Robust topology optimisation of bi-modulus structures

• Robust topology optimisation of bi-modulus material is developed.
• Multiple loading conditions are considered in simulation.
• Material replacement method is adopted for simplifying structural analysis.
• Sensitivity of robust compliance is derived.
• Optimal topology is found to be force-direction dependent when materials display bi-modulus behaviour.

This study proposes a robust topology optimisation method for the design of bi-modulus structures under uncertain multiple loading conditions (MLC). The objective of the design optimisation is to minimise the standard deviation of the weighted structural compliance. The gradient-based method is applied to perform a sensitivity analysis for the identification of optimal design variables. A material replacement method is used to overcome difficulty in the sensitivity analysis due to the stress-dependent behaviour of the original bi-modulus material. In the material replacement operation, two new isotropic materials are identified to replace the original bi-modulus material according to its two moduli. To reduce the side effects of the material replacement operation on the final design, the local stiffness is modified in terms of the stress state. Typical numerical examples are used to demonstrate the effectiveness of the proposed method to the final design, including the load uncertainty on the optimal bi-modulus layout, as well as other factors, such as loading direction and the ratio between the two moduli of the bi-modulus material. The comparison between layouts of isotropic and bi-modulus materials also shows that the final bi-modulus material distribution is sensitive to loading directions in practical designs.