The Isogeometric Boundary Element Method

Description

This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing. Front Matter ....Pages i-xiv Introduction (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 1-12 The Boundary Integral Equations (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 13-34 Basis Functions, B-splines (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 35-71 Description of the Geometry (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 73-92 Getting Geometry Information from CAD Programs (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 93-102 Numerical Treatment of Integral Equations (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 103-127 Numerical Integration (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 129-149 Steady State Potential Problems (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 151-168 Static Linear Solid Mechanics (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 169-183 Simulation with Trimmed Models (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 185-216 Body Force Effects (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 217-228 Treatment of Inhomogeneities/Inclusions (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 229-248 Material Non-linear Behaviour (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 249-259 Applications in Geomechanics (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 261-279 Viscous Flow Problems (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 281-305 Time Dependent Problems (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 307-317 Summary and Outlook (Gernot Beer, Benjamin Marussig, Christian Duenser)....Pages 319-320 Back Matter ....Pages 321-335