Reliability-based structural-thermal topology optimization of lightweight metal foam skeleton microstructure using the fully analytical adjoint method

In order to reduce the weight of integrated metal foam skeleton under the double constraints of target thermal and structural reliability indexes, this work proposes a three-dimensional (3D) thermal-structural reliability-based topology optimization (RBTO) method, in which the position uncertainty of the multi-structural-thermal loads is considered. The double reliability index constraints in RBTO are decoupled to a sequence of deterministic topology optimization (DTO) and inverse reliability assessment equivalently, based on performance measure approach (PMA). The inverse most probable failure points (IMPP) required by decoupling sequence are searched by the method of moving components. And the sensitivity required in skeleton topology update and IMPP searching are both quickly evaluated by complete analytical expressions using the adjoint method. Results show that 10.12–16.06% additional weight is introduced by RBTO compared to DTO when reliability index increases from 2 to 3, and the rod lattice topology obtained by RBTO is more complex than DTO. Furthermore, the plate-rod hybrid lattice topology is obtained when the load density increases under constant total loads. In addition, the uneven distribution of the multi-structural-thermal loads affects the structural and thermal failure positions significantly. More material is located below the higher loads and 3D tree-like topology is generated by RBTO, which is beneficial for force and heat redistributing and transferring uniformly. The above methods and findings have extensive application prospects in topology design of metal foam with efficient heat transfer and load-bearing capacity.