Stability of shallow shells with local changes in strength characteristics

Abstract

The authors deal with the structures of buildings in the form of shallow shells with some damage. The derivation of equations is given taking into account the geometric nonlinearity of the work of a thin-walled structure. A technique for solving systems of equations using the Bubnov - Galyorkin method is given. The work of the structure with various ways of fixing the edges is simulated. Damage is specified by changing the modulus of elasticity in an arbitrary section of the structure. The influence of the shape and location of the defect on the value of the critical load is investigated. The results of the studies carried out are given in a dimensionless form and illustrated by graphs, which makes it convenient to use them in engineering calculations. Recommendations are given for correcting the shape and thickness of coating structures in the form of shallow shells in order to maintain their bearing capacity in the event of defects. The proposed method can be used to determine and investigate the stress-strain state of structures in the form of shallow shells, taking into account the geometric nonlinearity of work in the presence of defects in them. The constructed graphs of the dependence of the critical load on various parameters make it possible to evaluate the operation of structures, taking into account changes in various factors at various stages of the structure's operation. The use of varying characteristics of the reduction in the modulus of elasticity, which appears because of the occurrence of a defect, shows results that are close to real conditions.