桁架形狀與構件離散斷面之兩階段最佳化設計法

Truss shape and members'' discrete cross-sectional areas optimization mathod

黃嘉進(Chia-chin Huang)

指導教授 ： 莊德興

國立中央大學/工學院/土木工程學系/碩士(2007年)

摘要

本文主要是針對桁架的形狀與構件的離散斷面積進行桁架結構輕量化設計，文中以結構最佳化演算法(Evolutionary Structure Optimization method, ESO)搭配Fully stress design(FSD)對桁架進行兩階段的最佳化設計，束制條件包括節點的位移、構件的應力和挫屈應力束制。設計先以ESO對桁架進行形狀最佳化設計，將節點的座標作為設計變數，屬於連續變數，使用敏感度分析(Sensitivity analyses)來決定桁架節點移動的方向，並以Kuhn-Tucker必要條件作為收斂條件，判斷是否達到形狀最佳化設計。第二階段再以FSD進行桁架構件斷面尺寸最佳化設計，其設計變數為構件斷面積，屬於離散變數，FSD是以構件應力與容許應力之間的比值來決定構件斷面積需求的下限，再以直接進位方式求得到各個構件的離散斷面積。反覆上述兩階段的設計程序求得輕量化設計結果。ESO-FSD的設計程序將透過數個桁架設計例來說明。

關鍵字

離散斷面積最佳化 ； 桁架形狀變數 ； 構件離散斷面積變數 ； 結構最佳化演算法 ； 輕量化設計

並列摘要

In this paper, a structural optimization algorithm which combines evolutionary structure optimization method and fully stress design method is proposed to optimize the shape and discrete sizing of a truss structure for weight minimization. Nodal coordinates and members’ cross-sectional areas are considered as design variables. The structure is subjected to stress, Euler buckling stress and nodal displacement constraints under multiple load cases. Two types of design variables with different natures are optimized separately: 1) the evolutionary node shift method is applied to optimize shape variables, and 2) a fully stressed design (FSD) algorithm is applied to optimize sizing variables, and then round up to discrete values. The evolutionary node shift method is following the idea of evolutionary structure optimization (ESO) method. Nodal position is shifted evolutionarily by means of sensitivity analysis. The Kuhn-Tucker optimality conditions are employed as the convergence criteria for shape optimization. Alternating procedure is implemented to couple the two types of design variables and to synthesize the obtained results. The optimum solution is achieved gradually from the initial design by the combination of the two methods.

並列關鍵字

evolutionary structure optimization method ； coordinate variables ； discrete sizing variables ； minimum weight design ； fully stress design

參考文獻

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