Abstract：A multi-resolution beam element with bending based on the Timoshenko theory is proposed. The multi-resolution analysis (MRA) performance of the element is formulated out of a nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the interval [0,1] of node shape functions extended from the traditional interval [0,1] to the [-1,1]. The MRA property enables this one proposed element to be re-meshed freely just by means of adjusting its resolution level, thus modulating its analysis accuracy accordingly. The extended shape functions make all the sub-elements connect together at the nodes as a whole as the initial proposed element in the re-meshing process, that is, the stiffness, the mass matrices and the equivalent node loading vectors can be obtained automatically without being reassembled artificially，thus, being seen as a technical secret for assembling artificially of node-related items in global matrix formation by the conventional. In addition, the proposed beam element can deal with the boundary conditions conveniently just as a conventional Timoshenko beam element does. In this sense, the MRA concept is fulfilled for the first time for a Timoshenko beam element and the mathematic essence, a nesting displacement subspace sequence, is found for meshing of beam structure in this paper.
2014, Vol. 35 
