权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Multiscale Stochastic Computation of Natural Frequencies for Beams Made of Metal Foam Based on Stochastic Geometry Models

基于随机几何模型的泡沫金属梁固有频率的多尺度随机计算

基本信息

批准号：
229246373
负责人：
Professor Dr.-Ing. Carsten Proppe
金额：
--
依托单位：
Bereich Dynamik / Mechatronik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2015-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/229246373?language=en
关键词：
Multiscale Stochastic Computation Natural Frequencies

项目摘要

Aim of the project is to develop a multiscale stochastic computation method which, starting from CT geometry data, allows for the determination of natural frequencies of beams made of metal foam as far as possible without ad hoc assumptions. To this end, the computation method developed by the applicants is extended and modified.With regard to the stochastic modeling of the microstructure geometry, the goal is to develop a statistical model fitting technique which avoids a prior selection of a tessellation model. For this purpose, a Laguerre tessellation is reconstructed from the cell system of the foam using a suitable distance measure. The set of generators of this tessellation is interpreted as a marked point process. Using classical point process statistics, a model is fit to this point process. The Laguerre tessellation of model realizations then provides three-dimensional samples of the microstructure geometry. The distance measure used in the model fitting steps has to be chosen such that both the geometrical characteristics of the structure as well as the material properties are reproduced correctly.By means of the geometry samples, boundary effect independent properties of the apparent material parameters are determined. For this purpose, by introduction of an additional length scale a difference is made between the volume element on which the boundary conditions are applied, and the volume element, over which stresses and strains are averaged. This allows to obtain boundary effect independent histograms of the one-dimensional marginal distributions and estimates of the autocorrelation function of material parameters. Using these data, a random field is modeled without assuming a distribution class for the marginal distributions. The goal is to develop a novel approach that starts from the truncated Karhunen-Loève expansion of the random field and generates iteratively realizations of the non-Gaussian random variables contained in the expansion. This approach offers the advantage that the random variables enter linearly in the Stochastic-FE-formulation of the eigenvalue problem for the determination of the natural frequencies, which facilitates a non-intrusive solution of the FE problem.Another goal of the project is the statistical description and the modeling of the occurrence of special inhomogeneities such as variable strut thickness distribution and defects in order to better understand the effect of the combination of these effects on the structural behavior.The developed computation method is validated step by step by means of sample images and results of experimental modal analysis.Another major objective of the proposed approach is to gain insights that are also transferable for the modeling of other heterogeneous materials. This applies particularly to the investigations of the generator set and of the boundary effect independent properties of apparent material parameters as well as to the random field modeling.

该项目的目的是开发一种多尺度随机计算方法，从CT几何数据开始，允许尽可能确定由金属泡沫制成的梁的固有频率，而无需特别假设。为此，对申请人开发的计算方法进行了扩展和修改。对于微观结构几何形状的随机建模，目标是开发一种统计模型拟合技术，避免事先选择镶嵌模型。为此，使用合适的距离测量从泡沫的单元系统重建拉盖尔镶嵌。该镶嵌的生成器的集合被解释为标记点过程。利用经典的点过程统计方法，对该点过程进行模型拟合。然后，模型实现的拉盖尔镶嵌提供微观结构几何形状的三维样本。在模型拟合步骤中使用的距离测量必须被选择为使得结构的几何特征以及材料属性都被正确地再现。通过几何样本，确定表观材料参数的边界效应独立属性。为此目的，通过引入附加的长度尺度，在施加边界条件的体积单元与应力和应变平均的体积单元之间产生差异。这允许获得一维边缘分布的边界效应独立直方图和材料参数的自相关函数的估计。使用这些数据，一个随机场建模，而不假设一个分布类的边缘分布。我们的目标是开发一种新的方法，从截断的Karhunen-Loève展开的随机场，并迭代地产生的非高斯随机变量的实现中包含的扩展。这种方法的优点是，随机变量线性地进入本征值问题的随机有限元公式，以确定固有频率，这有助于非-该项目的另一个目标是对特殊不均匀性的发生进行统计描述和建模，例如可变支柱厚度分布和缺陷，以便更好地了解本文的计算方法通过对结构的模态分析结果和样本图像的分析，逐步验证了本文方法的有效性。本文方法的另一个主要目的是为其它非均质材料的建模提供可借鉴的方法。这特别适用于发电机组的调查和边界效应的表观材料参数的独立属性，以及随机场建模。