Застосування згладжуючих кубічних сплайнів у моделюванні процесів повзучості лінійно-вʼязкопружних матеріалів за умов складного напруженого стану

Abstract

The processes of creep of thin-walled tubular elements made of linear viscoelastic materials under complex stress conditions are considered. The discrete values of basic experimental data on uniaxial tension and pure torsion are considered. These discrete values are used for identification of hereditary kernels normally used in creep modeling processes under complex stress conditions. As an example material, plexiglass ST1 is used for calculations. The area of linearity of the model is substantiated by the value of the quantile of statistics and the hypothesis of the existence of a unified creep function in a certain, predetermined confidence interval. The creep function is invariant with respect to stresses and is built with making use of the yield curves. Constitutive equations of the model contain a set of functions and coefficients determined from basic experiments. For further calculations, the experimental data are approximated by a power function followed by the smoothing with cubic splines. Approximation analysis is carried out by evaluation of the least squared deviation of experimental data from the calculated data. The approximating function is analyzed with making use of minimum of the quadratic deviation.