Topology Optimization of Metal and Carbon Fiber Reinforced Plastic (CFRP) Structures under Loading Uncertainties

Carbon fiber reinforced plastic (CFRP) composite materials have gained particular interests due to their high specific modulus, high strength, lightweight and perfect corrosion resistance. However, in reality, CFRP composite materials cannot be used alone in some critical places such as positions of joints with hinges, locks. Therefore, metal reinforcements are usually necessary in local positions to prevent structure damage. Besides, if uncertainties present, obtained optimal structures may experience in failures as the optimization usually pushes solutions to the boundaries of constraints and has no room for tolerance and uncertainties, so robust optimization should be considered to accommodate the uncertainties in practice. This paper proposes a mixed topology method to optimize metal and carbon fiber reinforced plastic composite materials simultaneously under nondeterministic load with random magnitude and direction. A joint cost function is employed to contain both the mean and standard deviations of compliance in the robust optimization. The sensitivities of the cost function are derived with respect to the design variables in a nondeterministic context. The discrete material and thickness optimization (DMTO) technique is applied to undertake robust topology optimization for CFRP composites and metal material while the casting constraint to prevent intermediate void was introduced. In this study, two examples are presented to demonstrate the effectiveness of the proposed methods. The robust topology optimization results exhibit that the composite structures with proper distribution of materials and orientations are of more stable performance when the load fluctuates.