Topology optimization method of strut-and-tie composite structure under uncertain load conditions

Many materials in practical engineering exhibit completely different mechanical properties under tension and compression, such as reinforced concrete materials and fiber-reinforced polymers, etc. However, the existing structural design methods usually assume that the mechanical responses of material structures under tensile and compressive loads are the same (i.e. Symmetrical tension and compression characteristics). Considering that the loads are deterministic, the obtained design results may not meet the service requirements and could potentially cause catastrophic damage. This paper proposes a topology optimization method for the strut-and-tie composite structure model under uncertain load conditions. First, a composite structural model is constructed using three-phase materials with different tensile and compressive properties. Then, the design domain is discretized using the hybrid stress element, and a criterion for determining the state of the element in tension and compression is developed. Furthermore, the bivariate dimension reduction method and Gaussian integration method are employed to quantify and propagate load uncertainty. Moreover, an additional method for determining the state of the element in tension and compression under multiple load conditions is developed. Finally, the sensitivity of the objective function concerning the design variables is derived for both single and multiple load cases. Several examples are used to verify the effectiveness of this method, and the influence of optimization parameters such as different load uncertainty levels and the ratio of the elastic moduli of the tensile material and the compressive material on the design results is studied in detail.