An axisymmetric nodal averaged finite element

Abstract A nodal averaging technique which was earlier used for plane strain and three-dimensional problems is extended to include the axisymmetric one. Based on the virtual work principle, an expression for nodal force is found. In turn, a nodal force variation yields a stiffness matrix that proves to be non-symmetrical. But, cumbersome non-symmetrical terms can be rejected without the loss of Newton-Raphson iterations convergence. An approximate formula of volume for a ring of triangular profile is exploited in order to simplify program codes and also to accelerate calculations. The proposed finite element is intended primarily for quasistatic problems and large irreversible strain i.e. for metal forming analysis. As a test problem, deep rolling of a steel rod is studied.