Papers by Keyword: Non-Linear Least Square Method

Abstract: Vapor liquid equilibria (VLE) of two binary mixtures (ethylene glycol + glycerol and 1,2-propylene glycol + ethylene glycol) were measured at 20Pa. The experimental data satisfy the thermodynamic consistency by Herington method. The vapor phase can be considered as ideal phase, while the non-ideality of the liquid phase was symbolized by Wilson and NRTL activity coefficient models. The experimental data were regressed and correlated by nonlinear least square method of Matlab optimization toolbox. It is found that under the medium vacuum the relative deviations between experimental data and calculated results by the activity coefficient models for low and moderate pressures are larger than 50%. Hence a cubic polynomial regarding the molar composition of liquid phase as the correction of the models was proposed and used in regression to get the interaction parameters. The results showed that the relative deviations between calculated and experimental data are smaller than 1%. The corrected models can provide a calculation basis or data reference for medium vacuum distillation.

Abstract: In this paper, transparent dynamic photoelastic experimental hybrid method for propagating cracks in orthotropic material was developed. Using transparent dynamic photoelastic experimental hybrid method, we can obtain stress intensity factor and separate the stress components from only isochromatic fringe patterns without using isoclinics. When crack is propagated with constant velocity, the contours of stresses components in the vicinity of crack tip in orthotropic material are similar to those of isotropic material or orthotropic material with stationary crack under the static load. Dynamic stress intensity factors are decreased as crack growth. It was certified that the dynamic photoelastic experimental hybrid method was very useful for the analysis of the dynamic fracture mechanics.

Abstract: hybrid experimental-numerical method is presented for determining the stresses around a circular hole in a finite-width, tensile loaded plate. Calculated fringes obtained by FEA provided the information about the external boundary of the hybrid element, and those fringes on straight lines were used for hybrid analysis. In order to see the effects of varying stress field, different numbers of terms in a power-series representation of the complex type stress function were tested. Actual and reconstructed fringes were compared. The hybrid results were highly comparable with those predicted by FEA. The result showed that this approach is effective and promising because isochromatic data along the straight lines in photoelasticity can be conveniently measured by use of phase shifting photoelasticity.

Abstract: The reflective photoelastic experiment can be used more effectively than the transparent of photoelastic experimental method in industrial fields. Therefore the reflective photoelastic experimental hybrid method for the fracture mechanics of isotropic material was developed in this research. Using the reflective photoelastic experimental hybrid method we can obtain stress intensity factors and separate stress components from only the isochromatic fringe patterns. The errors between the experimental values and theoretical values for stress intensity factors are less than 10%. It was verified that the reflective photoelastic experimental hybrid method is very useful for the static plane fracture problems, for the stress intensity factors and for the stress components at the vicinity of the crack-tip in isotropic materials.