Optimization of composite structures using a first fibre failure criterion

The usage of laminated composite materials within modern aircrafts provides many advantages such as weight reduction and an excellent strength to density ratio. During aircraft life they are subjected to a complex stress state. These loads cause several failure modes and scenarios challenging the sizing process. This paper presents the comparison and evaluation of different failure criteria for the design of composite structures based on Finite Element Method. The in house tool LAGRANGE of Cassidian Air Systems allows the analysis and multi disciplinary optimization of composite structures, whereas the usual goal is to minimize the weight considering the given constraints. Thereby the strength of the laminates can be predicted by several stress or strain based failure criteria. Two of them are the maximum strain criterion, predicting fibre failure and the first matrix failure criterion (FMC), which calculates matrix failure using the Puck criterion and fibre failure by means of the Yamada-Sun criterion. In addition to the existing approaches a first fibre failure criterion (FFC) is implemented based on the assumption that the respective layer fails after fibre failure and not after matrix cracking. Thereby fibre failure is again calculated by the Yamada-Sun criterion and matrix failure by the Puck criterion. However, if the latter is detected the respective ply stiffness is degraded. Afterwards the structure is recalculated and only fails, if either fibre failure occurs or all plies are degraded. This approach is implemented as a subroutine within the finite element analysis routine, which is part of the optimization loop of LAGRANGE. It is called element wise, whereas the fluxes and torque flows are kept constant, i.e. the load distributes within the respective finite element.The derivatives of the constraints with respect to the design variables, needed for the gradient based optimization algorithms, are provided by the sensitivity analysis. Those can be computed numerically or analytically, whereas the analytical sensitivities are more efficient, but otherwise involve a complex implementation. For the first fibre failure criterion corresponding derivatives are integrated. The first part of the present paper describes the first fibre failure criterion and illustrates the degradation process by a small example. In addition the adapted analytical sensitivities are explained briefly. The next part describes the optimization of composite structures of different complexities, using the newly implemented FFC approach and the already existing maximum strain and FMC criteria. The paper shows the influence of the criteria on the results of the optimization and the consequences for the final structure