A mixed-variational formulation for interlaminar stresses in thickness-tapered composite laminates

Stress fields in laminated plates containing an abrupt thickness taper are determined following Pagano's methodology of using the Hellinger-Reissner functional with the stress components approximated within layers by expressions explicit in the thickness coordinate [Pagano, N. J. (1978). Stress fields in composite laminates. Int. J. Solids Structures 14, 385-400; Pagano, N. J. (1983). Axisymmetric stress fields in involute bodies of revolution. In Advances in Aerospace Structures, Materials and Dynamics; A Symposium on Composites, AD-06, (eds U. Yuceoglu, R. L. Sierakowski and D. A. Glasgow) ASME, NY, pp. 57-64]. The Euler equations from the variational principle are a set of variable coefficient, differential-algebraic equations (DAEs) in the longitudinal coordinate. Difficulties with the number of differential equations and boundary conditions are resolved. Solution of the system is by higher-order one-step finite difference scheme. Numerical ill-conditioning encountered when modeling layers that are thin relative to other layers in a model was remedied by choosing stress shape functions and displacement weighting functions that are different than those used by Pagano. The example problems discussed are dropped-ply laminates (laminates with terminated internal plies), that are subjected to in-plane compression or shear under the assumption that the response is adequately modeled by generalized plane deformation elasticity. (C) 1996 Elsevier Science Ltd.