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Model order reduction for large-scale structures with local nonlinearities

机译：用当地非线性进行大规模结构的模型顺序减少

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摘要

In solid mechanics, linear structures often exhibit (local) nonlinear behavior when close to failure. For instance, the elastic deformation of a structure becomes plastic after being deformed beyond recovery. To properly assess such problems in a real-life application, we need fast and multi-query evaluations of coupled linear and nonlinear structural systems, whose approximations are not straight forward and often computationally expensive. In this work, we propose a linear-nonlinear domain decomposition, where the two systems are coupled through the solutions on a prescribed linear-nonlinear interface. After necessary sensitivity analysis, e.g. for structures with a high dimensional parameter space, we adopt a non-intrusive method, e.g. Gaussian processes regression (GPR), to solve for the solution on the interface. We then utilize different model order reduction techniques to address the linear and nonlinear problems individually. To accelerate the approximation, we employ again the non-intrusive GPR for the nonlinearity, while intrusive model order reduction methods, e.g. the conventional reduced basis (RB) method or the static-condensation reduced-basis-element (SCRBE) method, are employed for the solution in the linear subdomain. The proposed method is applicable for problems with pre-determined linear-nonlinear domain decomposition. We provide several numerical examples to demonstrate the effectiveness of our method. (C) 2019 Elsevier B.V. All rights reserved.
机译：在固体力学中，线性结构通常在接近故障时表现出（局部）非线性行为。例如，在变形超出恢复后，结构的弹性变形变为塑料。为了正确评估现实应用中的这些问题，我们需要快速和多查询的耦合线性和非线性结构系统的评估，其近似不是直接的，并且通常计算昂贵。在这项工作中，我们提出了一种线性 - 非线性域分解，其中两个系统通过在规定的线性非线性界面上的解决方案耦合。在必要的敏感性分析之后，例如对于具有高维参数空间的结构，我们采用了一种非侵入式方法，例如，高斯进程回归（GPR），用于解决界面上的解决方案。然后，我们利用不同的模型顺序减少技术来单独解决线性和非线性问题。为了加速近似，我们再次采用非侵入性GPR的非线性，而侵入式模型顺序减少方法，例如，传统的降低的基础（RB）方法或静缩 - 缩小基础元素（SCRBE）方法用于线性子域内的溶液。该方法适用于预定的线性非线性域分解的问题。我们提供了几个数字示例以证明我们方法的有效性。 （c）2019 Elsevier B.v.保留所有权利。

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