Non-Prismatic Beam-Like Structures with 3D Cross-Sectional Warping

Abstract

Many complex engineering structures, e.g. blades of wind turbines and helicopters, are beamlike and non-prismatic. They may be tapered, twisted and curved in their unstressed state, undergo large displacements of the centre-line, and cross-sectional warping in and out of plane. For their structural modeling, an approach based on beam elements can be the best compromise between computational efficiency and accuracy, but classical beam models (see, for example, the monumental Love's treatise) may not be sufficient. Better results may be obtained by exploiting geometrically exact and asymptotic approaches. This paper proposes a physical-mathematical model for the aforementioned non-prismatic structures. Analytical results obtained for small warping and strain fields are presented and compared to the results obtainable from nonlinear 3D-FEM analyses.

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