  A new multiresolution quadrilateral plate element is proposed and a
multiresolution finite element method is hence presented. The multiresolution
analysis (MRA) framework is formulated out of a mutually nesting displacement
subspace sequence, whose basis functions are constructed of scaling and
shifting on the element domain of basic node shape function. The basic node
shape function is constructed by extending shape function around a specific
node. The MRA endows the proposed element with the resolution level (RL) to
adjust the element node number, thus modulating structural analysis accuracy
accordingly. As a result, the traditional 4-node quadrilateral plate element
and method is a monoresolution 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 accuracy of a structural analysis is
actually determined by the RL, not by the mesh. The rational MRA enable the
implementation of the multiresolution element method to be more rational and
efficient than that of the conventional monoresolution plate element method or
other corresponding MRA methods such as the wavelet finite element method, the
meshfree method, and the natural element method etc.
