Isogeometric Analysis

Tectonic faults are commonly modelled as Volterra or Somigliana dislocations in an elastic medium. Various solution methods exist for this problem. However, the methods used in practice are often limiting, motivated by reasons of computational efficiency rather than geophysical accuracy. A typical geophysical application involves inverse problems for which many different fault configurations need to be examined, each adding to the computational load. In practice, this precludes conventional finite-element methods, which suffer a large computational overhead on account of geometric changes. This paper presents a new non-conforming finite-element method based on weak imposition of the displacement discontinuity. The weak imposition of the discontinuity enables the application of approximation spaces that are independent of the dislocation geometry, thus enabling optimal reuse of computational components. Such reuse of computational components renders finite-element modeling a viable option for inverse problems in geophysical applications. A detailed analysis of the approximation properties of the new formulation is provided. The analysis is supported by numerical experiments in 2D and 3D.Comment: Submitted for publication in CMAM

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“…Substituting the prior probability distribution and the likelihood into Bayes' theorem (7), we can rework terms to obtain the following result:…”

Section: Posterior Distributionmentioning

confidence: 99%

Discontinuities without discontinuity: The Weakly-enforced Slip Method

Zwieten

Brummelen

Zee

et al. 2014

Computer Methods in Applied Mechanics and Engineering

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“…Elastic rod was analyzed to investigate the performance of NURBS based FE in structural vibration. The order of basis function and three refinement methods were tested in one dimensional situation (Hughes and Evans, 2010). The convergence rate of the isogeometric bar element was also investigated with different boundary conditions (Lee and Park, 2011).…”

Section: Introductionmentioning

confidence: 99%

Free Vibrations of Plates and Shells with an Isogeometric RM Shell Element

Lee¹

2016

Architectural research

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Free vibration analysis of plates and shells is carried out by using isogeometric approach. For this purpose, an isogeometric shell element based on Reissner-Mindlin (RM) shell theory is developed. Non-uniform rational B-spline surface (NURBS) definition is introduced to represent the geometry of shell and it is also used to derive all terms required in the isogeometric element formulation. New anchor positions are proposed to calculate the shell normal vector. Gauss integration rule is used for the formation of stiffness and mass matrices. The proposed shell element is then used to examine vibrational behaviours of plate and shell structures. From numerical results, it is found to be that reliable natural frequencies and associated mode shapes can be predicted by the present isogeometric RM shell element.

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“…Although links between spline approximation and finite element analysis have been long known [20,21], the advent of so-called iso-geometric finite element analysis [8,15] has led to a burgeoning of interest in developing links between spline approximation, CAGD techniques, and finite element analysis.…”

Section: Introductionmentioning

confidence: 99%

A Bernstein–Bézier Basis for Arbitrary Order Raviart–Thomas Finite Elements

2014

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A Bernstein-Bézier basis is developed for H(div)-conforming finite elements that gives a clear separation between the curls of the Bernstein basis for the polynomial discretization of the space H 1 , and the noncurls that characterize the specific H(div) finite element space (Raviart-Thomas in our case). The resulting basis has two distinct components reflecting this separation with the basis functions in each component having a natural identification with a domain point, or node, on the element. It is shown that the basis retains the favorable properties of the Bernstein basis that were used in Ainsworth et al. (SIAM J Sci Comput 3087-3109, 2011) to develop efficient computational procedures for the application of the elements.Keywords Spectral/hp finite element · Bernstein polynomials · H(div) finite elements · Sum-factorisation · Raviart-Thomas space · Maxwell eigenvalue problem Communicated by Peter Oswald.

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Isogeometric Analysis

Cited by 6 publications

References 17 publications

Discontinuities without discontinuity: The Weakly-enforced Slip Method

Discontinuities without discontinuity: The Weakly-enforced Slip Method

Free Vibrations of Plates and Shells with an Isogeometric RM Shell Element

A Bernstein–Bézier Basis for Arbitrary Order Raviart–Thomas Finite Elements

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