Abstract
AbstractA direct vector combination procedure is developed for the formulation of finite element stiffness matrices. Only the homogeneous solution modes to governing equations of a problem and a uniquely defined interpolation displacement function along the element boundary are used to generate pairs of nodal displacement and nodal force vectors. The stiffness matrix is obtained by a simple multiplication of the nodal displacement and nodal force vectors. The element formed passes all the higher order patch tests for the order of solution modes included in the formulation. However, the stiffness matrix may become unsymmetrical. Restoring symmetry leads to compromising some of the higher order patch test performances. The present procedure is shown to have direct relations to those of the displacement model and the hybrid stress model. The present procedure presents new possibilities for the improvement of element performance. The procedure itself can also be used to study the limitations of element behaviour.
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