Polygonal Reissner-Mindlin shell element formulation

多边形 Reissner-Mindlin 壳单元公式

• 批准号: 529267576
• 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 Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/529267576?language=en
• 关键词: Polygonal; Reissner; Mindlin; shell; element

The development and analysis of numerical methods for the approximation of the solution to partial differential equations on polygonal meshes have undergone an explosive interest in recent years among the scientific community. In the research project, we want to exploit the inherent advantages of polygonal meshes for shell analysis. Polygonal meshes offer a very flexible framework to handle hanging nodes and different element shapes within the same mesh. Our main objective is to develop a computational framework that makes direct use of the polygonal mesh surface modeling technique. In the case of thin structures, we want to directly employ this mesh as a starting point for the computational analysis. Our primary goal is to develop a polygonal shell element formulation which is accurate, efficient, and allowing for large load step size. To achieve this, three objectives are defined. The first objective is the development of a polygonal shell finite element formulation based on the Reissner-Mindlin theory for the analysis of a wide class of non-linear structural mechanics problems. Methods will be developed to alleviate locking effects for low order polygonal elements. Our goal is a stable element without zero energy modes allowing for large load steps in the non-linear analysis. The quality of the polygonal element employing Voronoi and quadtree meshes will be investigated. The second objective is to exploit the various possibilities in mesh generation and refinement, which are provided by the polygonal element formulation. These are, highly localized mesh refinement, handling of hanging nodes, aligning element boundaries to the domain of interest, and simple remeshing of evolving domains. These features will be exploited to simulate brittle fracture in Reissner-Mindlin shells by employing a phase-field model. The third objective is a NURBS based polygonal shell formulation to exploit higher order continuity. The usage of B-spline polygonal patches offers the possibility to apply k-refinement and local refinement with hierarchical B-splines. The different meshing methods will be analyzed in terms of accuracy and computational cost. The flexibility of the element formulation opens up new possibilities to locally adjust and refine the mesh structure allowing for a tightly interleaved operation of mesh generation and simulation. We aim at methods applicable to a broad class of problems in solid mechanics, including geometric and physically nonlinear problems.

多边形网格上偏微分方程解的近似数值方法的发展和分析近年来在科学界引起了爆炸性的兴趣。在本研究计画中，我们希望利用多边形网格固有的优点来进行壳体分析。多边形网格提供了一个非常灵活的框架来处理同一个网格中的悬挂节点和不同的元素形状。我们的主要目标是开发一个计算框架，使直接使用的多边形网格表面建模技术。在薄结构的情况下，我们希望直接使用该网格作为计算分析的起点。我们的主要目标是开发一个多边形壳元公式，这是准确的，有效的，并允许大载荷步长。为实现这一目标，确定了三个目标。第一个目标是发展一个多边形壳有限元公式的Reissner-Mindlin理论的基础上，分析了广泛的一类非线性结构力学问题。将开发方法，以减轻锁定效应的低阶多边形元素。我们的目标是一个稳定的元素，没有零能量模式，允许在非线性分析的大负载步骤。采用Voronoi和四叉树网格的多边形元素的质量将被调查。第二个目标是利用网格生成和细化的各种可能性，这是由多边形元素制定。这些是，高度局部化的网格细化，悬挂节点的处理，对齐元素边界的领域的利益，和简单的网格重新划分的发展领域。这些功能将被利用来模拟脆性断裂Reissner-Mindlin壳采用相场模型。第三个目标是一个基于NURBS的多边形壳制定利用高阶连续性。B样条多边形面片的使用提供了应用分层B样条的k-细化和局部细化的可能性。不同的网格划分方法将在精度和计算成本方面进行分析。元素制定的灵活性开辟了新的可能性，局部调整和细化网格结构，允许网格生成和模拟的紧密交织操作。我们的目标是适用于固体力学中广泛的一类问题，包括几何和物理非线性问题的方法。