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# Finite Displacement Analysis Using Rotational Degrees of Freedom about Three Right-angled Axes

Humihiko Gotou1, Takashi Kuwataka1, Terumasa Nishihara1, Tetsuo Iwakuma1

Department of Civil Engineering, Tohoku University, Japan

Computer Modeling in Engineering & Sciences 2003, 4(2), 319-328. https://doi.org/10.3970/cmes.2003.004.319

## 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.

## Keywords

APA Style
Gotou, H., Kuwataka, T., Nishihara, T., Iwakuma, T. (2003). Finite displacement analysis using rotational degrees of freedom about three right-angled axes. Computer Modeling in Engineering & Sciences, 4(2), 319-328. https://doi.org/10.3970/cmes.2003.004.319
Vancouver Style
Gotou H, Kuwataka T, Nishihara T, Iwakuma T. Finite displacement analysis using rotational degrees of freedom about three right-angled axes. Comput Model Eng Sci. 2003;4(2):319-328 https://doi.org/10.3970/cmes.2003.004.319
IEEE Style
H. Gotou, T. Kuwataka, T. Nishihara, and T. Iwakuma "Finite Displacement Analysis Using Rotational Degrees of Freedom about Three Right-angled Axes," Comput. Model. Eng. Sci., vol. 4, no. 2, pp. 319-328. 2003. https://doi.org/10.3970/cmes.2003.004.319

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