Полуаналитический метод конечных элементов в задачах изгиба вафельных цилиндрических оболочек

Abstract

Предложен вариант полуаналитического метода конечных элементов, который позволяет двухмерную задачу расчета напряженно-деформируемого состояния вафельной цилиндрической оболочки свести к одномерной задаче. Для этого перемещения цилиндрической оболочки разлагаются в ряды по окружной координате. Исследуются свойства напряженно-деформируемого состояния вафельных оболочек.

Perfect cylindrical shell is considered. Stringers and frames are attached to the shell inside. The frames have the ring form. The constant internal pressure acts on the shell inside. This shell is the main element of the rocket tank. The static mode deformation is treated. It is assumed, that the shell displacements are small and the stresses and strains satisfy the Hooke’s law. As the shell is thin, the Kirchoff-Love hypothesizes are satisfied. The stringers are thin bars and they are described by Euler-Bernoulli beam theory. The frames are rings with constant cross sections. The strains of the rings cross-sectional plane are not taken into account. The stresses and strains of the stringers and frames satisfy the Hooke’s law. The displacements of the shell middle surface are the main unknowns. The displacements of the stringers and frames are expressed in terms of the shell displacements. The potential energy of the stringers and frames is expressed in terms of the shell displacements. The shell displacements are expanded into Fourier series. The coefficients of these series are the functions of the cylindrical shell longitu¬dinal displacements. The finite element method is used to obtain these coefficients. These functions are obtained in the form of Hermitian polynomials superposition.