COMPUTER-AIDED PHOTOELASTIC ANALYSIS OF ORTHOGONAL 3D TEXTILE COMPOSITES - PART 2 - COMBINING LEAST-SQUARES AND FINITE-ELEMENT METHODS FOR STRESS-ANALYSIS

An approach combining least squares methods and finite element methods (FEM) is presented for subsequent photoelastic stress analysis of ort hogonal 3D textile composites with R and alpha obtained in Part 1. Thr ough this approach, these photoelastic stresses are obtained over a re gion of interest as if the composites were homogeneous materials. The least squares method is used for requiring the solution strain fields to best correlate with the distribution of the two photoelastic strain data of epsilon(x)-epsilon(y) and gamma(xy) calculated directly from the measured R and alpha. The FEM uses the homogenized composite prope rties to construct the nodal force equilibrium equations as constraint s in the least squares formulation. As a result of combining this leas t squares method and FEM with Lagrange multipliers, a linear system of equations is formulated with the unknown nodal displacements. Once th ese nodal displacements are solved, the strains and stresses can be ca lculated through FEM formulations. This approach is tested with the tw o experimental results completed in Part 1 for the aluminum and compos ite plates. The stresses obtained for the aluminum plate show close ag reement with those obtained with the plain FEM computation. In the cas e of the orthogonal 3D composite plate, the local variations as observ ed in R and alpha are already necessarily eliminated from these solved photoelastic stresses. Furthermore, these stresses also match well wi th those computed with the plain FEM from the homogenized composite pr operties.