Abstract: The completeness analysis and building were conducted for the reduced basis space of structural static reduced responses with variable parameters. The solution precisions of structural static reduced responses were often influenced by the reduced spaces. An optimization model for selecting response basis was formed with applications of the vector subspace angle， which was used for quantifing the relationship between the response basis vector and subspace in the reduced basis. Subsequently， an optimization algorithm was utilized to choose the optimum basis vector in the response sets associated with the parameter domains step by step， in which the reduced basis space then tended towards more completeness and the obtained reduced responses of structure became also more accurate. The examples herein demonstrate the feasibility and effectiveness.

Key words: structural static response, reduced basis space, subspace angle, completeness, optimization algorithm

摘要： 对变参数结构静态减基响应的减基空间进行了完备性分析和构建。结构静态响应的减基求解精度往往直接受到减基空间的影响，以向量子空间夹角作为评判标准，将减基空间中响应基向量与子空间之间的关系用向量子空间夹角进行定量化，形成选择响应基的优化模型，在与参数域对应的响应集合中利用优化算法逐步挑选合适的基向量，在此过程中构建的减基空间趋于完备，由此获得的结构减基响应解也趋于精确。文中算例验证了该方法的可行性和有效性。

关键词: 结构静态响应, 减基空间, 子空间夹角, 完备性, 优化算法