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/).

非线性行为在许多工程应用中很常见，例如金属成型和车辆碰撞测试。与线性系统不同，非线性问题不能通过使用线性方程组来解决，并且不能保证可以找到唯一的解。在这项工作中，我们开发了一个统一的框架NLIGA（非线性等距几何分析），主要用于通过等几何方法在MATLAB平台上解决二维和三维非线性问题。在此阶段主要考虑非线性超弹性和弹塑性材料。牛顿-拉夫森法用于求解非线性控制方程。执行一系列示例以验证过程。首先，我们提供了许多脚本来解决线性弹性基准问题，包括平面和实体问题，泊松问题，板和壳问题，并将获得的数值解与精确解和FEA解进行比较。其次，我们进一步研究了考虑超弹性和弹塑性材料的几个非线性示例，并将结果与​​从商业软件获得的结果进行了比较。在此框架中还开发了可视化程序，以可视化获得的结果，包括位移，应力和数值误差。最后，NLIGA是一个开放源代码框架，可以免费使用（http://nliga.sourceforge.net/）。在此框架中还开发了可视化程序，以可视化获得的结果，包括位移，应力和数值误差。最后，NLIGA是一个开放源代码框架，可以免费使用（http://nliga.sourceforge.net/）。在此框架中还开发了可视化程序，以可视化获得的结果，包括位移，应力和数值误差。最后，NLIGA是一个开放源代码框架，可以免费使用（http://nliga.sourceforge.net/）。