A remeshing approach for the finite cell method applied to problems with large deformations

一种适用于大变形问题的有限单元法的重新网格划分方法

• 批准号: 505137962
• 负责人: Professor Dr.-Ing. Alexander Düster
• 金额: --
• 依托单位: Numerische Strukturanalyse mit Anwendungen in der Schiffstechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/505137962?language=en
• 关键词: remeshing; approach; finite; cell; method

The primary goal of the proposed research project is to further develop the finite cell method (FCM) - a high-order fictitious domain approach - for large deformation analysis including finite strain problems of elastoplasticity. Foamed materials will be used as a demonstrator application, as they feature complex geometries and a complex deformation behavior. Recently, we introduced a remeshing strategy to improve the robustness of the FCM for large deformations. Here, the deformed structure is remeshed when finite cells are distorted too severely. Since the FCM applies Cartesian grids, the remeshing is simple and can be carried out fully automatically. The method performs well for hyperelastic finite strain problems, and the structure under consideration can be deformed much further when applying the remeshing strategy. Nevertheless, there are still many open questions which we would like to address in this project. First of all, different remeshing criteria need to be developed and investigated in order to reliably determine when remeshing has to be initiated during the analysis. Another considerable challenge in elastoplastic analysis – because of the non-smooth data – is the interpolation of history data from the old to the new mesh. Therefore, error-controlled interpolation algorithms need to be developed. Since the computation of the element/cell matrices accounts for a significant part of the overall effort in high-order methods, special attention will be placed on this point. This is of great importance since the finite cell method requires a dense set of integration points to resolve the geometry of the broken cells. In addition, the nonlinear material models with an increased numerical effort at each integration point, combined with the repeated computation of the tangent stiffness matrix will increase the numerical effort. Thus, we aim at reducing the number of integration points. This can be achieved by applying the moment fitting where a quadrature rule is derived for every broken cell. To this end, we will extend and study the moment fitting for the case of finite strain elastoplasticity. In order to judge the robustness, accuracy, and efficiency of the overall remeshing approach, we will consider carefully selected benchmark problems and compare the proposed method with other finite element formulations.

拟议的研究项目的主要目标是进一步发展有限单元法（FCM）-高阶虚拟域方法-大变形分析，包括弹塑性有限应变问题。 泡沫材料将被用作演示应用，因为它们具有复杂的几何形状和复杂的变形行为。最近，我们引入了一个重新网格化的策略，以提高大变形的FCM的鲁棒性。在这里，当有限单元变形太严重时，变形的结构被重新网格化。由于FCM采用笛卡尔网格，网格重划分简单，可以全自动进行。该方法对超弹性有限应变问题有很好的计算效果，并且在网格重划分策略的作用下，结构可以进一步变形。尽管如此，在这个项目中，我们仍然有许多悬而未决的问题要解决。首先，需要开发和研究不同的网格重新划分标准，以便在分析期间可靠地确定何时必须启动网格重新划分。弹塑性分析中的另一个相当大的挑战-由于非光滑数据-是从旧网格到新网格的历史数据的插值。因此，需要开发误差控制的插补算法。由于单元/单元矩阵的计算占高阶方法总工作量的重要部分，因此将特别注意这一点。这是非常重要的，因为有限单元法需要一组密集的积分点来解决断裂单元的几何形状。此外，在每个积分点处具有增加的数值工作量的非线性材料模型与切线刚度矩阵的重复计算相结合将增加数值工作量。因此，我们的目标是减少积分点的数量。这可以通过应用矩拟合来实现，其中对于每个破碎的单元推导出求积规则。为此，我们将扩展和研究的情况下，有限应变弹塑性矩拟合。为了判断整体重新网格划分方法的鲁棒性，准确性和效率，我们将仔细选择基准问题，并将所提出的方法与其他有限元公式进行比较。