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中文摘要：
二级控制的意思是在自然设计变量和有限元网格节点之间加入设计单元，建立自然设计变量控制关键点坐标，关键点控制有限元网格节点，共两层控制关系。后一层控制关系借助有限元形函数描述设计单元，并引入相应的参数坐标，从而实现敏庋分析、结构形状变化的控制和网格的变动控制。本文使用二级控制理论有效地解决了二维连续体结构形状优化的一些困难，将形状优化问题处理成序列二次规划问题求解。使用MSC／PCL语言在MSC／Patran＆Nasntran平台上实现了优化模块的二次开发。本文设计思路的可行性和程序的有效性通过若干算例得到证实。
英文摘要：
Two-phase control means that middle-variables are inserted between natural design variables and nodes in the mesh. Two-phase control is established. 1） The coordinates of the key points are controlled by natural design variables; 2） The nodes in the FEM mesh are controlled by key points. The second control describes the design elements in terms of the shape function of FEM and the parameter coordinates are introduced. Then the sensitivity analysis, the control of change of structural shape and its mesh are realized. On the base of the two-phase control, some difficulties in the problem of shape optimization can be solved and the problem is approached as a Sequential Quadratic Programming problem to be solved. The program of shape optimization is carried out on MSC/Pastran＆Nastran platform and by using PCL language. The idea of the research is verified by some examples. The reliability, the accuracy and the high-efficiency of the program have been testified by the results of the examples.
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