Precursors of Isogeometric Analysis

This self-contained book addresses the three most popular computational methods in CAE (finite elements, boundary elements, collocation methods) in a unified way, bridging the gap between CAD and CAE.
It includes applications to a broad spectrum of engineering (benchmark) application problems, such as elasto-statics/dynamics and potential problems (thermal, acoustics, electrostatics). It also provides a large number of test cases, with full documentation of original sources, making it a valuable resource for any student or researcher in FEA-related areas.
The book, which assumes readers have a basic knowledge of FEA, can be used as additional reading for engineering courses as well as for other interdepartmental MSc courses.

1 Initial Attempts on CAD/CAE Integration. - 2 Elements of Arroximation and Computational Geometry. - 3 Coons Interpolation as a Vehicle to Derive Isoparametric Elements. - 4 Gordon s Transfinite Macroelements. - 5 Barnhill Interpolation and Relevant Isoparametric Elements. - 6 Bezier Interpolation and Relevant Isoparametric Elements. - 7: B-Splines Interpolation and Relevant Isoparametric Elements. - 8 Rational B-Spline (Nurbs-Based) Macroelements. - 9 Plate Bending Macroelements. - 10: Three-dimensional macroelements. - 11 Global Collocation Using Macroelements. - 12 Global Boundary Elements Using Macroelements. - 13 Mortality Issues. - 14 Global Review-Epilogue. - Appendix A: Green s Theorem. - Appendix B: Numerical Integration. - Appendix C: Chebyshev Polynomials.