Actual developments in the nonlinear shell theory - state of the art and new applications of the six-parameter shell theory

The theory of shells and plates is one of the oldest branches of solid mechanics. In many cases a dimension reduction of the three-dimensional partial differential equations of solid mechanics can be accepted since for shells, plates, beams, rods, etc., the geometry is given in such a manner that not all three dimensions have the same order: for shells and plates the thickness is much smaller than the other dimensions and for beams and rods the cross section dimensions are much smaller than the length of the beam or rod. The question arises how to reduce the dimension. There are several approaches - some of them will be briefly discussed here. The most attention will paid to the six-parameter nonlinear shell theory. Within the framework of the direct approach a shell can be considered as a deformable directed surface each point of which has six degrees of freedom, that is 3 translational and 3 rotational ones. Within the theory the drilling moment is also taken into account. In addition, we discuss some applications of the considered model of shells.