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Stochastic elastic-plastic finite elements

机译：随机弹塑性有限元

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摘要

A computational framework has been developed for simulations of the behavior of solids and structures made of stochastic elastic-plastic materials. Uncertain elastic-plastic material properties are modeled as random fields, which appear as the coefficient term in the governing partial differential equation of mechanics. A spectral stochastic elastic-plastic finite element method with Fokker-Planck-Kolmogorov equation based probabilistic constitutive integrator is proposed for solution of this non-linear (elastic-plastic) partial differential equation with stochastic coefficient. To this end, the random field material properties are discretized, in both spatial and stochastic dimension, into finite numbers of independent basic random variables, using Karhunen-Loeve expansion. Those random variables are then propagated through the elastic-plastic constitutive rate equation using Fokker-Planck-Kolmogorov equation approach, to obtain the evolutionary material properties, as the material plastifies. The unknown displacement (solution) random field is then assembled - using polynomial chaos - as a function of known basic random variables and unknown deterministic coefficients, which are obtained by minimizing the error of finite representation, by Galerkin technique.
机译：已经开发出一种计算框架，用于模拟由随机弹塑性材料制成的固体和结构的行为。不确定的弹塑性材料特性被建模为随机场，在控制力学的偏微分方程中作为系数项出现。提出了一种基于Fokker-Planck-Kolmogorov方程的概率随机本构积分的谱随机弹塑性有限元方法，用于求解具有随机系数的非线性（弹塑性）偏微分方程。为此，使用Karhunen-Loeve展开将随机场材料的属性在空间和随机维度上离散为有限数量的独立基本随机变量。然后，这些随机变量使用Fokker-Planck-Kolmogorov方程方法通过弹塑性本构关系方程传播，从而在材料塑化时获得材料的演化特性。然后，利用多项式混沌，将未知位移（解）随机场作为已知基本随机变量和未知确定性系数的函数进行组合，这些误差是通过Galerkin技术将最小化有限表示的误差而获得的。

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