Keywords: finite elements, large rotations, laminate frames, warping enhancement, isoparametric, positional.

This paper presents a positional finite element formulation for three-dimensional frame analysis. The formulation is based on the minimum potential energy theorem and includes consideration of warping and non-homogeneous material. Classical descriptions of finite rotations are not used in this paper. The adopted concept is the unconstrained generalized vector description of solids. The cross sections can be of any geometry, providing ramifications or holes.

The enhancement approach is based on the introduction of the warping mode and the rate of transverse variation. The warping mode is solved as a pre-processing object, coupled to the main program and the amount of additional calculation is relatively small whereas the number of finite elements, with the same cross-section increases. The warping mode is based on a two-dimensional free torsion (Saint-Venant) problem, considering a non-homogeneous material. A scheme that automatically generates shape functions and its derivatives allows the use of any degree of approximation for the frame elements developed. Selected examples demonstrate the accuracy and applicability of the proposed positional formulation.

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