Taking into account the shear stiffness of ribs in the study of the stress-strain state of reinforced slabs using the methods of L.V. Kantorovich and Ritz
https://doi.org/10.21822/2073-6185-2026-53-2-171-182
Abstract
Objective. The aim of the study is to develop a method based on a combination of L.V. Kantorovich and Ritz methods for calculating the stress-strain state of ribbed plates taking into account shear strains.
Method. The mathematical model is constructed based on the functional of the total potential energy of deformation. The solution is based on reducing the dimensionality of the two-dimensional problem to a one-dimensional one using L.V. Kantorovich's method and then applying the Ritz method for discrete approximation of displacements.
Result. In L.V. Kantorovich's method, it is proposed to obtain approximating functions from the calculation of a system of differential equations for the Timoshenko beam. In the Ritz method, for discrete approximation of displacements, the one-dimensional domain is divided into integration sections, and the stiffeners are taken into account using Dirac delta functions or unit columnar functions. Expressions for obtaining bending and shear stiffness for solid-wall and truss-type ribs are presented. Numerical experiments are conducted on several rib types with different heights and compared with the finite element method.
Conclusion. It is concluded that the developed method and the finite element method agree well for displacements, bending moments, and longitudinal forces in the ribs. It is found that the developed method yields more conservative values for shear forces at supports.
About the Authors
E. O. Afanasyeva
Saint Petersburg State University of Architecture and Civil Engineering
Russian Federation
Russian Federation
Elena O. Afanaseva, Graduate student, Department of Information Systems and Technologies
4, 2nd Krasnoarmeiskaya St., St Petersburg, 190005
V. V. Karpov
Saint Petersburg State University of Architecture and Civil Engineering
Russian Federation
Russian Federation
Vladimir V.Karpov, Dr. Sci. (Eng.), Prof., Consulting Prof., Department of Information and Mathematical Modeling Technologies
4, 2nd Krasnoarmeiskaya St., St Petersburg, 190005
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Review
For citations:
Afanasyeva E.O., Karpov V.V. Taking into account the shear stiffness of ribs in the study of the stress-strain state of reinforced slabs using the methods of L.V. Kantorovich and Ritz. Herald of Dagestan State Technical University. Technical Sciences. 2026;53(2):171-182. (In Russ.) https://doi.org/10.21822/2073-6185-2026-53-2-171-182
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