HYPERBOLIC PARABOLOID SHELL ANALYSIS VIA MIXED FINITE-ELEMENT FORMULATION

An isoparametric rectangular mixed finite element is developed for the analysis of hypars. The theory of shallow thin hyperbolic paraboloid shells is based on Kirchhoff-Love's hypothesis and a new functional is obtained using the Gateaux differential. This functional is written i n operator form and is shown to be a potential. Proper dynamic and geo metric boundary conditions are obtained. Applying variational methods to this functional, the HYP9 finite element matrix is obtained in an e xplicit form. Since only first-order derivatives occur in the function al, linear shape functions are used and a C degrees conforming shell e lement is presented. Variation of the thickness is also included into the formulation without spoiling the simplicity. The formulation is ap plicable to any boundary and loading condition. The HYP9 element has f our nodes with nine Degrees Of Freedom (DOF) per node-three displaceme nts, three inplane forces and two bending, one torsional moment (4 x 9 ). The performance of this simple, and elegant shell element, is verif ied by applying it to some test problems existing in the literature. S ince the element matrix is obtained explicitly, there is an important save of computer time.