Simulation of the stress-strain state of shells under internal pressure using the mixed finite element method, taking into account physical nonlinearity

Abstract

In this article, the finite element method (FEM) is used to model the stress-strain state (SSS) of shells experiencing internal pressure with elastic-plastic state being taken into account. Main geometric equations determining the location of an arbitrary point at load step are given. Mixed functionality used in implementation of FEM which allows to determine stresses and displacements simultaneously is obtained based on equality of possible and actual work of external and internal forces. Examples of stress-strain state of rotation shells with spherical and elliptical bottoms under internal pressure are provided. Static check of resultant external forces arising from applied pressure and resultant internal forces arising from stresses equality to zero is performed. Achieved results show correctness of the developed algorithm with elastic-plastic properties of the material being taken into account, ensuring that main requirements for the mathematical model are secured, namely adequacy, versatility and cost-effectiveness. Costs of resources computing are reduced by adopting a number of hypotheses and determination of stresses and strains at once ensuring cost-effectiveness and simplicity. Using developed scheme of the mixed functionality application in implementation of FEM the mathematical model acquires one of its main properties - “Potentiality”.