Heng Zhang

This paper presents a multi-constraint topology optimization strategy for rudder structures, integrating additive manufacturing (AM)-related overhang angle and flutter-performance considerations. To the best of our knowledge, this is the first study to couple AM overhang control with mass center (flutter) steering in a single density-based formulation for flight control rudder structures. The approach incorporates constraints on structural volume fraction, overhang angle for AM, and mass center positioning to address multi-function design objectives—structural lightweighting, stiffness, aerodynamic stability, and manufacturability. A build-direction-aware projection filter and a smooth Heaviside mass center constraint are introduced to enforce these requirements during every optimization iteration. The resulting layout converges to a sandwich-type rudder with balanced mechanical performance and AM feasibility. Simulation results show that enforcing overhang constraints reduces support material usage by 46.9% and residual deformation by 14.2%, significantly enhancing AM feasibility. Additionally, introducing center-of-mass constraints improves flutter velocity from 3327 m s⁻¹ to 3759 m s⁻¹, indicating a 6.84% increase over conventional optimization and demonstrating improved dynamic stability. These simultaneous gains in manufacturability and aeroelastic safety, achieved without post-processing, underline the novelty and practical value of the proposed constraint set. The strategy thus offers a practical and efficient design method for high-performance, AM-friendly rudder structures with superior mechanical and aerodynamic characteristics, and it can be readily extended to other mission-critical AM components.

This paper proposes a novel density-based concurrent topology optimization method to support the two-scale design of composite plates for vibration mitigation. To have exceptional damping performance, dynamic compliance of the composite plate is taken as the objective function. The complex stiffness model is used to describe the material damping and accurately consider the variation of structural response due to the change of damping composite material configurations. The mode superposition method is used to calculate the complex frequency response of the composite plates to reduce the heavy computational burden caused by a large number of sample points in the frequency range during each iteration. Both microstructural configurations and macroscopic distribution are optimized in an integrated manner. At the microscale, the damping layer consists of periodic composites with distinct damping and stiffness. The effective properties of the periodic composites are homogenized and then are fed into the complex frequency response analysis at the macroscale. To implement the concurrent topology optimization at two different scales, the design variables are assigned for both macro- and micro-scales. The adjoint sensitivity analysis is presented to compute the derivatives of dynamic compliance of composite plates with respect to the micro and macro design variables. Several numerical examples with different excitation inputs and boundary conditions are presented to confirm the validity of the proposed methodologies. This paper represents a first step towards designing two-scale composite plates with optional dynamic performance under harmonic loading using an inverse design method.