Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 1: Plane problems

Abstract

In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the inclusion may exhibit inelastic material behavior. In this paper only plane stress/strain problems are considered.In our approach the geometry of the inclusion is described using NURBS basis functions. The advantage over currently used methods is that no discretization into cells is required in order to evaluate the arising volume integrals. The other difference to current approaches is that Kernels of lower singularity are used in the domain term. The implementation is verified on simple finite and infinite domain examples with various boundary conditions. Finally a practical application in geomechanics is presented.

Advanced Boundary Element analysis of geotechnical problems with geological inclusions

“…Again, for the evaluation of the integrals Gauss integration is used and is described in detail in [23].…”

“…The simple scheme applied here leads to an increase in the accuracy for determination of the derivatives and for the evaluation of the associated integrals as the number of grid points is increased. The convergence of the solution as a function of the number of internal points is investigated in [23].…”

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

“…Important future work includes a detailed mathematical analysis of the method to prove a priori error estimates, and the investigation of this approach for other types of partial differential equations such as wave propagation. A detailed numerical analysis of the suitability of GIFT in a boundary element approach will follow the work of [6,33,4,8,7,34,69,5].…”

Computational monitoring in real time: review of methods and applications

“…For the last 50 years prediction of the behaviour of continuum mechanics systems, from geomechanics structures to human body organs, have been dominated by Finite Element Method (FEM) (Zienkiewicz 1965;Martin and Carey 1973;Zienkiewicz et al 1977;Bathe 1996) that uses a computational grid in a form of mesh of interconnected triangular or rectangular elements for 2-D problems and tetrahedral or hexahedral elements for 3-D problems. Application of FEM in geomechanics started in the sixties of twentieth century (Anderson and Dodd 1966;Zienkiewicz and Cheung 1966;Zienkiewicz et al 1966Zienkiewicz et al , 1968.…”