Multi-patch nonsingular isogeometric boundary element analysis in 3D

Abstract A multi-patch nonsingular isogeometric boundary element method (IGABEM) for 3D problems is presented that provides accurate solutions for multi-patch IGABEM. In order to conveniently implement this method, based on the Greville abscissae, a new collocation method moves the first and the last collocation points of each parametric direction inside of their patches, and a simple method for merging equations handles the extra equations. The numerical results verify the accuracy and efficiency of the present method by comparing it to the conventional IGABEM.

[1]  J. Trevelyan,et al.  Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems , 2013 .

[2]  Yuri Bazilevs,et al.  Fluid–structure interaction modeling of wind turbines: simulating the full machine , 2012, Computational Mechanics.

[3]  Thomas J. R. Hughes,et al.  Isogeometric boundary-element analysis for the wave-resistance problem using T-splines , 2014 .

[4]  E. Klaseboer,et al.  Non-singular boundary integral methods for fluid mechanics applications , 2012, Journal of Fluid Mechanics.

[5]  Thomas J. R. Hughes,et al.  Blended isogeometric shells , 2013 .

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

[7]  Norio Kamiya,et al.  Distance transformation for the numerical evaluation of near singular boundary integrals with various kernels in boundary element method , 2002 .

[8]  I. Temizer,et al.  A mixed formulation of mortar-based frictionless contact , 2012 .

[9]  David J. Benson,et al.  On the numerical integration of trimmed isogeometric elements , 2015 .

[10]  John A. Evans,et al.  Isogeometric analysis using T-splines , 2010 .

[11]  B. Simeon,et al.  A hierarchical approach to adaptive local refinement in isogeometric analysis , 2011 .

[12]  Wenjing Ye,et al.  A new transformation technique for evaluating nearly singular integrals , 2008 .

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

[14]  Evert Klaseboer,et al.  A note on true desingularisation of boundary integral methods for three-dimensional potential problems , 2009 .

[15]  T. Belytschko,et al.  X‐FEM in isogeometric analysis for linear fracture mechanics , 2011 .

[16]  Yuri Bazilevs,et al.  Isogeometric rotation-free bending-stabilized cables: Statics, dynamics, bending strips and coupling with shells , 2013 .

[17]  Xiaoping Qian,et al.  Full analytical sensitivities in NURBS based isogeometric shape optimization , 2010 .

[18]  Gernot Beer,et al.  The Boundary Element Method with Programming: For Engineers and Scientists , 2008 .

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

[20]  Thomas A. Cruse,et al.  An improved boundary-integral equation method for three dimensional elastic stress analysis , 1974 .

[21]  Hongping Zhu,et al.  The distance sinh transformation for the numerical evaluation of nearly singular integrals over curved surface elements , 2013, Computational Mechanics.

[22]  T. Cruse,et al.  Non-singular boundary integral equation implementation , 1993 .

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

[24]  C. Schwab,et al.  Boundary Element Methods , 2010 .

[25]  J. Watson,et al.  Effective numerical treatment of boundary integral equations: A formulation for three‐dimensional elastostatics , 1976 .

[26]  F. Rizzo,et al.  A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations , 1992 .

[27]  Sung-Kie Youn,et al.  Isogeometric topology optimization using trimmed spline surfaces , 2010 .

[28]  Yuri Bazilevs,et al.  Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines , 2012 .

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

[30]  L. Heltai,et al.  Nonsingular isogeometric boundary element method for Stokes flows in 3D , 2014 .

[31]  Guangyao Li,et al.  An improved exponential transformation for nearly singular boundary element integrals in elasticity problems , 2014 .

[32]  David Elliott,et al.  A sinh transformation for evaluating nearly singular boundary element integrals , 2005 .

[33]  Jianming Zhang,et al.  A general algorithm for the numerical evaluation of nearly singular integrals on 3D boundary element , 2011, J. Comput. Appl. Math..

[34]  Xiao-Wei Gao,et al.  An effective method for numerical evaluation of general 2D and 3D high order singular boundary integrals , 2010 .

[35]  Jianming Zhang,et al.  New variable transformations for evaluating nearly singular integrals in 3D boundary element method , 2013 .

[36]  Xiao-Wei Gao,et al.  The radial integration method for evaluation of domain integrals with boundary-only discretization , 2002 .

[37]  G. S. Sekhon,et al.  Large Deformation -I , 2003 .

[38]  B. Yun A generalized non‐linear transformation for evaluating singular integrals , 2006 .

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

[40]  Yijun Liu,et al.  Some identities for fundamental solutions and their applications to weakly-singular boundary element formulations , 1991 .

[41]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[42]  Y. Liu On the simple-solution method and non-singular nature of the BIE / BEM Ð a review and some new results , 2000 .

[43]  I. Akkerman,et al.  Isogeometric analysis of free-surface flow , 2011, J. Comput. Phys..

[44]  John A. Evans,et al.  An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces , 2012 .

[45]  Peter Wriggers,et al.  A large deformation frictional contact formulation using NURBS‐based isogeometric analysis , 2011 .

[46]  Thomas J. R. Hughes,et al.  Isogeometric Analysis for Topology Optimization with a Phase Field Model , 2012 .

[47]  Yuri Bazilevs,et al.  Rotation free isogeometric thin shell analysis using PHT-splines , 2011 .

[48]  Yijun Liu,et al.  New identities for fundamental solutions and their applications to non-singular boundary element formulations , 1999 .

[49]  Peter Wriggers,et al.  Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS , 2012 .

[50]  Yuri Bazilevs,et al.  Aerodynamic and FSI Analysis of Wind Turbines with the ALE-VMS and ST-VMS Methods , 2014 .

[51]  Huanlin Zhou,et al.  A semi-analytical algorithm for the evaluation of the nearly singular integrals in three-dimensional boundary element methods , 2005 .

[52]  Tg Davies,et al.  Boundary Element Programming in Mechanics , 2002 .

[53]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[54]  Guangyao Li,et al.  Isogeometric analysis in BIE for 3-D potential problem , 2012 .

[55]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

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

[57]  T. Hughes,et al.  Local refinement of analysis-suitable T-splines , 2012 .

[58]  Huanlin Zhou,et al.  Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems , 2008 .

[59]  Sung-Kie Youn,et al.  Isogeometric analysis with trimming technique for problems of arbitrary complex topology , 2010 .

[60]  T. Hughes,et al.  Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes , 2010 .

[61]  Hendrik Speleers,et al.  From NURBS to NURPS geometries , 2013 .

[62]  Carlos Alberto Brebbia,et al.  The Boundary Element Method for Engineers , 1978 .

[63]  T. Takahashi,et al.  An application of fast multipole method to isogeometric boundary element method for Laplace equation in two dimensions , 2012 .

[64]  Massimo Guiggiani,et al.  A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method , 1990 .

[65]  Thomas J. R. Hughes,et al.  A large deformation, rotation-free, isogeometric shell , 2011 .

[66]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

[67]  Hideyuki Azegami,et al.  Shape optimization of continua using NURBS as basis functions , 2013 .

[68]  Hendrik Speleers,et al.  Isogeometric analysis with Powell–Sabin splines for advection–diffusion–reaction problems , 2012 .

[69]  Hyun-Jung Kim,et al.  Isogeometric analysis for trimmed CAD surfaces , 2009 .

[70]  J. Telles,et al.  Third degree polynomial transformation for boundary element integrals: Further improvements , 1994 .