A three-dimensional finite-strain rod model. Part II: Computational aspects
Computer Methods in Applied Mechanics and Engineering
On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach
Computer Methods in Applied Mechanics and Engineering
Automatic generation of finite-element code by simultaneous optimization of expressions
Theoretical Computer Science - Special volume on computer algebra
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics
Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics
Integrating rotation from angular velocity
Advances in Engineering Software
Quaternion-based dynamics of geometrically nonlinear spatial beams using the Runge-Kutta method
Finite Elements in Analysis and Design
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The rotational quaternions represent a unique four dimensional parametrization of rotations in the three dimensional Euclidean space. In the present paper they are used as the basic rotational parameters in formulating the finite-element approach of geometrically exact beam-like structures. The classical concept of parameterizing the rotation matrix by the rotational vector is completely abandoned so that the only rotational parameters are the rotational quaternions representing both rotations and rotational strains in the beam. The space discretization based on the collocation method is used and the adjustment of the Newmark time-integration algorithm to the quaternion parameterizations of rotation is presented.