| Summary: | 碩士 === 國立中央大學 === 土木工程研究所 === 93 === Abstract
This research studies the minimum weight design of structures with linked discrete variables, static and dynamic response constraints. Three discrete Lagrangian based searching procedures are proposed in this report. The static response constraints include displacement, stress, buckling stress and slenderness ratio. The dynamic response constraints include frequency and frequency response amplitude. In this research, an update formula for the Lagrange multiplies is developed first. The difficulties in applying the DLM to solve for problems containing linked discrete variables and dynamic response constraints are then discussed. To resolve the difficulties, a dynamic extending neighborhood technique and an improving strategy for eliminating fluctuated searching trajectory are proposed. Finally, a restarting procedure for the DLM by scaling down the values of Lagrange multipliers is also proposed to help the search escaping from a local minimum to search for another one. The feasibility of three procedures is validated by several design examples. The results from comparative studies of the DLM against other discrete optimization algorithms are reported to show the solution quality of the proposed DLM procedures. The advantages and drawbacks of the three DLM algorithms are also discussed.
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