摘要
随着经济的发展和科技的进步，土木工程结构的形式也日趋复杂化和多样化，其中以塔式结构为代表的悬臂结构更是得到了广泛的应用。而随之而来的就是对结构优化设计方法提出了更高的要求，因此采用新的优化设计方法对悬臂结构进行优化设计就具有非常重要的工程实际意义。本文对悬臂结构的优化设计方法进行了系统的理论分析和数值计算。
本文分析了传统悬臂结构优化设计的缺点和现代的Taguchi稳健设计方法的局限，取长补短提出了优化设计和稳健设计相结合的稳健优化设计方法，先通过优化设计方法得到悬臂结构设计参数的优化解，在应用Taguchi稳健设计方法对参数进行再设计，此方法解决了Taguchi稳健设计方法只宜用于解决单目标、少变量和无约束的简单问题的局限性，并通过数值算例证明了方法的有效。
为了考虑设计中各种不确定性对悬臂结构性能的影响，对悬臂结构进行可靠性分析，研究多失效模式下的结构可靠度，针对极限状态函数为显式函数的情况，应用随机摄动理论确定结构各失效模式的前四阶矩以及不同失效模式间的相关性，进而应用四阶矩技术重新确定可靠性指标，并利用梯度算法确定结构可靠性对随机参数的灵敏度，讨论各个随机参数对结构可靠性影响的大小。
针对极限状态函数为隐式函数的情况，采用改进的响应面的方法进行可靠性分析，并采用了引入混合加权重要抽样函数的重要抽样法计算结构的多失效模式下的失效概率，并提出应用改进的一阶二次矩法计算失效概率对随机变量的灵敏度。
为了同时考虑结构设计中不确定性和随机波动对结构性能的影响，结合可靠性优化理论和稳健设计方法，建立悬臂结构的可靠性稳健优化数学模型，并把可靠性灵敏度引入到设计的目标函数中，将可靠性稳健设计归结为满足可靠性要求的多目标优化问题。
为求解可靠性稳健设计的数学模型，对多目标优化算法进行了对比分析，应用引导种群向Pareto前沿的方向上收敛的新的适应度函数和动态拥挤距离替代非劣分层遗传算法中的适应度函数和拥挤度，提出了改进的非劣分层遗传算法。
应用本文所提的可靠性稳健优化方法对上海某通信塔进行了优化设计，并与传统的优化设计结果相比较，验证了方法的实用性和有效性。
With the development of the economic science and technology, the civil engineeringstructures became more and more complex and diversiform, in which the cantileverstructures like tower structure are widely applied and developed. Higher requirement tothe structural optimization design method was put forward consequently. Therefore it is ofgreat practical significance to applied new optimization method to engineering. In thispaper, optimization design method to the cantilever structure was studied both by theoreticmethod and numerical method.
Disadvantages and limitations of traditional optimization design and Taguchi robustdesign method to the cantilever structure were analysed. To make up for each other'sdeficiencies, robust optimization design method was presented, in other words, combiningthe optimization design and robust design together. Firstly, optimization solutions ofdesign parameters of cantilever structure were obtained by optimization design method;then, the parameters were redesigned by using Taguchi robust design method, which isonly appropriate for single-objective, less-variable and unconstrained problem. Anumerical example is taken out to prove the method to be effective.
In order to consider the effect of the uncertain factor to the behaviour of cantileverstructures, reliability analysis was introduced. Structural reliability undermulti-failure-mode was studied. If the limiting status function was explicit function,random perturbation theory was applied to determine first four moments and dependenceof the different failure-modes. Four moments technology was applied to determine thereliability index, and gradient algorithm was applied to determine the sensitivity of therandom parameters. The effects of the random parameters to the structural reliability wereconsidered also.
If the limiting status function was implicitfunction, the modified response surfacemethod was applied to analyse the structural reliability. Importance sampling method wasintroduced to compute the structual failure probability. The modified First-order-second-moment method was applied to compute the sensitivity of failure probability to the random variable.
In order to consider the effects of uncertainty and random fluctuation to structuralbehaviour, the optimization design and robust design were combinned together.Mathematical models of reliability robust optimization design for the cantilever structurewere established. Reliability sensitivity was introduced to the objective function.Therefore, reliability robust design was boiled down to the multi-target optimizationproblem which satisfied the reliability requirement.
In order to solve the mathematical models of reliability robust optimization design,comparative analysis to the multi-target optimization algorithm was presented. Themodified non-inferiority delamination genetic algorithm was put forward.
The reliability robust optimization design method was applied to the optimizationdesign of a communication tower in Shanghai. By compaired with the traditionaloptimization design result, practical applicability and effectiveness were presented.
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