Strategy of selecting points via sphere of contact in probability density evolution method for response analysis of stochastic structures

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 involving multiple random variables,the strategy of selecting representative discretized points in the random variable space is of 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 identical radius in a 3-dimentional space is then evaluated.As a result,the centers of spheres of contact are selected as representative 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.