A COMPARISON OF 3-D SPLINE VARIATIONAL AND FINITE-ELEMENT SOLUTIONS FOR A CROSS-PLY LAMINATE WITH A CIRCULAR HOLE

A comparison of the finite-element method and the spline variational t heory is presented for the three-dimensional stress analysis of a rect angular plate with a circular hole under uniaxial tension. Isotropic, orthotropic, and cross-ply laminates are considered The finite-element (FE) formulation is based on traditional 20-node isoparametric brick elements. The spline variational theory, or spline variational elastic laminate technology (SVELT) employs a variational approach in which d isplacements and interlaminar tractions are approximated using sets of B-spline functions. For the isotropic plate and the orthotropic plate , both the FE and SVELT models were sufficiently converged such that v anishing stress components, i.e., the zero-traction conditions at the hole boundary, were reported as less than 0.5% of the average applied stress. A cross-ply laminate [0(2)/90(2)](S) was selected to study the effects of the hole-edge/ply-interface singularity on the model's per formance. Stresses approaching the singularity in a radial direction a long the ply interface at 0 degrees, 45 degrees and 90 degrees from th e load axis are reported. In the vicinity of singularities and steep s tress gradients, results indicate that SVELT can reduce problem sizes or degrees of freedom (DOF) by as much as a factor of 4 while obtainin g results of comparable accuracy.