Nonlinear Stochastic Finite Element Analysis Of Viscoelastic Structures

The large deformation problems of viscoelastic structureswith random parameters were investigated. The nonlinear viscoelasticstochastic principle of virtual work based on the Total Lagrangian approachwas established in which incremental method was applied to solve thehereditary integrals, local averaging method was adopted to discretize therandom field, and perturbation method was employed to consider therandomness of parameters. The uncorrelated transformed random variables wereintroduced into formulations by correlation matrix decomposition algorithm.Only a few independent random variables were required to represent the majorcharacteristics of stochastic structures. It simplified the formulation andsaved the computer cost. The geometrically nonlinear relations aswell as randomness between displacement and strain field were investigated.After deriving the stochastic constitutive relations between the secondPiola-Kirchhoff stress tensor and Green strain tensor, the nonlinearviscoelastic stochastic finite element formulae were put forward. TheNewton-Raphson iterative method was used for the solution of the nonlinearequilibrium equations. The combined influence of viscoelasticity,geometrically nonlinearity and randomness could be investigated using theinnovated method. Monte-Carlo simulation was used to verify the accuracy ofthe proposed methods. As a numerical illustration, the responses ofviscoelastic solid rocket motor grain under internal pressure werepresented. It is proved by the numerical results that the present method isespecially suitable for viscoelastic stochastic structures with largedeformation.