The first integrals of a system of ordinary nonlinear differential equations describing the bending, tension, and torsion of an elastic anisotropic layer have been derived using the conservation laws of the theory of finite strains in simple materials and materials with couple stresses. These integrals can be used for reducing the order of such systems of differential equations, obtaining exact solutions, and checking the calculation accuracy in numerical solution of the differential equations of nonlinear elasticity theory. For example, an exact solution of the problem of large strains under pure bending of an elastic plate is found in the class of iso-tropic incompressible micropolar materials.
展开▼
