Structural Optimization Design With Constraint Of Natural Frequency

In this paper, the trust region algorithm is applied to structural dynamics optimization design. The aim of this study is to solve the optimization problems which should meet the frequency constraints by changing the structural sizes, so that the quality of the structure can reach to a minimum. Lot of engineering structures in using is subject to strong vibration and shock. Natural frequency of the vibration structure is undoubtedly the most important one of the characteristics. The reaction of structure under dynamics load largely extent dependent on the previous order natural frequencies of the structure. When the dynamic load frequency bands close to natural frequency of the structure, there will be have over-vibration. Especially in the aviation, aerospace, automobile and civil engineering structure, the structural optimization design with constraints of frequency have great significance.Optimizing the frequency for structure usually make the optimal model to become to a group of highly nonlinear problems, the solution for the nonlinear optimization problem is almost all of the traditional linear search method, that is produced a search direction in each iteration, and then make a accurate or inaccurate one-dimensional search on the direction in order to obtain the next iterative point. But the viable domain for frequency optimization is a non-convex set, that is to say improper selection of the optimization methods could lead to no solution to optimization problems, so the selection for method of frequency optimization wants great care. And trust region methods are a class of very new methods, the algorithm is reliable, having a strong convergence, it is not only able to quickly resolve good-conditioning problem, but also effectively solve the ill-conditioning problem.In this paper, we proposed a kind of trust region method bound for the bar structure with the frequency constraints, this algorithm makes a combination of the quadratic programming and trust region techniques, dynamics select penalty factor in the iterative process, and enhance the adaptability and convergence speed of the algorithm. However, calculated Hessian matrix in the quadratic programming is so difficult for complexity structural of large-scale projects that we need spend much time on it. So we propose a improve trust region algorithm on this basis, this algorithm can adaptive regulate step size based on the idea of trust region, and avoid the algorithm failure caused by the large step. The algorithm only calculated the first derivative, significantly reduced the computation and had a good convergence.