STOCHASTIC GALERKIN FINITE ELEMENT METHOD FOR NONLINEAR ELASTICITY AND APPLICATION TO REINFORCED CONCRETE MEMBERS

IF 1.5 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal for Uncertainty Quantification Pub Date : 2022-01-01 DOI:10.1615/int.j.uncertaintyquantification.2022038435

Mohammad S. Ghavami, Bedrich Sousedik, Hooshang Dabbagh, Morad Ahmadnasab

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引用次数: 0

Abstract

We develop a stochastic Galerkin finite element method for nonlinear elasticity and apply it to reinforced concrete members with random material properties. The strategy is based on the modified Newton-Raphson method, which consists of an incremental loading process and a linearization scheme applied at each load increment. We consider that the material properties are given by a stochastic expansion in the so-called generalized polynomial chaos (gPC) framework. We search the gPC expansion of the displacement, which is then used to update the gPC expansions of the stress, strain, and internal forces. The proposed method is applied to a reinforced concrete beam with uncertain initial concrete modulus of elasticity and a shear wall with uncertain maximum compressive stress of concrete, and the results are compared to those of stochastic collocation and Monte Carlo methods. Since the systems of equations obtained in the linearization scheme using the stochastic Galerkin method are very large, and there are typically many load increments, we also studied iterative solution using preconditioned conjugate gradients. The efficiency of the proposed method is illustrated by a set of numerical experiments.

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非线性弹性随机伽辽金有限元法及其在钢筋混凝土构件中的应用

本文建立了非线性弹性的随机伽辽金有限元方法，并将其应用于具有随机材料特性的钢筋混凝土构件。该策略基于改进的Newton-Raphson方法，该方法由增量加载过程和每个增量加载时应用的线性化方案组成。我们认为材料的性质是在所谓的广义多项式混沌(gPC)框架中的随机展开式给出的。我们搜索位移的gPC扩展，然后用它来更新应力、应变和内力的gPC扩展。将该方法应用于混凝土初始弹性模量不确定的钢筋混凝土梁和混凝土最大压应力不确定的剪力墙，并与随机配置方法和蒙特卡罗方法的结果进行了比较。由于采用随机伽辽金法线性化方案得到的方程组非常大，并且通常存在许多荷载增量，因此我们还研究了使用预条件共轭梯度的迭代解。一组数值实验表明了该方法的有效性。

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来源期刊

International Journal for Uncertainty Quantification ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.60

自引率

5.90%

发文量

期刊介绍： The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.