elongation was observed in the experiments mentioned above, and limiting conditions were obtained reproducibly with respect to rate of extension and temperature. The brittle limits give the condition where the viscous resistance due to locally concentrated stress, i. e. the grip effect (5) exceeds cohesion of the materials, and development of the surface of separation is followed. At the dropping limits, the viscosities of the liquids may be too small to resist shrinking by surface tension with respect to the rate of extension. Although the theory of spinnability proposed here may be only tentative, it can be pointed out that surface tension plays some important role in spinning of viscous liquids of lower molecules. Concerning higher molecules, rubber-like elasticity as well as viscosity may become more important (6).

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Zusammenfassung Für beide Fälle, spröden Bruch und stufenweiser Bruch, wurde nur sehr geringe Deformation oder Verlängerung beobachtet und Grenzbedingungen hinsichtlich Dehnungsgeschwindigkeit und Temperatur reproduzierbar erhalten. Die Bruchgrenzen geben die Bedingungen, bei denen der viskose Widerstand entsprechend den lokalen Spannungskonzentrationen, d. h. entsprechend den grip-Effekt die Kohäsion des Materials übersteigt, und die Entwickelung der Trennfläche wird verfolgt. Bei der Grenzbelastung für das Absinken der Spannung mag die Viskosität der Flüssigkeiten zu gering sein, um dem Schrumpfen durch Oberflächenspannung im Vergleich mit der Dehnungsgeschwindigkeit entgegen zu wirken. Obgleich die Theorie der Spinnbarkeit, hier vorgeschlagen, nur einen Versuch darstellt, kann behauptet werden, daß die Oberflächenspannung beim Spinnen viskoser Flüssigkeiten mit kleineren Molekülen eine wichtige Rolle spielt. Für höhermolekulare Substanzen wird neben der Viskosität auch die Gummielastizität ausschlaggebend.

     

Tricolor photoviscoelastic technique and its application to moving contact

A new technique for simultaneous determination of both fringe order and principal direction of birefringence in practical photoviscoelastic analysis using white incident light with a set of the primary colors, called tricolor photoviscoelasticity, is described. This method can determine both the fringe order and principal direction of birefringence from a single-color photoviscoelastic image under plane polarization. Then, the authors evaluate time dependent stresses and strains around a contact region in a viscoelastic strip plate under nonproportional loading condition. The variations of the principal stresses and strains are easily obtained over a wide time range by use of the optical constitutive equations of photoviscoelasticity and the characteristic material property functions.     

Coordination characteristics of trivalent lanthanides and actinides in molten hydrate salts of Ca(NO<Subscript>3</Subscript>)<Subscript>2</Subscript> and CaCl<Subscript>2</Subscript>

Distribution behavior of Ce(III), Am(III), and Cm(III) between tri-n-butyl phosphate solution and molten calcium nitrate hydrate Ca(NO₃)₂·RH₂O or molten calcium chloride hydrate CaCl₂·RH₂O was studied radiochemically. In Ca(NO₃)₂·RH₂O systems, maximum separation factors of Ce and Cm to Am were observed to be 12 (Ce/Am) and 1.7 (Cm/Am). The distribution ratios of these elements increased with the decrease of water activity in the hydrates, and the extractabilities at the water deficient region was less sensitive compared to those at the water abundant region. This trend was similar to the coordination circumstance change observed in electronic absorption spectra of Nd(III) in the hydrates.     

Bounding Contingent Claim Prices via Hedging Strategy with Coherent Risk Measures

We generalize the notion of arbitrage based on the coherent risk measure, and investigate a mathematical optimization approach for tightening the lower and upper bounds of the price of contingent claims in incomplete markets. Due to the dual representation of coherent risk measures, the lower and upper bounds of price are located by solving a pair of semi-infinite linear optimization problems, which further reduce to linear optimization when conditional value-at-risk (CVaR) is used as risk measure. We also show that the hedging portfolio problem is viewed as a robust optimization problem. Tuning the parameter of the risk measure, we demonstrate by numerical examples that the two bounds approach to each other and converge to a price that is fair in the sense that seller and buyer face the same amount of risk.     

A converse of Hörmander’s L2-estimate and new positivity notions for vector bundles

Science China Mathematics - We study conditions of Hörmander’s L2-estimate and the Ohsawa-Takegoshi extension theorem. Introducing a twisted version of the Hörmander-type condition,...