Kinematically exact curved and twisted strain-based beam
- 作者：P. 膶e&scaron ; arek ; M. Saje ; D. Zupan ; dejan.zupan@fgg.uni-lj.si
- 关键词：Strain measure ; Constant strain ; Non-linear beam theory ; Three-dimensional beam ; Three-dimensional rotation
- 刊名：International Journal of Solids and Structures
- 出版年：2012
- 期刊代码：93_00207683
- 类别：et
- 出版时间：15 June, 2012
- 卷：49
- 期：13
- 页码：1802-1817
- 文件大小：1579 K
摘要
The paper presents a formulation of the geometrically exact three-dimensional beam theory where the shape functions of three-dimensional rotations are obtained from strains by the analytical solution of kinematic equations. In general it is very demanding to obtain rotations from known rotational strains. In the paper we limit our studies to the constant strain field along the element. The relation between the total three-dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed. The analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential. Despite the analytical relationship between rotations and rotational strains, the governing equations of the beam are in general too demanding to be solved analytically. A finite-element strain-based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals. Some interesting connections between quantities and non-linear expressions of the beam are revealed. These relations can also serve as useful guidelines in the development of new finite elements, especially in the choice of suitable shape functions.