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.

Offers an instructive and comprehensive presentation of the basics of CAD (Computer-Aided Design) interpolation formulas to enable readers to obtain a solid background for further reading Discusses CAD/CAE integration in detail Provides access to numerous full MATLAB codes with step-by-step tutorials

Inhalt

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.