Three‐dimensional stochastic finite element method for elasto‐plastic bodies
Three‐dimensional stochastic finite element method for elasto‐plastic bodies
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DOI：
10.1002/nme.165
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发表时间：
2001-06
影响因子：
2.9
通讯作者：
M. Anders;M. Hori
中科院分区：
文献类型：
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作者：
M. Anders;M. Hori
提出了一种新的随机材料特性三维软化弹塑性体的随机有限元方法。该方法基于卡尔胡宁-洛夫展开和多项式混沌展开，能够有效地估计响应的完全概率特征，如矩或PDF。为了降低三维情况下的计算复杂度，对作者先前提出的二维SFEM进行了两处改动。首先，严格推导了卡尔胡宁-洛夫展开的变异性保持修正，并将其应用于代表材料性质的随机场的随机离散化。其次，提出了一种高效的并行处理算法，其耗时与普通有限元相当，为蒙特卡罗模拟提供了一种有效的方法。通过蒙特卡罗模拟验证了该方法在应变局部化随机分析中的适用性。然后，将其应用于地震工程中最近关注的一个断层形成问题。地面表层用软化弹塑性体模拟，并详细分析了破裂过程的概率特征的演化。从随机的角度对断层形成的性质进行了一些实际的观察。版权所有©2001 John Wiley&Sons，Ltd.
A new stochastic finite element method (SFEM) is formulated for three‐dimensional softening elasto‐plastic bodies with random material properties. The method is based on the Karhunen–Loeve and polynomial chaos expansions, and able to efficiently estimate complete probabilistic characteristics of the response, such as moments or PDFs. To reduce the computational complexity in the three‐dimensional setting, two alterations are made with respect to the two‐dimensional SFEM proposed earlier by the authors. First, a variability preserving modification of the Karhunen–Loeve expansion is rigorously derived and applied in the stochastic discretization of random fields representing material properties. Second, an efficient algorithm for parallel processing is developed, with time consumption being the same order as for an ordinary FEM, rendering the proposed SFEM an effective alternative to Monte‐Carlo simulation. The applicability of the proposed method to stochastic analysis of strain localization is examined using Monte‐Carlo simulation. Then, it is applied to a fault formation problem which is a recent concern of earthquake engineering. Ground surface layers are modelled by a softening elasto‐plastic body, and the evolution of probabilistic characteristics of the rupture process is analysed in detail. Some practical observations are made regarding the nature of the fault formation from the stochastic viewpoint. Copyright © 2001 John Wiley & Sons, Ltd.