Multi-objective topology optimization filled with multiple microstructures

Multi-objective topology optimization is a type of optimization technique used in engineering design to simultaneously optimize multiple performance criteria for a given system. In topology optimization, the goal is to determine the optimal distribution of material within a given design space to achieve the desired performance objectives, subject to various constraints. Multi-objective topology optimization extends this concept by considering multiple performance objectives at the same time, such as minimizing weight, maximizing stiffness, and minimizing heat transfer. The objective is to find a set of solutions that represent a trade-off between these competing objectives, which is referred to as the Pareto front or Pareto set. To obtain the Pareto front, the optimization problem must be solved for each possible combination of objective weights, which can be time-consuming and computationally expensive. Therefore, efficient algorithms such as evolutionary algorithms, genetic algorithms, and particle swarm optimization are commonly used to obtain an approximation of the Pareto front.

The main goal of topology optimization is to find the ideal material distribution within a particular design area subject to a number of constraints and goals. While respecting design limitations like displacement restrictions, stress limits, and manufacturability constraints, the optimization method aims to minimize or maximize specific performance measurements, such as weight, stiffness, stress, displacement, or natural frequency. Previously, little attention was paid to utilize multi-objective optimization with different materials. Hence, the need for multiple-objective topology optimization filled with multiple microstructures arose.

In a new study published in peer-reviewed journal Composite Structures graduate student Wenjun Chen, Professor Yongfeng Zheng and Dr. Yingjun Wang from the South China University of technology developed a multi-objective topology optimization method where optimization of natural frequency and thermal compliance of system occur concurrently by maximizing the former and minimizing the latter. In contrast to previous research, this one focused on the results of multi-objective optimization when different material proportions are taken into account. It is possible to create optimized structures with a variety of attributes by changing the material ratios. Based on this realization, the authors proposed a self-selected weight sum method that, by adjusting the filling proportion, can approach and reach the desired result point. By directly achieving the intended result points and successfully extending the range of results that are achievable in multi-objective topology optimization, this method greatly shortens the design time.

There are many topology optimization methods such as homogenization method, solid isotropic material with penalization (SIMP) and level set method (LSM) etc. The authors used the SIMP method because it was broadly used due of its simplicity. In the context of macroscopic constructions with certain properties, the suggested method tries to minimize the discrepancy between the optimized outcomes and the design criteria. The technique employs the bisection method for optimization and uses a self-selected weight sum approach based on fitting functions of the outcome domains. The self-selected weight sum approach enables weight selection based on the precise design needs. The various objectives or criteria utilized in the optimization process are combined using these weights. The relationship between the design variables and the desired properties of the macroscopic structures is mathematically represented by the fitting functions of the outcome domains. These fitting functions aid in quantifying how well the optimized structures perform in relation to the design specifications.

The authors proposed a problem statement which establishes a multi-objective optimization model. Performances of both natural frequency and heat conduction were added in order to build the model. Sensitivity of heat conduction and natural frequency were combined and the results were shown in a differential equation. Optimality Criteria (OG) was used to reduce the computation time. A numerical optimization method called the bisection method was used which iteratively reduced the search space in order to identify the best answer. It entails splitting the search space in half, then choosing the half that is most likely to hold the ideal answer. The process is repeated until the ideal solution is identified within the desired tolerance. The suggested methodology intended to directly create optimized macroscopic structures with certain attributes by utilizing the self-selected weight sum method with fitting functions of the outcome domains and the bisection method for optimization. This might narrow the discrepancy between the optimized outcomes and the design specifications, improving the effectiveness and efficiency of the design of macroscopic structures.

Multi-objective topology optimization can be applied in structural engineering to improve the design of structures such as buildings, bridges, and mechanical components. In structural design, the goal is to achieve a balance between competing objectives such as strength, stiffness, weight, and cost. Multi-objective topology optimization can help in finding the optimal layout of a structure by simultaneously considering these competing objectives. For example, the optimization can determine the optimal distribution of material in a beam, truss, or shell structure to minimize weight while meeting certain constraints on strength and stiffness. The optimization process involves selecting a design domain, specifying boundary conditions and loads, defining the material properties, and choosing the optimization algorithm. The algorithm then searches the design space to find the optimal solution that balances the competing objectives. This solution is typically represented as a set of Pareto-optimal solutions that provide a trade-off between the different objectives. One advantage of multi-objective topology optimization in structural engineering is that it can lead to more efficient and sustainable designs. By optimizing the structure’s weight, it can reduce material usage, leading to cost savings and reduced environmental impact. Furthermore, by optimizing the structure’s stiffness and strength, it can ensure that the structure is safe and performs well under different loading conditions.

To conclude, the authors presented a design approach for structures that exhibit both lower thermal compliance and higher natural frequency concurrently. The design is based on steady-state heat conduction and eigenvalue methods. The effective properties of the microstructures used to fill the macrostructures are calculated using the homogenization method. It was found out that the method is feasible in both the single-phase and multi-phase material. The research will be useful in many applications such as mechanical component design, additive manufacturing etc. Multi-objective topology optimization in structural engineering is a powerful tool that can help designers find the best design solution that meets multiple objectives and constraints.