General theory for the deformation behaviour of thin shells in monoclinically convected coordinates

The general governing equations describing the finite deformations of thin shell structures developed in a system of monoclinically convected coordinate axes through the tensor geometrical approach are extended here to investigate the finite deformation phenomena of some particular types of deep shells. The results obtained thereby, ensure the scope of the present approach in such cases and call for enthusiastic appraisals from related quarters, through other methods. Further, the nonlinear behaviour of the above governing equation is theoretically developed through a very exacting analytical approach considering the deformed geometry of the shell in the monoclinically convected coordinates, which had been generally undermined or completely absent in similar investigations hitherto. The theoretical possibility of dealing with the problem of large deformations of thin shells in such an elaborate scale is strongly stressed here. The numerical simplicity of these equations are evident in their systematically structured expressions. This is illustrated further by presenting a numerical result obtained using these equations for a thin shallow circular cylindrical shell and its comparison with a published result.