دراسة مقارنة بين استخدام النظرية الغشائية ونظرية العناصر المحددة المختلطة لإيجاد الإجهادات بمنطقة الارتكاز بالخزانات الكروية المرفوعة

Abstract

This research aimed to find out the stresses in the fulcrum area of the upper spherical fluid tanks that are based on columns of fixed thickness under the influence of the hydrostatic load of the liquid, which represents the state of symmetry around the axis.

Membrane theory was used to find out the vertical axial forces and the circumferential axial forces. However, membrane theory cannot calculate the bending moments in the fulcrum area, which is considered a shortcoming in this situation. To obtain accurate results and account for the inability of membrane theory, mixed finite element method has been used. This method is an extension of the matrix methods in the structural analysis and is used to analyze the shells when subjected to stable and moving loads by using an appropriate number of curved circular elements.

The results, obtained from the membrane theory and the mixed finite element theory, have been compared. The results of the mixed finite element theory were more accurate and accounted for the shortcomings of the membrane theory and helped the researcher to get the axial forces, circumferential forces, moments and displacements, which are needed to determine the safe installation area (columns connection area with the tank).