Note on singular optima in laminates design problems

This paper studies the design of laminates subject to restrictions on the ply strength. The minimum weight design is considered. It is shown that this formulation includes singular optima, which are similar to the ones observed in topology optimization including local stress constraints. In laminate design, these singular optima are linked to the removal of 'zero thickness' plies from the stacking sequence. It is shown how the fiber orientation variables can circumvent the singularity by relaxing the strength constraints related to such vanishing plies. This demonstrates the key role of fiber orientations in the optimization of laminates and the need for their efficient treatment as design variables.