General theory of orthotropic shells. Part I

Modern mechanical engineering sets the tasks of calculating thin-walled structures that simultaneously combine sometimes mutually exclusive properties: lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of orthotropic materials and plastics seems quite justified. The article demonstrates the complex representation method of the equations of the orthotropic shells general theory, which allowed in a complex form to significantly reduce the number of unknowns and the order of the system of differential equations. A feature of the proposed technique for orthotropic shells is the appearance of complex conjugate unknown functions. Despite this, the proposed technique allows for a more compact representation of the equations, and in some cases it is even possible to calculate a complex conjugate function. In the case of axisymmetric deformation, this function vanishes, and in other cases the influence of the complex conjugate function can be neglected.
Verification of the correctness of the proposed technique was demonstrated on a shallow orthotropic spherical shell of rotation under the action of a distributed load. In the limiting case, results were obtained for an isotropic shell as well.