Mathematical Modeling of the Influence of Natural Factors on the Durability of Critical Structural Elements

The article is dedicated to modeling the influence of natural mechanical and physico-chemical factors on the localized failure and residual durability of critical structural elements. Localized failure is considered as the initiation and propagation of crack-like defects. By applying the laws of irreversible thermodynamics and physical chemistry, a mathematical model is constructed to determine the period of pre-critical crack growth in metallic structural elements under the action of wind loading and localized atmospheric corrosion. The mathematical model (differential equations with corresponding initial and boundary conditions) takes into account the loading on the structural element both from steady wind and gusts of wind. The application of the model is demonstrated through an example of calculating the residual durability of an ethylene production rectification column. The effectiveness and correctness of the proposed computational model are verified by comparing the obtained computational results of the column’s durability with real data on the failure of such columns in Ukraine.