On the Systematic Construction of Trial Functions for Hybrid Trefftz Shell Elements

<div class="line" id="line-5"> In this paper the possibility of applying the Tre&fflig;tz-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 &filig;eld. For the construction of the linearly independent Tre&fflig;tz trial functions both the Neuber/Papkovich solution representation and a complex variable approach of the author are considered. The di&ffilig;culty in constructing the solution functions for the displacement &filig;eld consists of two problems: i) How can we choose the functions in order to have a symmetric structure in the displacement &filig;eld 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?</div>