本論文主要在研究桁架結構承載負荷下之多目標尺寸及型態最佳化設計。文中考慮結構參數及其負荷為常態分布之隨機變數，再利用有限元素法分析桁架結構，搭配偏導規則(partial derivative rule)計算出節點位移與桿件應力之平均值與變異數，並以改良式粒子族群演算法來加速最佳化的收斂速度。文中以桁架之重量與桿件斷面積之數量為最佳化目標，以截斷面面積與節點座標為離散的設計變數，其拘束包含基於可靠度之桿件應力、節點位移和挫曲條件。最後以數個數值範例列舉本文提出方法之應用，其數值結果與蒙地卡羅模擬值相當吻合。

In the thesis both the sizing and shaping multiobjective optimizations of truss structures under loads are studied. The structural parameters and loads are considered as normal random variables. The mean and variance of the nodal displacement and truss stress are evaluated using the finite element method, associated with the partial derivative rule. The optimization process is performed using a modified particle swarm optimizer (PSO) to accelerate the convergence rate. The weight of truss and the number of cross-section area are chosen as the optimal objects. The cross-section area and the nodal displacement are taken into account as discrete design variables. The constraints include the stress, nodal displacement, and buckling conditions based on the reliability. The applications of the proposed approach are illustrated with several numerical examples, and their results are in good agreement with those calculated using the Monte Carlo simulation.

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