Combining isogeometric analysis (IGA), finite element methods (FEM) and embedded mesh (EM) coupling for contact problems

结合等几何分析 (IGA)、有限元方法 (FEM) 和嵌入式网格 (EM) 耦合来解决接触问题

• 批准号: 446494172
• 负责人: Professor Dr.-Ing. Alexander Popp
• 金额: --
• 依托单位: Institut für Mathematik und Computergestützte Simulation
• 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/446494172?language=en
• 关键词: Combining; isogeometric; analysis; IGA; finite

Contact processes and the physical phenomena typically associated with them (e.g. friction, wear) are still among the greatest challenges in modelling and numerical simulation in civil engineering based on finite element methods (FEM). The seemingly indissoluble link between FEM mesh generation in the volume of the bodies involved and on the contact surfaces with regard to usable discretization techniques, element sizes and element shapes is a particular obstacle. While at the discrete contact boundaries, especially in the case of curved surface geometries, a high continuity of the shape functions and fine boundary layer meshes prove to be advantageous, there is a strong desire for structured, ideally even Cartesian hexahedral grids and a flexible reusability of well-established finite element technology, for example to avoid locking, inside the volume. This research project is dedicated to the complete resolution of this dilemma by developing a novel discretization method for general nonlinear 3D contact problems based on a combination of FEM, isogeometric analysis (IGA) and so-called embedded mesh coupling methods. The new approach consists of the following core building blocks: the contact surfaces of the bodies involved are taken exactly from the CAD geometry model using isogeometric approaches with non-uniform rational B-splines (NURBS) and fulfill inherently high continuity properties (at least C1-continuity). A regular hexahedral grid is generated inside the domain, independent of the processes at the contact boundaries, which guarantees complete flexibility in the choice of element technology (e.g. classical C0-continuous FEM or again NURBS) and an optimal element shape (3D voxel) at least in the undeformed initial configuration. In order to connect these two parts, a surface-oriented boundary layer mesh is first generated from the discrete NURBS contact surface by extrusion. The project focuses on two new techniques to consistently couple IGA surface mesh and volume mesh. Since these two meshes overlap, most classical methods cannot be used without further ado due to their violation of discrete stability conditions. Instead, suitable embedded mesh coupling methods based on mortar / Lagrange multiplier methods as well as Nitsche methods will be developed. In contrast to currently available approaches, such as FEM smoothing methods, complete 3D NURBS meshing or NURBS enrichment methods, the resulting contact formulation will for the first time combine all the advantages of independent and in each case according to local requirements optimally generated boundary layer meshes and volume meshes for contact problems.

接触过程和通常与之相关的物理现象（如摩擦、磨损）仍然是基于有限元方法（FEM）的土木工程建模和数值模拟的最大挑战之一。涉及物体体积的有限元网格生成与接触面上可用的离散化技术、单元尺寸和单元形状之间似乎不可分割的联系是一个特别的障碍。虽然在离散接触边界，特别是在曲面几何形状的情况下，形状函数的高度连续性和精细的边界层网格被证明是有利的，但人们强烈希望结构化，理想情况下甚至是笛卡尔六面体网格和成熟的有限元技术的灵活可重用性，例如避免锁定，在体积内。本研究项目致力于通过开发一种基于有限元法、等几何分析（IGA）和所谓的嵌入式网格耦合方法的一般非线性三维接触问题的新型离散化方法来彻底解决这一难题。新方法由以下核心构建模块组成：所涉及的物体的接触面使用非均匀理性b样条（NURBS）等几何方法精确地从CAD几何模型中获取，并实现固有的高连续性（至少c1 -连续性）。在域内生成一个规则的六面体网格，独立于接触边界的过程，这保证了至少在未变形的初始配置中选择单元技术（例如经典的c0连续FEM或NURBS）和最佳单元形状（3D体素）的完全灵活性。为了连接这两个部分，首先通过挤压从离散的NURBS接触面生成面向表面的边界层网格。该项目专注于两种新技术，以一致地耦合IGA表面网格和体积网格。由于这两个网格重叠，大多数经典方法由于违反离散稳定条件而无法使用。相反，将开发基于砂浆/拉格朗日乘法和Nitsche方法的合适的嵌入式网格耦合方法。相对于现有的方法，如有限元平滑法、完整的三维NURBS网格法或NURBS富集法，所得到的接触公式将首次结合独立的所有优点，并在每种情况下根据局部要求最优地生成接触问题的边界层网格和体积网格。