Optimal Design of Smooth Shells both With and Without Taking into Account Initial Imperfections

• Main Author: Heorhii V. Filatov
• Format: Article
• Language: English
• Published: NAS of Ukraine, A. Pidhornyi Institute of Mechanical Engineering Problems 2020-03-01
• Series: Journal of Mechanical Engineering
• Subjects: thin-walled cylindrical shell; initial imperfections; optimal design; random search
• Online Access: https://journal-me.com/wp-content/uploads/2020/03/2020_1_7_eng.pdf
• ISSN: 2709-2984; 2709-2992

This paper considers the application of the random search method for the optimal design of both axially-compressed smooth cylindrical ideal thin-walled shells and a shell with initial imperfections. In stating a mathematical programming problem, the objective function is the minimum weight of the shell. As constraints imposed on the region of permissible solutions, the following constraints are adopted: on the critical load of local buckling, on the critical load of buckling of the shell axis; strength condition, and condition for constraining the dimensions of a shell (radius and wall thickness of a shell). With the optimal design of a shell with initial imperfections, the statement of the mathematical programming problem remains the same as for an ideal shell, with only local buckling constraint changing. The aim of this paper is both to study the zone of influence of the optimum shell weight on the value of compressive force and to determine the range of the external compressive loads at which the general and local buckling shell constraints are decisive. A numerical experiment was carried out. Dependences of the weight, wall thickness, radius of the middle surface, and the ratio of the middle surface radius to the wall thickness on the magnitude of the compressive load both for an ideal shell and a shell with initial imperfections were investigated. As a result of the numerical experiment, it was established that the presence of initial imperfections in an axially-compressed smooth cylindrical shell leads to an increase in its weight compared to that of an ideal shell. The weight does not increase over the entire range of compressive loads, but only with the loads at which both local and general buckling constraints are decisive. If the optimal solution pertains to the strength constraint, which is typical for large compressive loads, there is no influence of initial imperfections on the optimal design. The weight of an ideal shell and that of a shell with initial imperfections in the optimal design turn out to be the same.