About the authors
| First name, Middle name, Last name, Scientific degree, Scientific rank, Current position. Full and brief name of the organization, The organization address. | Nikolai A. Mishurenko, post-graduate student, Saint Petersburg State University of Architecture and Civil Engineering, Saint Petersburg, Russian Federation Email: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Alexey A. Semenov, candidate of technical sciences, associate professor, Saint Petersburg State University of Architecture and Civil Engineering, Saint Petersburg, Russian Federation Email: This e-mail address is being protected from spambots. You need JavaScript enabled to view it |
| Title of the article | Buckling of shallow shells of double curvature considering the presence of discretely introduced weakening |
| Abstract. | Problem statement. There are frequent cases of constructive weakenings as a part of shell structures. At the same time, considering the effect of weakenings on buckling significantly complicates the method of calculating these structures. The purpose of this work is to determine the effect of discretely introduced weakenings on the buckling of shallow shells of double curvature. The objectives of the study are to create a mathematical model that considers geometric nonlinearity, transverse shifts, orthotropy of the material, weakenings of the structure; choice of algorithm for studying the buckling of the shell; writing a program to implement the selected algorithm. Results. The paper presents a geometrically nonlinear mathematical model of deformation of orthotropic shallow shells of double curvature, weakened by notches. The model is based on the hypothesis of the Timoshenko-Reisner shell theory and is presented as a functional of the total potential strain energy. To find the minimum of the functional, the Ritz method is used, which reduces the problem to solving a system of nonlinear algebraic equations, the solution of which is carried out by the Newton method. The algorithm is implemented in the Maple 2022 software package. For the structures under consideration, it has been established that when up to 10 % of the structure volume is switched off from work, the decrease in the critical load does not exceed 25 %. Conclusions. The significance of the obtained results for structural mechanics lies in the fact that a mathematical model has been obtained that considers geometric nonlinearity, transverse shifts, material orthotropy, structural weakenings, the use of which will allow us to investigate the stress-strain state and buckling of shell structures with greater accuracy. |
| Keywords. | shells, weakenings, buckling, critical load, Ritz method, Newton method |
| For citations: | Mishurenko N.A., Semenov A.A. Buckling of shallow shells of double curvature considering the presence of discretely introduced weakening // News KSUAE, 2023, № 3(65), p. 6-17, DOI: 10.52409/20731523_2023_3_6, EDN: ASJURD |
