Structural Mechanics of Engineering Constructions and Buildings (Jan 2017)
TWO TYPES OF GOVERNING EQUATIONS FOR SHELLS WITH THE MIDDLE SURFACES GIVEN IN ARBITRARY CURVILINEAR COORDINATES
Abstract
Having taken curvilinear coordinates on the middle surface of shells in the lines of principle curvatures, we can determine the simplest system of 17 governing equations of the linear theory of shells. But sometimes, the problem of analytical determination of the equation of the middle surface in lines of principle curvatures is very difficult task and that is why it is necessary to use the system of 20 governing equations, derived by A.L. Goldenweiser 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 the author, was published. These equations contain internal force factors and external surface load decomposed along the axes of the basic orthogonal moving trihedral. His paper shows that these both systems of governing equation can transform one into other with the help of the equations of translation, i.e. the both systems of governing equations are equivalent.
