Precursors of Isogeometric Analysis: Finite Elements, Boundary Elements, and Collocation Methods

ISBN-13: 9783030038885 / Angielski / Twarda / 2019 / 587 str.

Christopher G. Provatidis

Spis treści

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.

Blurb

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.