Geometrically Nonlinear Stress Recovery in Composite Laminates

A procedure is presented to compute the interlaminar stresses in laminated plates using the intralaminar stresses and cross-section rotations from a plate analysis for cases in which geometric nonlinearities are important. The procedure is based on integrating the geometrically nonlinear equilibrium equations from the theory of elasticity simplified for the case of moderate rotations. Integration is accomplished numerically by using the intralaminar stresses and cross-section rotations from a finite-element plate analysis, finite-difference representations of the derivatives of these intralaminar stresses and rotations, and an iteration procedure (iteration being required because of the nonlinear nature of the problem). For purposes of illustration, the procedure is applied to two semi-infinite isotropic, cross-ply, and angle-ply plate example problems. One problem considers a transverse load acting on a portion of the plate, and the other considers a follower-type shear load. The problems are selected because they exhibit a variety of interlaminar stress responses, thereby providing a test for the developed procedure. The interlaminar stresses computed with the developed procedure are compared with the stresses computed using a three-dimensional finite-element analysis that serves as a benchmark. Comparisons are also made by using closed-form expressions for the intralaminar stresses in the developed procedure. The interlaminar stresses computed using the developed procedure agree well with the stresses as computed by both comparison approaches. Extensions of the procedure are discussed.