Hamiltonian formalization of constitutive relations of the linear theory of elastic shells of revolution

We propose a method to construct constitutive relations of the linear theory of shells of revolution in the complex Hamiltonian form. Based on Lagrange's variational principle, a model of an elastic multilayer orthotropic shell of revolution has been constructed. In this model, kinematic assumptions are made separately for each of the amplitudes of the harmonics in expansion of the field functions of the mechanical problem in a complex Fourier series. Explicit expressions have been obtained for the coefficients and right-hand sides of the complex Hamiltonian system of equations of the statics of the shell of revolution using its rigidity characteristics and acting forces.