ABSTRACT

Shells and plates are structural mechanics models of a certain class of solid deformable bodies which are characterized by the statement that one dimension (usually named thickness) is much smaller in comparison with the other two dimensions. Such structures can be analyzed with the help of the three-dimensional equations of continuum mechanics. But in this case as usual only numerical solution techniques (mostly based on the finite element method) can be applied. Regardless of the progress in numerical methods and computer power sometimes the solution of shell and plate problems results in difficulties. For example, it is well known that if the thickness is very thin (close to zero) two phenomena occurs: the existence of boundary layers and the presence of locking (Suri et al. 1995). However, this is one motivation for the development of lower-dimensional theories (Tu & Oru-Yang 2008) applying the thinness hypothesis (Krätzig & Bas¸ar 1985).