Analysis of bending of composite plates with account for the difference in resistance to tension and compression

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 of different modulus with different elastic properties under 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.