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中文核心期刊

含随机参数的非线性黏弹性有限元计算

Nonlinear Stochastic Finite Element Analysis Of Viscoelastic Structures

  • 摘要: 对具有随机参数的黏弹性结构大变形问题进行了研究,利用增量法处理遗传积分,采用局部平均法离散随机场,进行相关结构分解并降低其维数,应用摄动考虑参数的随机性,建立了基于Total Lagrangian方法的黏弹性随机虚功原理. 研究了位移场和应变场的几何非线性与随机性,导出了黏弹性作用下第2类Piola-Kirchhoff应力与Green应变之间的随机递推关系, 建立了能够考虑大变形的黏弹性随机有限元方程,给出了Newton-Raphson方法求解的迭代公式. 能够同时考虑结构的黏弹性、大变形以及随机性的影响

     

    Abstract: 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.

     

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