A macro plane triangle element from the individual element test

A simple way to make the closed forms stiffness matrix of macro triangle elements is proposed through the individual element test and the computational algebra system in this paper. The newly developed element consists of three constant strain triangles, which only satisfy the convergence conditions according to the individual element test. Computational algebra system MAPLE and the free formulation framework are used to combine the stiffness matrix with the free parameters in terms of the algebraic symbols. The assembly of three constant strain triangles produces the linear strain modes in the resulted macro elements. The rigid body modes and constant strain modes of elements and the newly produced linear strain modes of the macro element are systematically assembled in the basic stiffness and the higher order stiffness in the free formulation procedure. The parameter of the decomposed higher order stiffness was tuned through the bending test. The results of numerical examples show the advantages of the proposed macro element in the distorted mesh and elements with the high aspect ratio.