In one embodiment, a morphable composite three-dimensional structure is disclosed. The morphable composite three-dimensional structure comprises a flexible fiber-reinforced ceramic composite comprising a fiber preform and a ceramic matrix material infused therein. The flexible fiber-reinforced ceramic composite defines a flowpath having a three-dimensional cross-section. The cross-section of the flowpath is variable along the length of the flowpath. A plurality of anchors are integrally formed in the fiber preform. The plurality of anchors extend through a thickness of the ceramic matrix. The plurality of anchors are configured to couple to at least one actuator. The at least one actuator is actuatable to vary the three-dimensional cross-section of the flowpath.