Extension of field consistence approach into developing plane stress elements Original Research Article

In this research paper, the possibilities for extending the field consistence approach [L. Yunhua, On shear locking in finite elements, Licentiate Thesis, Stockholm 1997; L. Yunhua, Explanation and elimination of shear locking and membrane locking with field consistence approach, Comput. Methods Appl. Mech. Engrg., in press], starting from different variational principles, to plane stress elements are investigated. In the extension, two main difficulties are: explicitly solving a set of coupled partial differential equations and satisfying inter-element compatibility. The first one is alleviated by constructing element interpolations from a set of quasi-general solutions, rather than the real general solutions, to the Euler—Lagrangian equations. The second one is solved by combining the field consistence approach with the iso-parametric interpolation technique. The traditional assumed stress method is improved and an efficient plane stress element is obtained. It seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach.