The stochastic finite element third-order perturbation method for linear
static problems is formulated. The stress-strength interference model, Monte Carlo
simulation and a new iterative method (NIM) of reliability calculation for the linear
static problem and linear vibration are proposed. Reliability calculation methods
using modified iteration formulas by the homotopy perturbation method (MIHPD)
and second- order reliability method for a nonlinear static problem and nonlinear
vibration are proposed.
Keywords: The third-order Taylor expansion, Perturbation method, Linear static problem, Linear vibration, Nonlinear static problem, Nonlinear vibration, Stressstrength interference model, Monte Carlo simulation, A new iterative method, Modified iteration formulas, Homotopy perturbation method.