Mykhailova I. Methods and means of mathematical modelling of temperature fields in technological processes of contactless laser deformation research

The goal of the dissertation is development of methods and means of mathematical modelling of thermal fields in technological process of contactless laser deformation while ensuring required quality of modelling considering high speed of processes and gradients. Object of the research is thermal processes, which accompany technological realisation of contactless laser deformation. Mathematical models of temperature fields of plate irradiated by two laser beams and mathematical models of distribution of power density of laser ray weredeveloped. Method of adaptive grid building was modified to be used with balance method. Parallelization of adaptive method was introduced. Mesh method was improved using Kochanek-Bartels splines for interpolation of the result. Method of accuracy estimation of modeling results is proposed. Designed models, methods and algorithms were implemented in practice in software tools, which are used for manufacturing and in appropriate courses.