考虑二阶效应的空间刚架结构布局优化

针对三维空间刚架布局优化问题，以七自由度节点梁柱单元二阶弹性理论推导考虑构件几何非线性和截面翘曲变形的非线性刚度矩阵，通过整合梁柱单元非线性刚度矩阵对刚架结构进行整体的二阶弹性分析，建立满足刚架结构强度、刚度和稳定性要求的布局优化数值模型；并针对复杂刚架结构布局优化数值求解问题，改进遗传搜索算法（GA），提出可靠拓扑和引导型遗传算法双向控制方法（KLGA）. 该方法一方面将拓扑变量从布局设计变量中分离，以构件重要度评定结构可靠拓扑变量组合，再与设计变量整合；另一方面将结构特有的引导信息加入算法中，为GA提供全局最优解的指引路径. 通过两种典型的刚架算例表明二阶效应模型和KLGA算法的可行性和有效性，例如算例2中基于二阶效应模型的KLGA得到的最优结构质量比GA减轻了24.5%，波动幅度从9.61%提升到1.39%，算法更加稳定. 

Layout Optimization of Spatial Rigid Frame by Second-Order Effect Analysis

In order to handle three-dimensional spatial frame layout optimization, nonlinear rigidity matrix of the beam-column element with seven degrees of freedom was deduced by second-order elastic theory, while the geometric nonlinearity and restrained torsional warping were considered. An overall second-order analysis for rigid-frame structure was conducted by integrating the nonlinear rigidity matrices of all beam-column elements. A numerical layout optimization model of spatial rigid frame was built, which was able to satisfy the requirements for structural strength, stiffness and stability. In order to solve the numerical model, a two-way control method of reliable topology and guided genetic algorithm (KLGA) was proposed based on the improvement of the genetic algorithm (GA). In one respect, this method enables the separation of the topological variables from the layout design variables, and then integrates them after evaluating the reliable topological variable combinations based on component importance. In addition, the guidance information of structure was added in the algorithm to guide the path of global optimal solution for GA. Finally, two typical examples of rigid frame structure are presented to validate the feasibility and effectiveness of the second-order effect model and optimization method KLGA. For example, in the second-order effect model of example 2, the optimal structural mass acquired by KLGA is 24.5% less than that of GA, and its range of fluctuation promotes from 9.61% to 1.39%, indicating the stability of KLGA.