Development of a three-dimensional mixed variational model for woven composites. II. Numerical solution and validation

A mixed three-dimensional variational model, derived in an adjoining paper, is solved numerically for stress analysis with a finite element approach. Since the mixed model calculates the stress field by taking variations of d isplacement and stresses independently and satisfying equilibrium of stress es pointwise, accurate interlaminar stresses are predicted at the yarn inte rface. The interface continuity conditions are implemented through a penalt y method by adding an additional variational energy of two constraint condi tions: the displacements must be continuous along the interface between two stacked subregions, and interfacial normal and shear stresses must be in e quilibrium at the interface. After performing the thickness integration, th e three-dimensional variational energy equation is evaluated for each yarn (subregion) two-dimensionally with 16 stress-related and 13 displacement-re lated unknown variables. Rayleigh-Ritz approximation yields a system of lin ear equations by taking derivatives of the variational energy equation with respect to the independent unknown variables, The present mixed method is applied to analyze a flat laminated composite with a free edge, and the rep resentative volume element of woven fabric composites. The displacement and stress results of the present method are compared and validated with the c onventional displacement-based finite element solutions and/ or the previou s analytic solution. (C) 2001 Elsevier Science Ltd. All rights reserved.