The paper presents the application of the newly developed method of the solution of nonlinear equations to the adaptive modelling and computer simulation. The approach is suitable when the system of equations can be arranged in such a way that it consists of a large number of linear equations and a smaller number of nonlinear equations. This situation occurs in the case of adaptive modelling of mechanical systems using finite elements or finite differences techniques. In this case the classical least square method becomes very effective. The paper presents several examples of the application of the method. A solution to the, so called, “black box” problem is also presented.
In the paper, the author presents experimental analysis of propagation of plastic zones in two-dimensional models with different stress concentrators. The experimental tests were carried out by photoelastic coating method on duralumin stripes loaded by tensile stresses. For various levels of loading, the photographs of isochromatic pattern were taken under loading and after removing loading. On the basis of isochromatic pattern recorded for loaded models, the boundaries of plastic zones were determined using the Treska-Coulomb yield condition. The isochromatic pattern taken for the unloaded, but previously partly plastified elements, show the picture of the residual strain remaining in the material. A discussion of the results is presented.
In the paper, the author presents the application of thermography method for investigation of elastic-plastic states in two-dimensional models. The experimental testing was carried out on the duralumin elements with different stress concentrators loaded by uniformly distributed tensile stresses. The changes of temperature distribution on the surface of the models during loading process were recorded by a thermovision camera. On the basis of calibrating test carried out on the stretched element, the relationship between loading, temperature increment and specimen elongation was determined. Quantitative temperature distribution in chosen cross-sections of the models was determined using thermograms received for various levels of loading. On the basis of the obtained results, the author estimated the accuracy of the method as well as its usability for investigation of the plastic zones' localization and propagation.