The well-posedness of the statics problem of the non-linear theory of shallow elastic shells

The continuity of the dependence of the non-singular solution on small pert urbations of the dimensions and form of the shell is proved using methods d escribed earlier [1]. These perturbations lead to a change in the region in to which the middle surface of the shell is mapped (for example, an increas e or decrease in the aperture angle of a shallow spherical cupola). The con tinuity of the dependence on small changes in parts of the boundary along w hich some form of boundary conditions is realized (for example, there is so me part of the boundary rigidly clamped with respect to the displacement of points in the direction of normal to the middle surface) is also proved. ( C) 1998 Elsevier Science Ltd. All rights reserved.