Nine-node Isoparametric Element Research Articles

Comments on the accuracy of nine-noded isoparametric finite elements

The reduction in accuracy in stress of nine-noded quadratic isoparametric elements related to the locations of the mid-side and centre nodes is shown to be due to erroneous relationships between strains and nodal displacements. The effect of nodal position on the calculated strains is discussed and criteria for the proper positioning of mid-side and centre nodes are provided. Errors associated with the use of curved sides are also examined and examples involving body force loading are used to illustrate the errors involved in the non-optimum location of nodes. The possibility of degenerating quadrilateral nine-noded isoparametric elements into triangular shaped elements is also studied. Recommendations to the user of finite element programs, in which nine-noded elements are incorporated are included.