Применение метода конечных разностей для решения задачи о напряженно-деформированном состоянии оболочки стержневого твэла

Abstract

Рассмотрены математические формулировки задачи о напряженно-деформированном состоянии оболочки твэла. Показано, что более удобными являются формулировки относительно независимых напряжений и перемещения, поскольку они не содержат производных температурных зависимостей характеристик материала оболочки твэла, хотя и содержат больше уравнений, чем формулировка относительно перемещения. Показано, что применение метода конечных разностей является перспективным для решения задач об определении напряженно-деформированного состояния оболочек твэлов.

The stress-strain behavior definition is required to simulate the behavior of the shell of a fuel element and it requires the solution of appropriately formulated problem on the mechanics of strained solid body taking into consideration the geometric shape, fastening conditions, external influence factors and material characteristics. The purpose of this scientific paper was to study the opportunities of the method of finite differences to solve the problem on the definition of the stress-strain behavior of the shells of fuel elements used by nuclear reactors. Stress-strain behavior of the shell is viewed within the bounds of known hypothesis of axisymmetric plane deformation. Consideration is given to different mathematical formulations of the problem on the stress-strain behavior of the shell of fuel element. It has been shown that the most promising formulation is the one with independent unknown stresses and displacements, because it has no derivatives of temperature relationships for material characteristics. The method of finite differences is rather promising for the solution of problems solved to define the stress-strain behavior of the shells of fuel elements. Though the method of finite differences is believed to be well-studied, however the use of this method for differential equations that satisfy the mathematical formulation with independent unknown stresses and displacements requires additional studies and itshould be noted that particularly such formulations are of great interest