Formulation of Composite Laminate Robustness Constraint in Lamination Parameters Space

In composite laminate design there are many practical constraints that are customarily imposed on the selection of a suitable stacking sequence. These practical constraints empirically restrict the design space. Some practical constraints impose knock down factors on strength or strain allowables, while others impose a priori restrictions on laminate stacking sequence selection regardless of actual response calculations. One commonly applied practical constraint is the ten percent rule. In the context of laminates made of 0 ◦ , 90 ◦ and ±45 ◦ plies, the rule states that the fibres of a minimum of ten percent of laminate plies need to be along these predetermined directions. The philosophy behind the rule is that by having a minimum required amount of fibres in all four directions, the stack will be robust enough against secondary loading that cannot be easily modelled during the design process. In this paper, we attempt to formulate a robustness rule to replace the ten percent rule that would be easily applicable where the ply angles are not restricted to the traditional set (0 ◦ , 90 ◦ and ±45 ◦ ). The proposed formulation is based on constraining the ratio of minimum to maximum stiffness of the laminate. Several formulations are given depending on how minimum and maximum stiffness of a laminate are defined. By basing the definition on stiffness properties rather than ply count, it is possible to formulate the rule mathematically in the lamination parameters design space. The feasible regions based on these formulations in lamination parameters space are compared and the merits of each are discussed and compared.