Finite Displacement Analysis Using Rotational Degrees of Freedom \\ about Three Right-angled Axes
Humihiko Gotou; Takashi Kuwataka, Terumasa Nishihara and Tetsuo Iwakuma

doi:10.3970/cmes.2003.004.319
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 4, No. 2, pp. 319-328, 2003
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Keywords Euler's angles, rotational pseudo-vector, rotational degrees of freedom
Abstract The stiffness equation in finite displacement problems is often derived from the virtual work equation, partly in order to avoid the complicated formulation based on the potential functional. Describing the virtual rotational angles by infinitesimal rotational angles about three axes of the right-angled Cartesian coordinate system, we formulate tangent stiffness equations whose rotational degrees of freedom are described by rotational angles about the three axes. The rotational degrees of freedom are useful to treat three rotational components in nodal displacement vectors as vector components for coordinate transformation, when non-vector components like Euler's angles are used to describe finite rotations. In this paper accuracy of the formulations is numerically demonstrated.
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