A finite element model for the analysis of the nonlinear mechanical behavior of hybrid composite materials

用于分析混合复合材料非线性力学行为的有限元模型

• 批准号: 433734847
• 负责人: Professor Dr.-Ing. Sven Klinkel
• 金额: --
• 依托单位: Lehrstuhl für Baustatik und Baudynamik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/433734847?language=en
• 关键词: finite; element; model; analysis; nonlinear

The research project deals with a non-standard discretization method. It is based on the fundamental paradigm of scaling the boundary surfaces with respect to a center. It leads to a finite element mesh with star-convex elements that allow hanging nodes, reentrant corners and curved edges. For the resulting polygon or polyhedron-like structures, the corresponding element formulations are developed. In order to enable a general application, these are designed for geometrical and physically non-linear 2D and 3D problems. We are aiming for an element formulation, which combines the advantages of the finite element method and the geometrically exact description of the boundary geometry. The element allows for an arbitrary number of sides. Straight edges or plane surfaces are possible as well as curved edges or surfaces, which are described by e.g. non-uniform rational B splines. In combination with the fast Quadtree or Octree algorithm and a local refinement strategy, it leads to a recursive discretization method. Initially, it starts with the boundary representation of a solid and then automatically continues with a block partitioning of the structure. In this manner, internal interfaces originating from different materials or voids are resolved, and the curved boundary is embedded in the finite element mesh.At first, a Quadtree or Octree decomposition of the domain into star-convex subdomains or elements provides a rough initial discretization. Further mesh refinements are needed to reduce the approximation error of the stresses and displacements. There are two refinements options. One recursively applies Quadtree or Octree decomposition to create the next finer level of discretization. The other considers the parameterization on the element, where the refinement applies either in circumferential direction along the boundary or in radial direction. Note that this step may be completely restricted to a subdomain or the element under consideration. It is not necessary to refine neighboring elements due to so-called hanging nodes. Therefore, it is a local refinement, which can be applied in different ways. It is possible to introduce additional nodes at the boundary edges and/or in the interior of an element, or it is possible to increase the polynomial degree at element level. The different refinement strategies need to be evaluated based on meaningful criteria.The discretization concept with the embedded element formulation results in a general numerical finite element method, which is suitable for the analysis of heterogeneous materials with inclusions and voids. The aim of the project is to contribute to reliable and robust numerical analysis to meet the requirements for the design of modern hybrid composites.

本研究计画探讨一种非标准离散化方法。它基于相对于中心缩放边界表面的基本范例。它导致了一个有限元网格与星凸元素，允许悬挂节点，凹角和弯曲的边缘。对于由此产生的多边形或多面体状结构，相应的元素配方开发。为了实现一般应用，这些设计用于几何和物理非线性2D和3D问题。我们的目标是一个元素配方，它结合了有限元法的优点和边界几何形状的几何精确描述。该元素允许任意数量的边。直边或平面表面以及弯曲边或表面都是可能的，其通过例如非均匀有理B样条来描述。结合快速四叉树或八叉树算法和局部细化策略，得到一种递归离散化方法。最初，它从实体的边界表示开始，然后自动继续对结构进行块划分。通过这种方式，可以解决源自不同材料或空隙的内部界面，并将弯曲边界嵌入有限元网格中。首先，将域四叉树或八叉树分解为星凸子域或单元，提供粗略的初始离散化。为了减小应力和位移的近似误差，需要进一步细化网格。有两个改进选项。递归地应用四叉树或八叉树分解来创建下一个更精细的离散化级别。另一种考虑了单元的参数化，其中细化应用于沿边界的周向方向沿着或径向方向。请注意，此步骤可能完全限于考虑中的子域或元素。由于所谓的悬挂节点，没有必要细化相邻元素。因此，它是一个局部细化，可以以不同的方式应用。可以在边界边缘处和/或在元件的内部引入额外的节点，或者可以在元件级增加多项式次数。不同的细化策略需要根据有意义的标准进行评估。嵌入单元列式的离散化概念导致了一种通用的数值有限元方法，适用于分析含夹杂和空隙的非均匀材料。该项目的目的是有助于可靠和强大的数值分析，以满足现代混杂复合材料的设计要求。