  A triangular plate-bending element with a new multi-resolution analysis (MRA)
is proposed and a novel multiresolution element method is hence presented. The
MRA framework is formulated out of a displacement subspace sequence whose basis
functions are built out of scaling and shifting on the element domain of basic
full node shape function. The basic full node shape function is constructed by
means of extending the shape function triangle domain for a split node at the
zero coordinates to the hexagon area enclosing the zero coordinates. As a
result, a new split-full node notion is presented and a novel rational MRA
concept together with the resolution level (RL) is constituted for the element.
Via practical examples, it is found that the traditional triangular plate
element and method is a mono-resolution one and also a special case of the
proposed element and method. The meshing for the monoresolution plate element
model is based on the empiricism while the RL adjusting for the multiresolution
is laid on the rigorous mathematical basis. The analysis clarity of a plate
structure is actually determined by the RL, not by the mesh. Thus, the accuracy
of a structural analysis is replaced by the clarity, the irrational MRA by the
rational and the mesh model by the RL that is the discretized model by the
integrated. The continuous full node shape function unveils secrets behind
assembling artificially of node-related items in global matrix formation by the
conventional FEM.
