Nonlinear Stochastic Finite Element Analysis Of Viscoelastic Structures
含随机参数的非线性黏弹性有限元计算

The large deformation problems of viscoelastic structures with random parameters were investigated. The nonlinear viscoelastic stochastic principle of virtual work based on the Total Lagrangian approach was established in which incremental method was applied to solve the hereditary integrals, local averaging method was adopted to discretize the random field, and perturbation method was employed to consider the randomness of parameters. The uncorrelated transformed random variables were introduced into formulations by correlation matrix decomposition algorithm. Only a few independent random variables were required to represent the major characteristics of stochastic structures. It simplified the formulation and saved the computer cost. The geometrically nonlinear relations as well as randomness between displacement and strain field were investigated. After deriving the stochastic constitutive relations between the second Piola-Kirchhoff stress tensor and Green strain tensor, the nonlinear viscoelastic stochastic finite element formulae were put forward. The Newton-Raphson iterative method was used for the solution of the nonlinear equilibrium equations. The combined influence of viscoelasticity, geometrically nonlinearity and randomness could be investigated using the innovated method. Monte-Carlo simulation was used to verify the accuracy of the proposed methods. As a numerical illustration, the responses of viscoelastic solid rocket motor grain under internal pressure were presented. It is proved by the numerical results that the present method is especially suitable for viscoelastic stochastic structures with large deformation.