FINITE ELEMENT ANALYSIS OF STRESSES AT NEUBER NOTCHES

Two-dimensional elastic plates with symmetric hyperbolic notches in their sides and subjected to transverse tension are treated. By drawing on the classical work of Neuber, a formal statement of this class problems can be made and a closed-form expression for attendant stress concentration factors obtained. By varying notch acuity, stress concentration factors ranging from just less than 3 to just greater than 90 are produced. These configurations are subjected to finite element analysis with four-node quadrilateral elements. The elements are arranged in structured meshes that are uniform in elliptic-hyperbolic coordinates. Element sides are successively halved to examine convergence, the finest resulting mesh having about three hundred thousand elements. For all problems so analyzed, converging results are obtained for respective stress concentration factors. For the smaller stress concentration factors (3, 9), results have also converged well (within 0.2%). For the higher factors (28, 90), further mesh refinement would be needed to obtain truly converged results. Such analysis can be more readily performed using submodeling and is the subject of ongoing study