A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis

By R. Simpson, Stéphane P.A. Bordas, Jon Trevelyan, Timon Rabczuk. 2012

421 citations recorded by the source corpus.

The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/fb93f66a1e99bb3e81a6b70a75eca0d51d1a04af

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory (2013, neutral): “Isogeometric analysis has been applied to a wide range of practical mechanics problems such as structural vibrations [23], linear and non-linear elasticity and plasticity [24], and structural shape optimization [25], Kirchhoff-Love shell [26, 27, 28], Reissner-Mindlin plate/shell [29, 30], laminated”
Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems (2013, methodology): “[7] applied the approach to elastostatic analysis, coining the term IGABEM; Politis et al.”
Implementation of regularized isogeometric boundary element methods for gradient‐based shape optimization in two‐dimensional linear elasticity (2016, methodology): “(3) More importantly, we use regularized boundary integral equations [57, 62–64] for sensitivity analysis, which is in opposition to existing work in the literature [56, 60].”
Isogeometric boundary-element analysis for the wave-resistance problem using T-splines (2014, neutral): “problem to be treated [16, 17, 4, 18, 19, 20, 21].”
Isogeometric boundary element analysis using unstructured T-splines (2013, methodology): “More recently, isogeometric boundary element analysis using NURBS curves and surfaces was developed in [62, 63, 64].”
Isogeometric analysis: An overview and computer implementation aspects (2012, methodology): “Isogeometric boundary element methods for elastostatic analysis were presented in [118, 126], demonstrating that mesh generation can be completely circumvented by using CAD discretizations for analysis.”
A well‐conditioned and optimally convergent XFEM for 3D linear elastic fracture (2016, methodology): “The boundary element method has recently been coupled with isogeometric analysis [3, 4].”
Extended finite element method with global enrichment (2015, methodology): “The boundary element method has recently been coupled with isogeometric analysis [3,4].”
A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields (2014, methodology): “Thirdly, many meshless methods employ the J-integral or contour integral scheme for the calculation of SIF, which is performed as a post-processing step applied to the stress results, such as in the formulations using the FEM described in [15-19] and partition of unity enriched boundary element meth”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, positive): “IGA has been successfully applied in a variety of areas, such as structural vibrations [2,8], incompressibility [10,11], shells [12–15], fluid–structure interaction [16–18], turbulence [19,20], phase field analysis [21–24], contact mechanics [25–28], shape optimization [29,30], immersed boundary met”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, methodology): “The conjoint use of IGA and BEM (IGABEM) permits the direct use of the CAD model, without any mesh generation and was developed for stress analysis [63,62,64], shape optimization [65–67].”