Full-field stress tailoring of composite laminates

The Hellinger-Reissner mixed variational principle is used to derive a higher-order zig-zag theory for the stretching and bending of highly heterogeneous, laminated, variable stiffness beams. The derivation is presented in generalised form such that the order of the theory can be chosen a priori without the need for re-writing the governing equations. The model is used to analyse the bending of variable stiffness beams under different boundary conditions and validated against 3D finite element results. Combined with findings in previous work the present model captures the full 3D stress field of laminated beams accurately without the need for a posteriori stress recovery steps. The model is then used within a genetic algorithm to find a compromise between maximising bending stiffness and minimising the likelihood of delaminations in simply-supported and clamped beams. It is found that the greater design space of variable stiffness laminates facilitates a better compromise compared to quasi-isotropic straight-fiber laminates. This enhanced response is possible because variable stiffness laminates can be designed to guarantee high global bending stiffness while locally tailoring the 3D stress-field at areas of stress-concentration to delay the onset of delaminations. Thus, the present work shows the capability of variable stiffness laminates to favourably re-distribute through-thickness stresses.