Beyond isogeometric and stochastic collocation: maximizing efficiency in stochastic non-linear computational solid mechanics

超越等几何和随机搭配：最大化随机非线性计算固体力学的效率

• 批准号: 392510585
• 负责人: Professorin Dr. Laura De Lorenzis
• 金额: --
• 依托单位: Departement Maschinenbau und Verfahrenstechnik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/392510585?language=en
• 关键词: Beyond; isogeometric; stochastic; collocation; maximizing

Actual computations or simulations of stochastic non-linear solid mechanics models can be very costly. This project will contribute to a reduction of the computational cost of assembling and solving the governing equations. For the spatial description isogeometric analysis with NURBS bases from CAD is used, which offers high order of convergence and accuracy on a per-unknown (degree of freedom) accounting. In a similar vein, the stochastic description will adaptively choose the basis and multi-element segmentation for a high per-unknown accuracy. Furthermore, the terms in the governing equations have to be computed through numerical integration, sampling at evaluation points . This is a considerable part of the total cost, and “collocation” -- the focus of the previous project phase -- uses the minimum possible number of evaluation points, but can be unstable. In the present phase we want to proceed beyond collocation and achieve stability and fast convergence (i.e. efficiency) with as few as possible evaluation points. To this purpose, a variational framework will be used to understand and analyse the respective computations as numerically perturbed variational terms, resp. in the light of mixed variational formulations. The variational framework allows to directly estimate the stability and accuracy of the computations. This becomes especially important when computing irreversible material models such as plasticity, which have internal phenomenological variables in their descriptions. A further reduction of the number of evaluation points is to be achieved through the use of “Bayesian integration”, which uses ideas from "probabilistic numerics".

随机非线性固体力学模型的实际计算或模拟可能非常昂贵。该项目将有助于降低组装和解决管理方程式的计算成本。对于空间描述，使用了来自CAD的NURBS基础的ISODENEDRITIC分析，该分析提供了高度的融合和准确性（自由度）会计。同样，随机描述将自适应地选择基本和多元素分段，以获得高度不确定的精度。此外，管理方程式中的术语必须通过数值集成，在评估点进行采样来计算。这是总成本的考虑部分，“搭配”（上一个项目阶段的重点）使用了最小可能的评估点数量，但可能是不稳定的。在目前的阶段，我们希望以尽可能少的评估点实现稳定性和快速收敛（即效率）。为此，将使用多种框架来理解和分析各自的计算，以数值扰动的变异项，分别。鉴于混合变异公式。变分框架可以直接估计计算的稳定性和准确性。当计算不可逆的材料模型（例如可塑性）时，这一点尤其重要，这些模型在描述中具有内部现象学变量。通过使用“贝叶斯集成”，将进一步减少评估点的数量，该集成使用“概率数字”。