Computational Approaches to Inelastic Media with Uncertain Parameters
Computational Approaches to Inelastic Media with Uncertain Parameters
复制标题
具有不确定参数的非弹性介质的计算方法
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
H. Matthies
中科院分区：
文献类型：
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作者：
B. Rosi;H. Matthies
在本文中，我们将考虑用不确定参数（如体积模量和剪切模量以及屈服应力）描述的非弹性材料，这些参数被描述为对数正态随机场。不确定性也可能出现在平衡方程的右侧。这些不确定性定义了随机非弹性问题，通过 Karhunen-Loève 展开和多项式混沌展开进行计算处理。我们只观察到一个重要点，其中随机场变成对数正态随机变量。在这里，我们基于众所周知的确定性径向返回映射引入一个材料点的随机径向返回映射，假设弹塑性评估独立于各向同性材料情况下的所有其他材料点。使用蒙特卡罗方法计算参考解，并与随机伽辽金方法进行比较。结果表明，两种方法得到的结果几乎相同，而伽辽金方法比蒙特卡罗方法更有效。
In this paper we will consider inelastic material described with uncertain parameters like bulk and shear modulus as well as yield stress, described as lognormal random fields. Uncertainty also can appear on the right hand side of the equilibrium equation. These uncertainties define stochastic inelastic problem, computationally treated by Karhunen-Loève expansion and polynomial chaos expansion. We observed just one material point, where the random fields become lognormal random variables. Here, we are introducing a stochastic radial return mapping for one material point based on the well-known deterministic radial return mapping, assuming that the elastoplastic evaluation is independent of all other material points for the case of isotropic material. The reference solution is calculated using a Monte Carlo method and compared with the stochastic Galerkin method. The results show that both methods give almost the same results, while the Galerkin method is more effective than the Monte Carlo method.