AbstractFiber-reinforced polymer (FRP) composite frames are the ideal main support structure in civil and aerospace engineering applications because of their excellent material and structural properties for high stiffness ratio, high strength ratio, large span, and so forth. This paper investigated strong singularity optimum problems of FRP composite frames under fundamental frequency constraints. An area/moment of inertia-density strategy, the adapted polynomial material interpolation (APLMP) strategy, was adopted. The APLMP strategy changes the physical relationship of a tube’s bending stiffness and cross-sectional area to relax the local vibration frequency constraint. The specific manufacturing constraints for laminated composite were considered in the mathematical model with fixed fiber winding angles and sequence according to certain guidelines to reduce the heavy calculation burden. The artificial densities of the APLMP strategy, which are a function of the areas of the composite frame, were defined as the size and topology optimization variables. Extensive large-scale two-dimensional and three-dimensional numerical examples demonstrated the validity of the APLMP interpolation strategy for topology design optimization of FRP frames. It was proved that the APLMP strategy can solve the challenge of the strongly singular optimum for structure topology design optimization of composite frames with frequency constraints.