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中文摘要：
发展了随机结构反应概率密度演化分析中随机参数空间的切球选点法。密度演化方法是一类直接获取随机结构动力反应概率密度函数及其演化过程的有效方法。在多个随机变量时，随机变量空间中的离散代表点选点规则直接关系到密度演化方法的精度和效率。本文构造了平面内等半径相切圆圆心分布定位的算法，以此为基础，建立了三维空间中等半径相切球球心坐标定位的计算公式。从而给出随机变量空间中的离散代表点及其赋得概率。计算表明，基于空间切球法的选点规则具有良好的精度和效率，在2个和3个随机变量情况下是较为理想的选点方法。
英文摘要：
The strategy of selecting points via sphere of contact in probability density evolution method for the response analysis of stochastic structures is presented. The probability density evolution method （PDEM） is an effective approach capable of capturing instantaneous probability density functions and its evolution as well. In the analysis of stochastic structures involv- ing multiple random variables, the strategy of selecting representative discretized points in the random variable space is oi paramount importance to the accuracy and efficiency of the PDEM. In the present paper, the location of centers of circles of contact with identical radius in a plane is specified, and based on which, the location of centers of spheres of contact with i- dentical radius in a 3-dlmentional space is then evaluated. As a result, the centers of spheres of contact are selected as repre- sentative discretized points with assigned probability. The case studies indicate that the proposed strategy of selecting points is of accuracy and efficiency in the problem involving two and/or three random parameters.
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