A concave-admissible quadrilateral quasi-conforming plane element using B-net method

• Present element adapts perfectly concave or extremely distorted mesh.
• The convergence rate of the strains to mesh size is proved to be 2.
• B-net functions are used to enhance the performance.

Severe accuracy loss will be caused on the occasion of mesh distortions and the calculation will even fail to be finished when the element becomes concave. This is a problem worth researching in finite element method. In this study, a novel concave-admissible quadrilateral plane element is developed within the framework of assumed displacement quasi-conforming finite element method. The B-net method is used for calculation of area integral items and gives results with high precision within convex and even concave quadrangles. Analysis shows the presented element can represent exactly displacement fields with second order polynomial terms in the Cartesian coordinates. Numerical results and comparisons with existing elements show that present element exhibit a remarkable insensitivity with extreme mesh distortions, as well as good accuracy.