Isogeometric Boundary Element Method for Analysis and Design Optimization—A Survey

Analysis of potential problems related to fluid flow and heat transfer can be solved effectively with Boundary Element Methods (BEMs) due to the reason that the interaction takes place at boundaries. BEMs too suffer the traditional problem of approximated geometry. A recent method called Isogeometric Analysis (IGA) was proposed for exact geometric analysis. The combination of the IGA and BEM leads to Isogeometric Boundary Element Method (IGBEM), which has the feature of exact boundary analysis. It suits well for the problems where boundaries of the domains are of interest like fluid structure interaction, shape optimization, etc. This paper provides a brief review on IGBEM by clearly explaining its methodology, applications, limitations and future directions.

[1]  Thomas-Peter Fries,et al.  Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 1: Plane problems , 2016 .

[2]  Hari K. Voruganti,et al.  Static Structural and Modal Analysis Using Isogeometric Analysis , 2016 .

[3]  Panagiotis D. Kaklis,et al.  Ship-hull shape optimization with a T-spline based BEM-isogeometric solver , 2015 .

[4]  B. H. Nguyen,et al.  An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems , 2016 .

[5]  M. Guiggiani,et al.  Direct computation of Cauchy principal value integrals in advanced boundary elements , 1987 .

[6]  G. Beer,et al.  Isogeometric Boundary Element Analysis of steady incompressible viscous flow, Part 1: Plane problems , 2017 .

[7]  C. Y. Dong,et al.  An isogeometric boundary element method for three dimensional potential problems , 2017, J. Comput. Appl. Math..

[8]  Panagiotis D. Kaklis,et al.  An isogeometric BEM for exterior potential-flow problems in the plane , 2009, Symposium on Solid and Physical Modeling.

[9]  Stéphane Bordas,et al.  Implementation of regularized isogeometric boundary element methods for gradient‐based shape optimization in two‐dimensional linear elasticity , 2016 .

[10]  C. Dong,et al.  Effective elastic properties and stress states of doubly periodic array of inclusions with complex shapes by isogeometric boundary element method , 2015 .

[11]  P. Kerfriden,et al.  Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth , 2017 .

[12]  D. F. Rogers,et al.  An Introduction to NURBS: With Historical Perspective , 2011 .

[13]  A. Becker.  The Boundary Element Method in Engineering: A Complete Course , 1992 .

[14]  T. Rabczuk,et al.  A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis , 2012 .

[15]  Hari K. Voruganti,et al.  Spline Parameterization of Complex Planar Domains for Isogeometric Analysis , 2017 .

[16]  J. Telles.  A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals , 1987 .

[17]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[18]  P. K. Banerjee,et al.  Boundary element methods in engineering science , 1981 .

[19]  Kang Li,et al.  Isogeometric analysis and shape optimization via boundary integral , 2011, Comput. Aided Des..

[20]  Hari K. Voruganti,et al.  Shape optimisation of two-dimensional structures using isogeometric analysis , 2017 .

[21]  P. Kerfriden,et al.  Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines , 2017 .

[22]  John A. Evans,et al.  Isogeometric boundary element analysis using unstructured T-splines , 2013 .

[23]  Jianming Zhang,et al.  B-spline approximation in boundary face method for three-dimensional linear elasticity , 2011 .