NLIGA: A MATLAB framework for nonlinear isogeometric analysis

Published on Jun 1, 2020in Computer Aided Geometric Design1.23
· DOI :10.1016/J.CAGD.2020.101869
Xiaoxiao Du3
Estimated H-index: 3
(Beihang University),
Gang Zhao6
Estimated H-index: 6
(Beihang University)
+ 3 AuthorsJiaming Yang1
Estimated H-index: 1
(Beihang University)
Sources
Abstract
Abstract 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/ ).
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Complex geometric models are usually built with multiple NURBS patches with non-conforming interfaces, which bring difficulties within the isogeometric analysis. In this paper, Nitsche’s method is employed to glue different patches for nonlinear isogeometric analysis of hyperelastic material models which are widely used to describe the material behavior of rubbers, foams, biological tissues, etc. Nitsche based weakly governing equations and discretized stiffness matrices are detailedly developed...
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