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中文摘要：
结构随机分析的传统响应面法通常用于显化表示某一随机响应量在结构特定点的涨落，属于标量型响应面法。为克服传统响应面法的局限性，提出了结构总体节点位移向量显化表示的层递响应面法，属于向量型响应面法。首先利用Karhunen．Loeve级数线性展开随机刚度矩阵和节点荷载向量，并定义随机场均值处的刚度矩阵作为预处理器，进而生成预处理Krylov子空间：然后将结构总体节点位移向量在该空间中层递展开，建立向量型的层递响应面，有效保持了节点位移之间的协调性；最后分析了层递响应面与混沌多项式之间的关系，给出了样本点选取原则，建立了节点位移向量的均值和协方差计算公式。通过算例分析，验证了层递响应面法的高精度、全域性和快速收敛性。
英文摘要：
Conventional response surface methods （RSM） are of scalar type and usually developed for a specific random quantity at a given point attached to a stochastic structure. A vectorial response surface method called as a cooperative response surface method （CRSM） is presented and developed for a global nodal displacement vector so as to overcome the limitation of the conventional RSM. The Karhunen-Lorve series is employed to expand the stiffness matrix and nodal force vector. A preconditioner is defined as the global stiffness matrix evaluated at the mean of the random field so that a preconditioned Krylov subspace can be determined. The nodal displacement vector could be expanded in the space and a vectorial cooperative response surface is developed so that the cooperativity still holds among the components in a displacement vector. The relationship between the compatible response surface and the polynomial chaos is presented so that the sample points can be defined. The explicit expressions are developed for the mean and covariance of the displacement vector. Examples demonstrate the high accuracy, global applicability and fast convergence of the cooperative response surface method.
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