Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures
Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures
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DOI：
10.1016/j.cma.2014.09.033
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发表时间：
2015-02-01
影响因子：
7.2
通讯作者：
Bletzinger, K. -U.
中科院分区：
文献类型：
--
作者：
Breitenberger, M.;Apostolatos, A.;Bletzinger, K. -U.
针对通过分析进行设计的工作流，提出了计算机辅助设计分析的新概念。该概念将基于非均匀有理B-样条线(NURBS)的B-Rep模型用于整个工作流程。此类模型由修剪的NURBS曲面组成，在行业中被认为是标准的，尤其是对自由形式的几何体进行建模。文中还介绍了AiCAD中新发展的等距B-Rep分析方法(IBRA)。IBRA可以被认为是等距分析(IGA)的推广，它除了使用与IGA中相同的基函数来近似解场外，还使用设计模型的边界表示(B-Rep)。IBRA提供了从计算机辅助设计(CAD)以一致的有限元方式创建直接和完整的分析模型的框架。对于裁剪曲面的数值积分，引入了嵌套雅可比方法和NURBS曲面的概念。此外，为了适应不同类型的边界条件或力学实体，还引入了一种新的有限元类型--等距B-Rep单元。这种类型的单元允许实施例如耦合或狄里克莱特边界条件。在此基础上，给出了基于罚函数法的求解方法，并对壳体结构的曲面造型和几何非线性分析进行了实例实现。详细说明了标准分析程序和AiCAD工作流程之间的区别。各种数值算例证实了所提出的IBRA概念的准确性、灵活性和健壮性，从而突出了其在实现具有统一几何表示的设计到分析工作流程方面的优势。(C)2014爱思唯尔B.V.保留所有权利。
A new concept called analysis in computer aided design (AiCAD) is proposed for design-through-analysis workflow. This concept uses non-uniform rational B-Splines (NURBS)-based B-Rep models for the entire workflow. Such models consist of trimmed NURBS surfaces and are considered standard in the industry, especially for modeling free-form geometries. The newly developed isogeometric B-Rep analysis (IBRA) used in AiCAD is also presented. IBRA can be considered as a generalization of isogeometric analysis (IGA) that uses the boundary representation (B-Rep) of the design model in addition to the same basis functions as in IGA for approximating the solution fields. IBRA provides the framework for creating a direct and complete analysis model from computer aided design (CAD) in a consistent finite-element-like manner. Thus, IBRA allows analyzing a CAD model without remodeling and meshing, even for complex geometries.For the numerical integration of trimmed surfaces, the concept of nested Jacobian approach (NEJA) with NURBS surfaces is introduced. In addition, for enforcing the different types of boundary conditions or mechanical entities, a new finite element type called isogeometric B-Rep element is introduced. Elements of this type permit enforcing, e.g., coupling or Dirichlet boundary conditions. A corresponding formulation based on a penalty approach is presented as well.The proposed workflow is realized exemplarily for surface modeling and the geometrical nonlinear analysis of shell structures. The differences between the standard analysis procedure and the AiCAD workflow are explained in detail. Various numerical examples confirm the accuracy, flexibility, and robustness of the proposed IBRA concept, thus highlighting its advantages for the realization of design-through-analysis workflow with a uniform geometry representation. (C) 2014 Elsevier B.V. All rights reserved.