Nonlinear behaviors are commonplace in many engineering applications, e.g., metal forming and vehicle crash tests. Different from linear systems, nonlinear problems cannot be solved by using a system of linear equations and there is no guarantee that a unique solution can be found. In this work, we develop a unified framework, NLIGA (Non-Linear Isogeometric Analysis), for mainly solving two and three-dimensional nonlinear problems on the MATLAB platform by using the isogeometric method. Nonlinear hyperelastic and elastoplastic materials are primarily considered at this stage. The Newton-Raphson method is used to solve the nonlinear governing equations. A series of examples are performed to validate the procedures. First, we provide dozens of scripts to solve linear elastic benchmark problems including plane and solid problems, Poisson problems, plate and shell problems and compare the obtained numerical solutions with exact solutions and FEA solutions. Second, we further investigate several nonlinear examples considering hyperelastic and elastoplastic materials and compare the results with that obtained from commercial software. The visualization procedures are also developed in this framework to visualize the obtained results including displacements, stresses and numerical errors. Finally, NLIGA is an open-source framework and free to use (http://nliga .sourceforge .net/).

Xiaoxiao Du

Gang Zhao

Wei Wang

Mayi Guo

Ran Zhang

Jiaming Yang

Computer Aided Geometric Design

计算机辅助几何设计杂志面向研究人员、学者和软件开发人员，他们处理从 CAD/CAM 到机器人技术和科学可视化等领域出现的几何对象描述的数学和计算方法。该杂志发表原创研究论文、调查论文和最多 3 页的快速编辑决策。感兴趣的主要对象是曲线、曲面和体积，例如样条曲线 (NURBS)、网格、细分曲面以及生成、分析和操作它们的算法。本刊将报道 CAGD 及其应用的新进展，包括但不限于以下内容：-数学和几何基础-曲线、曲面和体积生成-CAGD 在数值分析、计算几何、计算机图形学或计算机视觉中的应用-工业、医学和科学应用。目的是在一本期刊上收集和传播有关计算机辅助设计的信息。为用户社区提供表示曲线和曲面的方法和算法。通过有趣的应用程序来说明计算机辅助几何设计。将曲线和曲面方法与计算机图形学相结合。用计算机图形学来解释科学现象。专注于理论与应用之间的相互作用。揭露实践中未解决的问题。开发计算机辅助几何的新方法。

The journal "Computer Aided Geometric Design" is aimed at researchers, scholars, and software developers who deal with mathematical and computational methods for describing geometric objects in fields such as CAD/CAM, robotics, and scientific visualization. The journal publishes original research papers, survey papers, and rapid editorial decisions of up to three pages. The main objects of interest include curves, surfaces, and volumes, such as spline curves (NURBS), meshes, and subdivision surfaces, along with the algorithms for generating, analyzing, and manipulating them. The journal reports on new advancements in CAGD and its applications, including but not limited to: - Mathematical and geometric foundations - Generation of curves, surfaces, and volumes - Applications of CAGD in numerical analysis, computational geometry, computer graphics, or computer vision - Industrial, medical, and scientific applications. The aim is to collect and disseminate information related to computer-aided design on a single platform, providing the user community with methods and algorithms for representing curves and surfaces. It illustrates computer-aided geometric design through interesting applications, combines curve and surface methods with computer graphics, uses computer graphics to explain scientific phenomena, focuses on the interaction between theory and application, reveals unresolved issues in practice, and develops new methods for computer-aided geometry.

《Computer Aided Geometric Design》杂志面向研究人员、学者和软件开发人员，探讨在CAD/CAM、机器人技术和科学可视化等领域中几何对象描述的数学和计算方法。该杂志发表原创研究论文、调查论文以及最多3页的快速编辑决策。主要关注的对象包括曲线、曲面和体积，例如样条曲线（NURBS）、网格、细分曲面，以及生成、分析和操作这些对象的算法。期刊将报道计算机辅助几何设计及其应用的新进展，包括但不限于以下内容：- 数学和几何基础 - 曲线、曲面和体积的生成 - CAGD在数值分析、计算几何、计算机图形学或计算机视觉中的应用 - 工业、医学和科学应用。期刊的目的是在一个平台上收集和传播有关计算机辅助设计的信息，为用户社区提供表示曲线和曲面的算法和方法。通过有趣的应用程序来展示计算机辅助几何设计，将曲线和曲面的方法与计算机图形学结合，利用计算机图形学解释科学现象，关注理论与应用之间的相互作用，揭示实践中未解决的问题，并开发计算机辅助几何的新方法。

NLIGA: A MATLAB framework for nonlinear isogeometric analysis

A unified framework for mainly solving two and three-dimensional nonlinear problems on the MATLAB platform by using the isogeometric method, NLIGA (Non-Linear Isogeometric Analysis), is developed.

Category	Quartile
计算机科学	4
计算机科学, 计算机软件工程	4
计算机科学, 应用数学	4

NLIGA: A MATLAB framework for nonlinear isogeometric analysis

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Journal Info

Category	Quartile
MATHEMATICS, APPLIED	2