Optimization of variable stiffness laminates with gap-overlap and curvature constraints

Abstract

In the present study, the gap-overlap and curvature constraints on fiber tows are considered in the design optimization of variable stiffness laminates. The optimization problem is formulated in a framework proposed in our previous studies in which the fiber angle arrangement of a laminate is described by a continuous function constructed through the Shepard interpolation. In order to deal with the gap-overlap constraint, a gap-overlap-free rectangle is defined for each finite element. The fiber angles of the elements within this rectangle are constrained to be equal to each other, thus ensuring the fiber tows that pass through this rectangle are parallel. In order to control the curvature, a curvature-constrained rectangle is defined for each finite element. Within this rectangle the differences between fiber angles of the elements are constrained to be smaller than a user-specified upper bound. The compliance minimization with manufacturability constraints is considered, and it is solved with the MMA optimization algorithm. The results of numerical examples prove that the proposed method is effective.