Use of interpolation methods for modeling the stress-strain state of operated oil storage tanks

Abstract

The aim of the research is the comparison of two approaches for computer modeling of the stress-strain state of thin-walled shells of engineering structures, considering the imperfections of the geometric shapes arising due to their operation. The object of the study is the operated steel vertical cylindrical reservoir with imperfections of the geometric shape intended for storage of petroleum products. The first, so-called classical, approach provides geometric modeling of the surface of the tank's shell with the subsequent import of the geometric model into one of the systems of finite element analysis to calculate the stress-strain state of the structure and determine its technical condition, and the possibility of further operation. The geometric modeling of the shell surface with imperfections was performed using a two-dimensional interpolation method based on the 1st order smoothness outlines implemented in the point calculus. The calculation of the stress-strain state of the shell was carried out in the SCAD Office computer complex, taking into account geometric and structural non-linearity on the basis of the octahedral tangential stress theory. The second approach assumes modeling of an array of functions of vertical deflection of the tank wall by means of interpolation, solution of an array of differential equations of the elastic cylindrical shell under axisymmetric loading, improved by introduction of vertical deflection functions of the wall, followed by two-dimensional interpolation and analysis of the deformed state of the shell based on displacements arising in the tank wall from the hydrostatic load. As a result of the effective use of two-dimensional interpolation in the process of implementing the second approach, it was possible to achieve a significant increase in the speed of the numerical solution while maintaining sufficient accuracy for engineering calculations.