Application and Practice of Mathematical Optimization Method in Structural Mechanics Design

This paper discusses the application of mathematical optimization method in structural mechanics design, and emphasizes its importance in improving the efficiency and accuracy of structural design such as buildings and bridges. Traditional design methods are limited by empirical formulas and trial-and-error methods, and they are unable to solve complex structural problems, while mathematical optimization methods can better find the global optimal solution. This paper introduces several optimization algorithms, including scatter-based, gradient-based and heuristic algorithms. Taking a truss structure as an example, it shows how to use genetic algorithm (GA) to optimize the design. The results show that the optimized truss structure has achieved significant weight reduction under the constraint conditions. At the same time, compared with the gradient-based method, the advantages of GA in global optimization are highlighted. Finally, the paper discusses the challenges and solutions encountered in practice, such as improving the algorithm, introducing parallel computing and synthesizing various optimization methods. These studies provide valuable reference for engineers and promote the development of this field.