A multiresolution finite element method based on a new quadrilateral shell element

Abstract

Initially based on a split node shape function for a quadrilateral shell element, the basic full node shape function is constructed by extending the split node shape function to other three quadrants around the coordinate zero point and a displacement subspace sequence is constituted out of scaling and shifting of the basic full node shape function on the element domain, which brings about a simple, clear and rigorous mathematical basis for the multiresolution analysis (MRA). After that, the multiresolution quadrilateral shell element and method is formulated through applying the minimum potential energy principle. Hence, the MRA concept is established and the resolution level ( RL ) for the element is introduced. Finally, through the numerical examples, the following conclusions are drawn: traditional 4-node quadrilateral shell element and method is essentially a mono-resolution one and also a special case of the proposed element and method. Due to the full nodes in the element domain, the structural model for a numerical analysis by the proposed multiresolution element is an integrated one by RL , not a discretized one by mesh just as by the conventional monoresolution element. The proposed finite element method is a rational MRA method and overperforms all those irrational MRA methods in numerical analysis efficiency, also can consolidate those irrational MRA methods. The clarity of a structural analysis is defined by the RL , not mesh. The continuity of the full node shape functions unveils the secretes behind artificial assemblage of the corresponding items of the stiffness, mass matrices and the equivalent node loading vectors at common nodes by the conventional quadrilateral shell element.