Abstract: In this paper, a dimensional splitting method for three dimensional nonlinear elastic shell is established under a semi-geodesic coordinate system ($S$-coordinate). Then the nonlinear elastic operator can be decomposed into the sum of a membrane and bending operators in the $S$-coordinate system. Assume that the solution of the 3D nonlinear elastic shell can be expressed as the Taylor expansion with respect to the transverse variable, the approximation modelling with one-order and two order respectively are established. Meanwhile, we give the 2D-3C partial differential equations satisfied by the terms of zero-order, prove the existence of solution, give the related functions in the terms of first and second orders with respective to the term of zero-order without solving partial differential equations to obtain the terms of first and second orders.

Key words: nonlinear elastic shell, dimensional splitting method, semi-geodesic coordinate system, 2D-3C partial differential equation