On a special class of boundary-value problems in the theory of shells and plates

This paper is concerned with problems in shell theory in which displacement s are specified on a major surface of a three-dimensional shell like body. It is unclear whether the theory of shells is in fact applicable to such pr oblems; in virtually any treatment of shells, the equations of motion are d erived by assuming that the tractions on both major surfaces are known. The se known tractions manifest themselves as body forces in the resulting two- dimensional set of equations. We demonstrate in this paper that provided ce rtain modifications are made, the latter set can indeed be used to solve pr oblems in which displacements are specified on a major surface. These modif ications are essential; they in fact reduce the number of differential equa tions and change the nature of the boundary conditions. We outline a clear procedure to treat such problems, The procedure is general in that it is va lid for finite deformations of shells made of any material. We illustrate t he efficacy of the final set of equations by presenting some examples from the linear theory of elastic plates. (C) 1999 Elsevier Science Ltd. All rig hts reserved.