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. | Serazutdinov Murat Nurievich, Doctor of Physical and Mathematical Sciences, Professor Kazan National Research Technological University, Kazan, Russian Federation Email: This e-mail address is being protected from spambots. You need JavaScript enabled to view it |
| Title of the article | Analytical solutions for curved rods based on the relations for a rectilinear rod |
| Abstract. | The article presents analytical solutions and a method for calculating curved rods based on the use of formulas for calculating deformations of a rectilinear rod. The relevance of the results obtained is due to the fact that structural elements in the form of curved rods are traditionally used in construction, and recently the range of applications of curved structures has been significantly expanded due to the use of new structural materials - composites with glass filler. The Kosser-Timoshenko hypotheses are accepted, analytical solutions are obtained by the variational method using the Lagrange functional. The peculiarity of the method is that the formulas for calculating deformations do not include parameters characterizing the curvature of the longitudinal axis of a curved rod. Previously, this method was used to obtain numerous calculations of the statics of rod systems in linear and physically nonlinear formulations, as well as for calculations of thin-walled curved rods. Numerical methods were used. The article presents solutions for curved rods obtained by the analytical method. The main purpose of the research presented in this paper is to obtain analytical solutions that allow determining the stress-strain state of curved rods, to show the versatility, originality and comparative simplicity of the method. To achieve this goal, it is necessary to solve the following tasks: select a curved rod, the results of calculating the stress-strain state of which are published in the scientific literature; determine the type of functions approximating the desired parameters; describe in detail the analytical calculations of the method; show the reliability of the analytical results obtained based on comparing the results of the solution with known data. |
| Keywords. | curved rods, variational method, analytical solutions |
| For citations: | Serazutdinov M.N. Analytical solutions for curved rods based on the relations for a rectilinear rod // News KSUAE 2023 № 2 (64), p.70-79, DOI: 10.52409/20731523_2023_2_70, EDN: YWXCUL |
