Пружно-пластичне деформування систем тіл при дії електромагнітних полів

Abstract

У статті розглядається проблема пружно-пластичного деформування систем електропровідних тіл за умов дії електромагнітних полів. Надано загальну математичну постановку задачі, яка базується на застосуванні принципу мінімуму повної енергії системи тіл та запропоновано чисельний метод аналізу пружно-пластичного деформування тіл. Проведено розрахунки системи "індуктор – заготовка" для технологічної операції магнітно-імпульсної обробки матеріалів.The electromagnetic fields are condition the work of many technical and technological systems. There are different systems of deformed solid bodies designed to convert the energy (electric generators and transformers); elements of power equipment; systems that generate pulsed electromagnetic fields for various technological purposes and much more. It is known, that the interaction of electromagnetic fields with conductive bodies leads to appearance of eddy currents. Eddy currents interact with the currents of the source, which leads to movement and deformation of the conductive bodies. Values of electromagnetic field energy can be so significant, that will cause irreversible deforming or destruction of the conductive bodies. Thus, creating effective methods of computational analysis of stress-strain state of electrically conductive bodies in the presence of an electromagnetic field is an important task in scientific and practical terms. The correct analysis of the stress-strain state in the presence of the electromagnetic field must be preceded by an analysis of the distribution of electromagnetic field components in the conductive body. Under the process of developing of analysis methods, we must use the appropriate models thermo-mechanical continuum. A modern view of the task suggests that the analysis of the distribution of the vector component of the electromagnetic field and tensor components of the deformation process must be carried out within the framework of coupled statements. In addition, when considering the composite conductive bodies we must adequately consider the effects of contact interaction. Existing analytical and numerical-analytical method of analysis of the stress-strain state of the conductive bodies under the action of the electromagnetic field may be applied directly only to bodies of canonical shape.