Contact problem of bending of a multilayer composite plate taking into account different moduli of elasticity for tension and compression

The paper considers the contact problem of bending a multilayer composite plate. Each layer of the composite is a material reinforced with thin parallel fibers. The mathematical model is constructed based on the assumptions of the existence of a neutral surface in the plate and the fulfillment of Kirchhoff's hypotheses. Using the Lagrange variational principle, the bending equation generalizing the Sophie—Germain equation is obtained. The elastic energy functional is obtained taking into account the different resistance of the material to tension and compression. The contact problem of bending plates and membranes with the of a rigid contact is considered. To solve the contact problem of bending a plate with a rigid stamp, a Lagrangian was constructed with a constraint in the form of an inequality. For the numerical solution of the problem, the finite element method using the triangular Bell element was applied. The results of calculations of the bending of laminated rectangular plates with different directions of fiber laying and different shapes of the stamp are presented.