Comparison of Two Systems of Governing Equations for the Thin Shell Analysis

At present, three types of systems of governing equations of linear theory of thin shells given in arbitrary system of curvilinear coordinates are known. Having taken curvilinear coordinates on the middle surface of shells in the lines of principle curvatures, one can determine the simplest system of 17 governing equations of the linear theory of shells. The system of 20 governing equations was derived by A.L. Goldenveizer for an arbitrary system of curvilinear coordinates with taking into account the condition of decomposition of the vectors of internal forces and moments and external surface load along the axes of the basic non-orthogonal moving trihedral. Later, the system of 20 governing equations, derived by S.N. Krivoshapko, was introduced into practice. These equations contain internal force factors and external surface load decomposed along the axes of the basic orthogonal moving trihedral. The presented paper shows that these both systems of governing equation are practically equivalent. The third system of governing equations, derived by Y.M. Grigorenko and A.M. Timonin, was presented in tensor form and realized for cyclic shells. All three systems of the equations after transition to coordinates in the lines of principle curvatures coincide. © 2022 American Institute of Physics Inc.. All rights reserved.