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UBC Theses and Dissertations

A new eighteen parameter triangular element for general plate and shell analysis Bearden, Terrance William

Abstract

The purpose of this investigation was to develop an eighteen parameter flat triangular finite element for analyzing plate and shell structures. The development of the element was accomplished by combining a plate bending element with a new plane stress element. The well known nine parameter triangle using the normal displacement and two slopes at each vertex was used for the plate bending element. This element contains an incomplete cubic for the normal displacement. For the in-plane element, complete cubics were used initially for the displacements and then various constraints were imposed to reduce the number of generalized co-ordinates to nine, namely the two in-plane displacements and an in-plane rotation at each vertex. One of the constraints, namely that the included angle at each vertex was invariant, destroyed the completeness of the element. However, the element was compatible in the plane. A patch-type test of the in-plane element showed that it could not represent all constant strain states exactly. However, the errors were small. The complete element was then tested on a plane stress cantilever beam, a square plate subjected to membrane stresses only, a cylindrical shell, a spherical shell and a non-prismatic folded plate structure. In all cases, reasonable engineering accuracy was achieved with modest grids of elements. Thus it was concluded that the incompleteness of the in-plane element was not too important. Finally, a compatible beam element was formulated and tested to supplement the triangular element. The beam element formulation included unsymmetric crosssections.

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