Abstract
Two 4-node generalized conforming quadrilateral membrane elements with drilling DOF, named QAC4θand QAC4θM, were successfully developed. Two kinds of quadrilateral area coordinates are used together in the assumed displacement fields of the new elements, so that the related formulations are quite straightforward and will keep the order of the Cartesian coordinates unchangeable while the mesh is distorted. The drilling DOF is defined as the additional rigid rotation at the element nodes to avoid improper constraint. Both elements can pass the strict patch test and exhibit better performance than other similar models. In particular, they are both free of trapezoidal locking in MacNeal’s beam test and insensitive to various mesh distortions.
Highlights
It is well known that adding the drilling degree of freedom (DOF) at each node of a plane membrane element can enhance the element performance without increasing the number of the element nodes
A plane membrane element with drilling DOFs can be combined with a plate bending element to form a flat-shell element, which can avoid the problem of singular coefficients associated with the DOFs in the direction normal to the plane of the shell element
Example 3
Summary
It is well known that adding the drilling degree of freedom (DOF) at each node of a plane membrane element can enhance the element performance without increasing the number of the element nodes. Chen et al [31] proposed two 4-node quadrilateral membrane elements AGQ6-I and AGQ6-II, which exhibit excellent performance in high-order benchmark examples; both can perfectly pass MacNeal’s thin beam test [32] These two 4node elements arouse the interests in further studies on the QACM-I. Since the QACM-I contains four area coordinate components (L1, L2, L3, and L4), among which only two are independent, users may be confused on how to formulate a complete high-order polynomial In view of this disadvantage, Chen et al [52] proposed the second kind of quadrilateral coordinate method QACM-II. By introducing a generalized bubble displacement field in terms of QACM-II into the element QAC4θ, a more accurate and robust element, denoted by QAC4θM, was constructed Both elements can pass the strict patch test and exhibit better performance than other similar models. It is demonstrated again that the quadrilateral area coordinate methods are effective tools for developing high-performance quadrilateral finite element models
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