Study On The Method For Dynamic Optimum Design Of Structures Based On Trust Region Method

Structural Optimum Design (SOD) is a renovation in structural design both conceptual and methodological, it replaces the traditional trial-and-error manual methods with more systematic, standard and object-oriented methods. In recent years, large scale grid space structures and other complicated structures are taking place. This brings great challenge to traditional design methods on the one hand, and offers great space for development of SOD on the other. Structural dynamic design is a significant step in structural design, however, its optimization has not been sufficiently studied yet. It is commonly believed that the dynamic characteristics of structures can be effectively manipulated through optimum design of preset fixed frequency-constraining structures. This paper mainly studies problems relevant to structural frequency optimum design:First, the paper discusses the existence of frequency limits, as well as the relationship between frequency limit and distribution of stiffness. Truss structures might have frequency limits, therefore it is necessary to judge whether a solution is possible before starting optimizing the structures, and this will avoid vainly optimizing efforts. In addition, when the stiffness distribution of truss structures is comparatively even, the fundamental frequency can reach its maximum.Trust region algorithm is regarded as a new nonlinear programming with high reliability, robustness and convergence. In this paper then, a new algorithm, Trust Region Improving Algorithm of Frequency Limit (TRIAFL) is proposed, according to characteristics of space grid structure and the method of frequency optimum design. This new algorithm borrows the idea of automatically modulating the step size from the Trust Region Method (TRM),avoiding the usual failure resulted from over large step size. Compared with other algorithms, this algorithm requires only the first order sensitive information and much less calculation, and it gives rise to quick converges.In the case of optimizing those structures constrained by multi-conditions, such as frequency, stress and so forth, this paper proposes another new algorithm, Trust Region Synthesis Algorithm (TRSA). This algorithm makes a combination of the sequential quadratic programming and trust region techniques. On the basis of TRSA, Trust Region Algorithm of Non-Frequency-Band (TRA-NFB) is designed to forbid any frequency following in the band. TRA-NFB presets the principles of selecting concerned frequencies, and makes the selection dynamically to form frequency constraints, consequently enhancing the applicability of the algorithm.And finally, as demonstrated by series of numerical examples, the trust region algorithms presented in this paper are both effective and robust.