8-node quasi-conforming plane element by using Bernstein basis functions

Bernstein basis functions are used extensively in geometric modeling for their excellent merits. In this paper, a new 8-node assumed stress quasi-conforming plane element is proposed by using Bernstein basis functions. Firstly, the fundamental analytical solutions, which satisfy both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of the element. Then the stress-function matrix is adopted as the weighted function to weaken the strain-displacement equations. Finally, the Bernstein polynomials are chosen as string-net functions on the boundary of the element for the process of strain integration. The formulations of the element are simple and concise, and the element is immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The characteristics of Bernstein polynomials to approximate models' geometry accuracy make the element competitive when compared with other solutions, especially for the curved-edge structures, which is proven by the numerical tests.