In a search for complex instability phenomena, rather specific demands are put on the finite elements used for the discretization of the problem. A large number of finite elements have been derived using symbolic software, such as Maple and Mathematica; the expressions are semi-automatically transferred to an object-oriented library and C++ code.

The symbolic tools have here been used to show aspects of equivalence between 'co-rotational' and 'total displacement' elements. The conclusion from the latter tests is that the co-rotational formulations of the non-linear problems can reproduce all relevant types of instabilities, with simple local formulations.

The symbolic derivation of element expressions has a number of advantages. It allows a systematic approach for all element classes. Clear information is obtained on the limitations of the validity of the formulation. The main advantage, however, lies in the efficient code being produced. The alternative formulations are based on a more far-reaching development of the element expressions in the derivation process, in the limit as explicit expressions for the terms in the stiffness matrix. The improvements in efficiency are most obvious for the simplest element classes, where the interpolation functions are of low order.

The paper presents the findings from a study of symbolic formulation methods for efficient, simple, linear elements. It is shown how these can lead to substantial improvements in efficiency. The paper also discusses how a 'field consistence' approach can be one method to understand the locking behaviour in the elements; it can also give accurate formulations.

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