粘弹性随机有限元

以近似不可压缩粘弹增量有限元和摄动法为基础，利用增量法处理遗传积分，应用参数摄动考虑随机性，采用局部平均方法对随机场进行离散，通过相关结构分解减少计算量，发展了一种粘弹性随机有限元方法。研究表明，尽管粘弹性材料本构关系具有时间相依性，其随机摄动格式并不存在“长期项”的影响。应用该方法进行粘弹性结构的随机模拟，程序实施简单，计算效率较高，精度较高。

VISCOELASTIC STOCHASTIC FINITE ELEMENT

One difficult aspect of treating statistical uncertainty in viscoelastic structures is the consideration of coupled interaction between the randomness of parameters and the viscoelasticity. The near-incompressibility of some materials increases the difficulties. Based on the perturbation method and incremental FEM suitable for incompressible materials, a new type of viscoelastic stochastic finite element method is proposed. The incremental method is applied to solving the hereditary integrals, and the perturbation method is used to consider the randomness of parameters. The local averaging method is used to discretize the random field. By transforming the correlated random variables to a set of uncorrelated random variables, a simplified formulation is obtained. The influence of random parameters is discussed. Although the viscoelastic constitutive relation is time-dependent, the application of stochastic perturbation method for viscoelastic problems doesn't result in the emergence of undesirable secular terms. Numerical results reveal that the approach proposed has the advantages of the simple and convenient program implementation, and is accurate and effective for viscoelastic stochastic problems.