A NURBS boundary-only approach in elasticity
Keywords:
Isogeometric analysis, integral equations, boundary conditions, boundary element methodAbstract
An improvement to the classical application of the isogeometric approach to the two-dimensional boundary element method is proposed. In the classical isogeometric approach the boundary conditions are imposed directly to the control variables that are not always interpolatory of the governing variables, thus introducing an error that may also be large. The issue has been debated in the finite element method context where it has recently motivated various alternative techniques, but it is still open in other numerical methods. In the present paper the approach, introduced by the authors in a previous paper, to correctly impose any general boundary condition in the boundary element method framework, is theoretically and numerically investigated. Comparison with analytical solutions, classical boundary element solutions and isogeometric boundary element solutions are carried out to demonstrate the improved performance of the proposed approach.
Downloads
References
Beer, G., Marussig, B., & Duenser, C. (2013). Isogeometric boundary element method for the
simulation of underground excavations. Géotechnique Letters, 3, 108–111.
Costantini, P., Manni, C., Pelosi, F., & Sampoli, M. L. (2010). Quasi-interpolation in
isogeometric analysis based on generalized B-splines. Computer Aided Geometric Design,
, 656–668.
De Luycker, E., Benson, D. J., Belytschko, T., Bazilevs, Y., & Hsu, M. C. (2011). X-FEM in
isogeometric analysis for linear fracture mechanics. International Journal for Numerical
Methods in Engineering, 87, 541–565.
Embar, A., Dolbow, J., & Harari, I. (2010). Imposing Dirichlet boundary conditions with
Nitsche’s method and splinebased finite elements. International Journal for Numerical
Methods in Engineering, 83, 877–898.
Hughes, T. J. R., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite
elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied
Mechanics and Engineering, 194, 4135–4195.
Mallardo, V., & Ruocco, E. (2014). An improved isogeometric boundary element method
approach in two dimensional elastostatics. CMES: Computer Modeling in Engineering and
Sciences, 102, 373–391.
Munoz, J. J. (2008). Modelling unilateral frictionless contact using the null-spacemethod and
cubic B-spline interpolation. Computer Methods in Applied Mechanics and Engineering,
, 979–993.
Peake, M. J., Trevelyan, J., & Coates, G. (2013). Isogeometric boundary element analysis
using unstructured T-splines. Computer Methods in Applied Mechanics and Engineering,
, 197–221.
Piegl, L., & Tiller, W. (1997). The nurbs book. Berlin: Springer.
Sevilla, R., Fernández-Méndez, S., & Huerta, A. (2008). NURBS-enhanced finite element
method (NEFEM). International Journal for Numerical Methods in Engineering, 76, 56–83.
Sevilla, R., Fernández-Méndez, S., & Huerta, A. (2011). 3D NURBS-enhanced finite element
method (NEFEM). International Journal for Numerical Methods in Engineering, 88,
–125.Simpson, R. N., Bordas, S. P. A., Lian, H., & Trevelyan, J. (2013). An isogeometric boundary
element method for elastostatic analysis: 2D implementation aspects. Computers and
Structures, 118, 2–12.
Simpson, R. N., Bordas, S. P. A., Trevelyan, J., & Rabczuk, T. (2012). A two-dimensional
isogeometric boundary element method for elastostatic analysis. Computer Methods in
Applied Mechanics and Engineering, 209-212, 87–100.
Szabo, B., & Babuska, I. (1991). Finite element analysis. New Jersey, NJ: John Wiley & Sons.
Verhoosel, C. V., Scott, M. A., de Borst, R., & Hughes, T. J. R. (2011). An isogeometric
approach to cohesive zone modeling. International Journal for Numerical Methods in
Engineering, 87, 336–360.
Wang,D.,&Xuan, J. (2010).Animproved NURBS-based isogeometric analysis with enhanced
treatment of essential boundary conditions. Computer Methods in Applied Mechanics and
Engineering, 199, 2425–2436.
Wrobel, L. C., & Aliabadi, M. H. (1996). The boundary element method, Vol. 2: Applications
in solids and structures. New Jersey, NJ: John Wiley & Sons.
