多约束膜结构截面优化及在MSC/Nastran上的程序实现

Sectional Optimization of Membrane Structures under Multi-Constraint and Development of Optimization Module Based on MSC/Nastran

将准则法和数学规划法相结合,借助满应力准则将应力约束转化为动态尺寸约束,利用单位虚载荷法将位移约束转化为设计变量的显式表达式建立优化模型,然后用数学规划法求解;采用无量纲设计变量实现设计变量连接,对膜结构的厚度进行优化设计;根据对偶理论,应用对偶规划精确映射原问题,再按泰勒展式建立对偶问题的二阶近似。为了提高优化效率,采用射线步调整结构性态,运用粗选有效约束技术筛选约束,并采用主、被动变量循环确保收敛稳定。以MSC/Nastran软件作为结构分析的求解器,以MSC/Patran软件作为开发平台,完成了膜结构截面优化程序。对膜结构的单变位、多变位的结构优化问题进行了优化计算,并与MSC/Nas-tran优化模块的计算结果进行比较。算例结果表明程序的可靠性、高效性和稳定性以及理论算法的优越性。

Combining the optimality criteria method and mathematical programming, the optimization model was found and solved. The stress constraint was transformed into movable size constraint with the full stress criterion and the displacement constraint was transformed into an approximate explicit function of design variables with the unit virtual load method. Adopting the dimensionless design variables, the design variables were linked to design the thickness of membrane structures. According to the dual theory, the dual programming was used to map the original problem exactly and the second approximation of the dual problem was set up by Taylor's expansion. In order to improve the optimization efficiency, the scaling step was adopted to adjust the structural performance, the technique of constraints selection was used before optimization, and the active and inactive variables were alternated to ensure the convergence stability. With MSC/Nastran software as structural analysis solver and MSC/Patran software as developing platform, the sectional optimization software of membrane structures was accomplished. The optimization problems with single and multiple displacement constraints were carried out and the results were compared with the results obtained by MSC/Nastran software. The examples results show the reliability, efficiency and stability of the program and the advantage of the theoretical algorithm..