LAUSR

Using the point interpolation method, this study proposes a distinctive node selection scheme, T33-scheme, to construct the approximation over all triangles in the mesh. By the T33-scheme, we always selects out six nodes to take part in the interpolation to any element, creating a T33 element with a displacement approximation of completely quadratic polynomials. The six nodes may be real nodes in the mesh or assistant nodes temporarily generated during the calculation of the element matrices. The degrees of freedom of assistant nodes can be easily condensed off once the matrices of the element, which has one boundary edge, are formed. The T33 element can pass the patch test exactly and reproduce the displacement mode of quadratic polynomials. Numerical experiments confirmed that the T33 elements have an outstanding performance in its accuracy, convergence rates and stability.