Abstract
The finite element method is used to develop a computational algorithm for solving a limited class of problems on the bending of composite plates reinforced with systems of unidirectional high-strength fibers. It is assumed that a neutral plane exists in the region of the plate and behaves similarly to a flexible nondeformable membrane. The displacements of the plate in the longitudinal direction are linear in thickness. In the case of fiber composites with different elastic moduli in tension and compression, the neutral plane, generally speaking, does not coincide with the median plane. The problem of minimizing the elastic energy functional in accordance with the Lagrange variational principle yields a fourth-order elliptic differential equation for the deflection. The bending stiffnesses of the plate included in the coefficients of the equation are calculated with account for the fact that the elastic characteristics of the reinforcing fibers under tension and compression are significantly different. The numerical solution of the equation is obtained via the finite element method with the help of a Bell triangular element. The paper presents computational results for the bending of rectangular laminated plates in which the fibers are laid in different directions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (At the University Press, Cambridge, 1892).
V. Z. Vlasov, General Theory of Shells and Its Applications in Engineering (National Aeronautics and Space Administration, 1964).
S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1959).
N. A. Alfutov, P. A. Zinov’ev, and B. G. Popov, Calculation of Composite Multilayer Plates and Shells (Mashinostroenie, Moscow, 1984) [in Russian].
V. V. Bolotin and Yu. N. Novichkov, Multilayer Structure Mechanics (Mashinostroenie, Moscow, 1980) [in Russian].
P. Cao and K. Niu, “New Unified Model of Composite Sandwich Panels/Beams Buckling Introducing Interlayer Shear Effects," Composite Structures 252, 112722 (2020).
K. Delavari and H. Dabiryan, “Mathematical and Numerical Simulation of Geometry and Mechanical Behavior of Sandwich Composites Reinforced with \(1\times 1\)-Rib-Gaiting Weft-Knitted Spacer Fabric; Compressional Behavior," Composite Structures 268, 113952 (2021).
V. M. Sadovskii, O. V. Sadovskaya, and I. E. Petrakov, “On the Theory of Constitutive Equations for Composites with Different Resistance in Compression and Tension," Composite Structures 268, 113921 (2021).
B. D. Annin, V. M. Sadovskii, I. E. Petrakov, and A. Yu. Vlasov, “Strong Bending of a Beam from a Fibrous Composite, Differently Resistant to Tension and Compression," J. Sib. Federal Univ.: Math. Phys. 12 (5), 533–542 (2019).
P. G. Ciarlet, The Finite Element Method for Elliptic Problems (SIAM, 2002).
S. Pissanetzky, Sparse Matrix Technology (Academic Press, 2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 5, pp. 172-183. https://doi.org/10.15372/PMTF20210517.
Rights and permissions
About this article
Cite this article
Petrakov, I.E., Sadovskii, V.M. & Sadovskaya, O.V. ANALYSIS OF BENDING OF COMPOSITE PLATES WITH ACCOUNT FOR THE DIFFERENCE IN RESISTANCE TO TENSION AND COMPRESSION. J Appl Mech Tech Phy 62, 851–860 (2021). https://doi.org/10.1134/S0021894421050175
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894421050175