Akin E. Isogeometric Analysis for Engineers via MatLAB 2025

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Akin E. Isogeometric Analysis for Engineers via MatLAB 2025

Textbook in PDF format 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. Preface 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 Bezier and Lagrange Extractions Appendix