Nonlinear Stochastic Finite Element Method

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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 element method.