The number theoretical method in response analysis of nonlinear stochastic structures

A strategy of determining representative point sets through the number theoretical method (NTM) in analysis of nonlinear stochastic structures is proposed. The newly developed probability density evolution method, applicable to general nonlinear structures involving random parameters, is capable of capturing instantaneous probability density function. In the present paper, the NTM is employed to pick out the representative point sets in a hypercube, i.e., the multi-dimensional random parameters space. Further, a hyper-ball is imposed on the point sets to greatly reduce the number of the finally selected points. The accuracy of the proposed method is ensured in that he error estimate is proved. Numerical examples are studied to verify and validate the proposed method. The investigations indicate that the proposed method is of fair accuracy and efficiency, with the computational efforts of a problem involving multiple random parameters reduced to the level of that involving only one single random parameter.