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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