Abstract: The purpose of this paper is to investigate, to some extent, the influnce of variational constraints on the finite element properties, which are based on different types of variational principles. Taking axisymmetrical elements of thin shell of revolution (abbreviated as TSR element) as comparative elements, and with the same geometrical description, we derive seven kinds of TSR hybrid elements and two kinds of TSR conforming elements corresponding to three types of hybrid variational principles and potential energy principle respectively. By analysing the element stiffness formulations and comparing the numerical calculations, such as corrugated shell, we discuss the differences in properties of different models, and the adaptability, limitation as well as relationship between two types of models. We also point out a divergence case of TSR hybrid displacement element, and suggest two kinds of more acceptable TSR elements.

Key words: approximate sampling theorem, bivariate continuous signal, refinement equation, mask of refinement equation