The article is devoted to the improvement of the methodology for the examination of the operation the vehicles in extreme conditions that occur during road traffic accidents (RTA). Of great interest in the field of road safety are the tasks of determining the causes of RTA and the conditions under which they occur. There are computer systems that allow modeling the processes of interaction automobile vehicles with obstacles and among themselves during an accident. These developments based on various mathematical models of the car collision process. The most reliable and promising are systems that based on methods for analyzing plastic deformations and destruction of car structural elements during an accident. The basis of these methods is the law of conservation energy or the model of the transition of the kinetic energy of a moving vehicle into the potential energy of a structure deformed after an accident. This process described with the help of the parameter – the energy equivalent of the speed. The analysis of the object is study – automobile body structures carried out. They classified as thin-walled shell structures that are easily plastically deformed. The available methods for solving the problems of analysis the elastic-plastic deformations in such structures do not allow providing the high accuracy of the solution necessary for the examination of the RTA.
 Purpose – improvement of the methodology for conducting an autotechnical examination of an accident.
 Methodology: solution of inverse problems of continuum mechanics.
 Results: a variant of the finite element representation of the design and a method of the variational approach to determining the energy criteria of the process under study were developed. It provides the greatest accuracy in solving the tasks.
 Practical implications: it is expedient to apply the obtained results when carrying out an autotechnical examination of an accident.
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