Considering the influence of random factors on the structure, three
stochastic finite element methods for general nonlinear problems are proposed. They
are Taylor expansion method, perturbation method and Neumann expansion method.
The mean value of displacement is obtained by the tangent stiffness method or the
initial stress method of nonlinear finite elements. Nonlinear stochastic finite element
is transformed into linear stochastic finite element. The mean values of displacement
and stress are obtained by the incremental tangent stiffness method and the initial
stress method of the finite element of elastic-plastic problems. The stochastic finite
element of elastic- plastic problems can be calculated by the linear stochastic finite
Keywords: Nonlinear stochastic finite element method, Taylor expansion, Perturbation technology, Neumann expansion, Elastic-plastic problem.