Multi-material topology optimization for dual-alloy turbine disk considering accurate stress prediction and control

The dual−alloy turbine disk can fully leverage the advantages of dissimilar materials and has broad application prospects. Multi−material topology optimization (MMTO) provides possibilities for its innovative design. However, the coupling between multi−material design variables and centrifugal loads poses challenges, including insufficient stress prediction accuracy, ineffective stress control, and difficulties in optimization convergence. Therefore, a new MMTO method that considers accurate stress prediction and control under centrifugal loads is proposed herein. The core ideas are as follows. (1) Introducing the multi−material predicted density to reduce the number of gray elements, proposing a multi−material transition factor for flexible selection of stiffness matrix interpolation, and thus developing an innovative accurate multi−material stress prediction method. (2) By modifying the normalized global stress method and utilizing a fixed step size to update the multi−material global stress relaxation coefficient, the maximum stress of the design domain is effectively controlled. (3) Deriving the stress sensitivity of axisymmetric problems under the complex coupling of centrifugal loads and multi−material design variables to improve the optimization convergence of stresses. Then MMTO for a turbine disk is conducted using two popular alloys (GH4169 and K418B). The results show that the proposed MMTO method effectively controls maximum stress, fully utilizes the advantages of both alloys and achieves a novel dual−alloy turbine disk structure.