GENERALIZED CONFORMING QUADRILATERAL PLANE ELEMENTS BASED ON ANALYTICAL TRIAL FUNCTIONS

Three generalized conforming quadrilateral plane elements are developed in this paper. From the governing equations of the elastic plane problem and the Airy stress function, the fundamental analytical solutions are first derived and then used as the trial functions to formulate the elements: ATF-Q4a, ATF-Q4b and ATF-Q4θ. Numerical examples show that two of the proposed elements, ATF-Q4a and ATF-Q4θ, are free from mesh sensitivity and exhibit excellent performance.