Studies generalization of shape change of equipotential surfaces of stress-deformed objects

Abstract

The vast majority of analytical studies of the stress-strain state of various objects of technical systems, performed at the stage of their development and design, show that the operational characteristics of these technical objects are determined by the geometric parameters of their shape change to a much greater extent than by the parameters of their stress state. The specified geometric parameters of the deformed objects are determined by the contours of the shape-changing profile of these objects and the contours of their cross-sections, which are identically described by sections of closed curves of the 4th order, which in general are the corresponding lemniscates. On the basis of the analysis of numerous analytical and experimental studies of various technical objects consisting of transversally isotropic and isotropic media, a grapho-analytical analog model of the dynamics of shape change of the contours of equipotential surfaces and plane sections of deformed technical objects in the form of a section of the Cassini oval with three characteristic inflection points is offered. The possibility of practical modeling of the shape change of the contours of the surfaces of deformed objects is considered using the examples of the dynamics of the deformation of the pneumatic shell of the periphery of the wheel drive of mobile wheeled equipment and the layer-by-layer deformation of the transverse profile of the soil by the elastic wheel drive of a mobile vehicle. The evaluation of the developed grapho-analytical model, which is analogous to the dynamics of the shape change of surface contours and flat cross-sections of technical objects, shows that the average level of confidence in such a model in comparison with the assessment of the degree of deformation according to the Genki and Swainger criteria is 86,8 %. At the same time, the minimum level of confidence probability, determined by the Henki deformation measure criterion, cannot be less than 82,3 %.

Keywords

• cassini oval
• lemniscate
• model
• equipotential surface
• shape change dynamics