Rib Reinforcement Bionic Topology Optimization under Multi-Scale Cyclic Excitation

Thin-walled structures have problems such as low stiffness, large deflection, and vibration. The layout of rib reinforcement in thin-walled structures plays a vital role in providing structural strength and rigidity and reducing structural weight. A multi-scale bionic topology optimization method with a cyclic variable load is proposed in this paper to optimize dynamic flexibility by simulating the growth law of leaf vein formation and distribution. A material interpolation method is adopted to penalize the material attributes of rib reinforcement according to their thickness, based on polynomial interpolation. Combined with the layout of rib reinforcement and SIMP, the mathematical model of rib reinforcement layout optimization with cyclic variable loading is proposed, and the sensitivity of thin-walled dynamic flexibility to the rib reinforcement thickness is analyzed. Two typical examples of thin-walled structures are presented to validate the proposed method. Considering the impact effect of multi-scale cyclic loads such as wind speed, pressure, and raindrops acting on the leaf vein, the natural frequencies of bionic topological structures of heart-shaped and elliptical leaf veins are increased by 63.44% and 47.2%, respectively. Considering the change in radial thickness, the mass of the automotive door inner panel with a bionic topological structure increased by 3.2%, the maximum stress value was reduced by 1.4% and 36.8%, and deformation was reduced by 37.6% and 27.1% under the anti-concave and sinking conditions, respectively. Moreover, the first-order natural frequency of the automotive door’s inner panel with a bionic topological structure increased to 30.45%, 3.7% higher than the original.