EXISTENCE THEOREM AND FINITE ELEMENT METHOD FOR STATIC PROBLEMS OF A CLASS OF NONLINEAR HYPERELASTIC SHELLS

In this paper, various boundary value problems of hyperelastic shells are considered. It is assumed that the storede-nergy function W（x, F） of the material,of which the shell is made, satisfies polyconvex conditions proposed by Ball[2].Existence of minimum points of the total energy of the shell in suitably chosen function spaces, and in suitably chosen finite element spaces is proved. Convergence of the finite element solutions is proved under certain regular conditions on the minimum points and some additional assumptions on W（x, F）. A Gradient type computing scheme for solving the finite element solutions is given, and global convergent result is obtained.