The paper is devoted to the plane stress state of a multilayer composite plate. Polymer-based composite reinforced by thin carbon fibers is used as a material for the plate. Each layer is an unidirectional fibrous composite. This type of material has different tensile and compression moduli, since the fibers having high tensile stiffness and low stiffness upon compression. Generalized rheological method is used: a rheological scheme was composed and the constitutive equations were constructed using the projection of the strain tensor onto the cone of admissible deformations according to the norm, consistent with the tensor of additional elastic moduli. The projection is calculated by the Uzawa algorithm. The elastic moduli of unidirectional composite under tension and compression were obtained from experimental data. Hooke's law was written for unidirectional composite in the coordinate system associated with the orientation of the fibers, and in the system obtained by rotation around an axis perpendicular to the reinforcement plane. The elastic moduli of the layered composite are used in nonlinear constitutive equations. The problem of plane static loading was solved numerically using the finite element method with the obtained constitutive equations. As a result, a new mathematical model taking into account different resistance of fibrous composite to tension and compression was created and the problem of static loading of a multilayer fibrous composite plate in a plane stress state was solved.

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