Eliminating spurious outlier frequencies and modes in IGA - strong and variational removal, outlier-free Bézier extraction, and advantages in explicit dynamics and nonlinear analysis

等几何分析（伊加）的核心思想是使用相同的光滑和高阶样条基函数来精确表示基于物理的场解的几何和有限元近似。伊加的主要优点之一是本征频率和本征模式的准确性和数值上的有利行为。不幸的是，样条离散化的离散谱在高端具有伪频率和模式，表示为“离群值”。虽然它们在线性静态分析中不起作用，但异常值不必要地减少了显式动力学中的关键时间步长，并且在存在强非线性的情况下会影响精度和鲁棒性。到目前为止，一个实用的技术离群删除不存在。我们最近开发了新的基本思想，如何从一个给定的张量积样条离散化，基于额外的一致的高阶边界约束的边界离群值。该项目的总体目标是推动我们最初的有希望的结果走向一个精心设计和全面的实用方法离群值去除，包括边界和界面离群值。为此，我们将首先巩固边界离群点的强离群点去除的基本组成部分。特别是，我们将开发一个有效的算法框架，用于生成新的无异常基函数和相关的无异常Bézier提取算子。然后，我们将扩展的离群点删除技术界面离群点，专注于变分策略删除离群点，由于C^0连续补丁接口。最后，我们将表明，由此产生的一组离群值去除技术可靠地消除离群值从给定的多补丁样条离散。我们还将展示效率和鲁棒性的提高，在实际的仿真场景中，离群值去除的结果，专注于显式动力学和结构的非线性分析。Bézier提取格式将使我们能够直接将无异常值的样条离散化馈送到商业有限元软件包LS-DYNA中，在该软件包中，可以在全方位的实际相关有限元技术的背景下研究数值优势，例如壳单元，大变形，非线性材料模型，摩擦接触和质量集中方案。本研究所开发的离群点剔除技术将填补实际离群点剔除技术的差距，从而进一步推动伊加作为一种更高精度、更高效的分析设计方法的建立。

The core idea of isogeometric analysis (IGA) is to use the same smooth and higher-order spline basis functions for the exact representation of the geometry and the finite element approximation of physics-based field solutions. One of the key advantages of IGA is the accuracy and numerically favorable behavior of eigenfrequencies and eigenmodes. Unfortunately, discrete spectra of spline discretizations feature spurious frequencies and modes at the high end, denoted as “outliers”. While they do not play a role in linear static analysis, outliers unnecessarily reduce the critical time step in explicit dynamics and can affect accuracy and robustness in the presence of strong nonlinearities. To date, a practical technique for outlier removal does not exist. We recently developed new fundamental ideas on how to remove boundary outliers from a given tensor-product spline discretization, based on additional consistent higher-order boundary constraints. The overarching goal of this project is to drive forward our initial promising results towards a well-elaborated and comprehensive practical methodology for outlier removal, covering both boundary and interface outliers. To this end, we will first consolidate fundamental components of strong outlier removal for boundary outliers. In particular, we will develop an efficient algorithmic framework for generating new outlier-free basis functions and associated outlier-free Bézier extraction operators. We will then extend the outlier removal technology to interface outliers, focusing on variational strategies for removing outliers due to C^0-continuous patch interfaces. We will finally show that the resulting set of outlier removal techniques reliably eliminates outliers from given multi-patch spline discretizations. We will also demonstrate improvements in efficiency and robustness as a result of outlier removal in practical simulation scenarios, focusing on explicit dynamics and nonlinear analysis of structures. The Bézier extraction format will enable us to directly feed outlier-free spline discretizations into the commercial finite element package LS-DYNA, where numerical advantages can be studied in the context of the full range of practically relevant finite element technology, such as shell elements, large deformations, nonlinear material models, frictional contact, and mass lumping schemes. The outlier removal technology developed in this project will help fill the gap of practical outlier removal and will thus help further propel the establishment of IGA as a higher-order accurate and efficient design-through-analysis method.