A path integration algorithm for stochastic structural dynamic systems

A numerical integration scheme based on closed Newton-Cotes formulas is first proposed for calculating the response statistics of a dynamic system under Gaussian white noise excitation. Accurate system response results down to very low probability levels have been obtained by utilizing the high-degree closed Newton-Cotes formulas for the numerical integration algorithm. The computational efficiency of the numerical integration scheme is found to be very high. The proposed Newton-Cotes scheme is also compared with the Gauss-Legendre scheme in the existing literature. It is found that the Newton-Cotes algorithm is easy to develop because Newton-Cotes quadrature uses values of the integrand at equally-spaced abscissas and the values of the quadrature coefficients are easily calculated.