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| Stability analysis of spatial beam based on corotational formulation |
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Abstract Based on the element independent corotational formulation (EICR), a geometrically linear shear locking free Timoshenko beam element was extended to the geometrically nonlinear analysis of spatial beams with arbitrarily large displacements and rotations but small strain. On considering the non-communitativity of finite rotations in three-dimensional analysis, which means that rotational degrees of freedom can't be updated by addition rule as vector quantities, therefore, the quaternion was used to store and update the rotational degrees of freedom. And a modified Riks arc-length method suitable for three-dimensional geometrically nonlinear analysis with large rotations was also presented. Several numerical examples for geometrical nonlinear analysis of spatial beams using the present beam element were also presented and the results demonstrate that the proposed element and methods are efficient and accurate.
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Received: 07 January 2013
Published: 28 February 2014
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2014, Vol. 35 
