On the systematic construction of trial functions for hybrid Trefftz shell elements

In this paper the possibility of applying the Trefftz-method to thick and thin shells is discussed. A mixed variational formulation is used in which the assumed strain and stress functions are derived from the three-dimensional solution representation for the displacement field. For the construction of the linearly independent Trefftz trial functions both the Neuber/Papkovich solution representation and a complex variable approach of the author are considered. The difficulty in constructing the solution functions for the displacement field consists of two problems: i) How can we choose the functions in order to have a symmetric structure in the displacement field and not to bias the solution in any direction? ii) How can we avoid to get linearly dependent terms for displacements, strains and stresses when seeking polynomial solution terms?