Finite Element Method with Python: An Essential Course with AI Enhanced Approaches
About this ebook
Presented in an innovative Jupyter Notebook format, this text bridges the gap between theory and execution. Rather than treating FEM as a black-box numerical tool, it emphasizes the internal algorithmic logic behind simulation software. Readers are guided step-by-step through fundamental theories, shape functions, and global assembly, all the way to advanced concepts like Nodal Submatrix Analytical Formulations (NSAF) and high-performance matrix vectorization.
By leveraging modern computational libraries like NumPy, SciPy, SymPy, and Matplotlib, alongside AI-assisted development tools, this book demonstrates how symbolic derivation and numerical optimization transform classical engineering analysis. Complete with fully executable, open-source Python solvers, it empowers students, researchers, and practicing engineers to modify, experiment, and build their own simulation tools.
Whether you are an advanced undergraduate, a graduate student, or an engineering professional in aerospace, automotive, or civil infrastructure, this book provides the definitive blueprint for mastering computational mechanics in the modern digital era.
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About the author
Dr. G.R. (Gui-Rong) Liu is an expert in computational mechanics and numerical methods, currently serving as a Professor of Aerospace Engineering and Engineering Mechanics at the University of Cincinnati. A prolific researcher and educator, Dr. Liu is recognized for pioneering meshfree methods, smoothed finite element methods (S-FEM), and smoothed particle hydrodynamics (SPH). These innovations have significantly advanced simulation techniques in both solid and fluid mechanics.
In recent years, Dr. Liu has authored several textbooks and reference works for courses and research in areas such as artificial intelligence, machine learning, mathematics, computational methods, mechanics of materials, solid mechanics, engineering mechanics, applied mechanics, and fluid dynamics.
