One approach to the construction of the basic equations of the theory of nonthin shells with variable thickness

A method for determining the principal curvatures of medium-thickness shells through the vector representation of local bases is proposed based on the parametrization of the base median surface of a shell and its front surfaces. Repeated partial derivatives of vector functions with respect to variable Gaussian coordinates, which is a standard practice in theory of shells when calculating the curvatures as coefficients of the second quadratic form, are not used. Such an approach allows us to accurately account for the geometry of the front surfaces of the shell in determining its stress-strain state.