ISOGEOMETRIC ANALYSIS FOR ENGINEERS VIA MATLAB
This unique compendium approaches the relatively new Isogeometric Analysis (IGA) methods at senior undergraduates level in engineering or applied mathematics. It describes the differences between the well-established Finite Element Analysis (FEA) methods and why they are being replaced, or enhanced, by the latest developments in IGA.
The book begins with summaries of the concepts of B-splines, NURBS, and 'knot vectors' which define them as exact representations of the geometry and as powerful analysis functions having higher continuity than the FEA use of Lagrange polynomials.
The useful reference text includes Appendices with Matlab scripts for creating B-spline basis functions, topics in computer aided geometric design (CAGD) from which IGA arose, and matrix operations common to IGA and FEA. It also informs FEA users of the enhancements offered by IGA.
Contents:
- Preface
- About the Author
- IGA Notations
- Comparing IGA and FEA Methods
- Knot Vectors, Knots, and Control Points
- Parametric and Physical Derivatives
- Review of PDEs and Boundary Conditions
- Methods of Weighted Residuals
- Numerical Integration
- Second-Order Elliptic ODEs via B-Splines
- Fourth-Order Elliptic ODEs via B-Splines
- Second-Order Partial Differential Equations
- Elasticity
- Eigenanalysis
- Transient and Dynamic Solutions
- T-Spline Basis Functions
- Appendix
- Supplementary Material
- Bibliography
- Index
Readership: Researchers, professionals, academics and senior undergraduate students in acoustics, dynamic systems and aerospace engineering.
Dr Akin is Professor of Mechanical Engineering, and Professor of Computational and Applied Mathematics at Rice University. He is the author of nine other books including Finite Element Analysis with Error Estimators, and Computer Assisted Mechanical Design. He has published more than 140 referred technical articles. Prof. Akin serves on the Editorial Board of the Journal of Multiscale and Multidisciplinary Modeling, Experiments and Design; and is a registered professional engineer.
