Premium
An incompatible and unsymmetric four‐node quadrilateral plane element with high numerical performance
Author(s) -
Huang Yingqing,
Huan Yakun,
Chen Haibo
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6363
Subject(s) - quadrilateral , finite element method , polygon mesh , discretization , mathematics , node (physics) , quadratic equation , interpolation (computer graphics) , lagrange multiplier , numerical analysis , lagrange polynomial , displacement (psychology) , mathematical analysis , geometry , computer science , structural engineering , mathematical optimization , engineering , computer graphics (images) , polynomial , psychotherapist , animation , psychology
Recent studies show that the unsymmetric finite element method exhibits excellent performance when the discretized meshes are severely distorted. In this article, a new unsymmetric 4‐noded quadrilateral plane element is presented using both incompatible test functions and trial functions. Five internal nodes, one at the elemental central and four at the middle sides, are added to ensure the quadratic completeness of the elemental displacement field. Thereafter, the total nine nodes are applied to form the shape functions of trial function, and the Lagrange interpolation functions are adopted as the incompatible test shape functions of the internal nodes. The incompatible test displacements are then revised to satisfy the patch test. Numerical tests show that the present element can provide very good numerical accuracy with badly distorted meshes. Unlike the existing unsymmetric four‐node plane elements in which the analytical stress fields are employed, the present element can be extended to boundary value problems of any differential equations with no difficulties.