A Refined Quadrilateral Flat Plate Finite Element Based on the Extended Field Method.
MARYLAND UNIV COLLEGE PARK DEPT OF AEROSPACE ENGINEERING
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A new quadrilaterial finite element for the problem of bending of a uniform, homogeneous, isotropic, flat plate having an arbitrary number of nodal points and allowing an arbitrary level of refinement is developed from solution functions to the governing differential equation. Interelement continuity to the appropriate level of normal derivatives is provided in least error fashion by the use of spline functions for the edge displacement quantities and minimization by the Galerkin technique. Even for general quadrilateral domains no numerical quadrature is required for developing this finite element since all required integrals are taken over straight boundary edges and can be evaluated explicitly. With this new type of element, an improvement in accuracy is expected to result when large quadrilateral regions are modeled by a single element with an appropriate number of edge nodal points, because the error of this finite element approximation is associated with the boundary region of the elements. The force vector corresponding to the transverse pressure is derived from a series solution to the inhomogeneous differential equation, so that the effect of the forcing function in the element interior can be evaluated to any degree of accuracy desired. Author
- Theoretical Mathematics