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A New Family of Mixed Finite Elements for Elasticity

  • Kartonierter Einband
  • 176 Seiten
Applications from engineering sciences, medicine, and other fields demand computational simulations of mechanical problems to pred... Weiterlesen
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Beschreibung

Applications from engineering sciences, medicine, and other fields demand computational simulations of mechanical problems to predict deformations and stress fields. In a mathematical framework, this leads to partial differential equations which can be effectively treated by the finite element method. State of the art are the primal method using continuous displacements, Hellinger-Reissner and weak symmetry mixed methods. However, all of these methods have their drawbacks, such as locking effects for thin structures or nearly incompressible materials, or high computational complexity. In this work, the TD-NNS (Tangential-Displacement-Normal-Normal-Stress) method is introduced, which overcomes all above difficulties. Here, the displacement is sought in the Sobolev space H(curl), ensuring tangential continuity of the displacement vector. The stresses lie in the newly introduced, normal-normal continuous space H(divdiv). The variational formulation is analyzed thoroughly. A finite element scheme of arbitrary order is presented, stability and optimal orders of approximation are shown. Also, the method is robust when applied to nearly incompressible materials or thin structures.

Autorentext

Dr. Astrid Sabine Sinwel, born in 1983, studied TechnicalMathematics at the Johannes Kepler University Linz. She obtainedher PhD focusing on Computational Mathematics in 2009.



Klappentext

Applications from engineering sciences, medicine, andother fields demand computational simulations ofmechanical problems to predict deformations andstress fields. In a mathematical framework, thisleads to partial differential equations which can beeffectively treated by the finite element method.State of the art are the primal method usingcontinuous displacements, Hellinger-Reissner and weaksymmetry mixed methods. However, all of these methodshave their drawbacks, such as locking effects forthin structures or nearly incompressible materials,or high computational complexity.In this work, the TD-NNS(Tangential-Displacement-Normal-Normal-Stress) methodis introduced, which overcomes all abovedifficulties. Here, the displacement is sought in theSobolev space H(curl), ensuring tangential continuityof the displacement vector. The stresses lie in thenewly introduced, normal-normal continuous spaceH(divdiv). The variational formulation is analyzedthoroughly. A finite element scheme of arbitraryorder is presented, stability and optimal orders ofapproximation are shown. Also, the method is robustwhen applied to nearly incompressible materials orthin structures.

Produktinformationen

Titel: A New Family of Mixed Finite Elements for Elasticity
Untertitel: A Robust Computational Method for Mechanical Problems
Autor:
EAN: 9783838107042
ISBN: 978-3-8381-0704-2
Format: Kartonierter Einband
Herausgeber: Südwestdeutscher Verlag für Hochschulschriften AG
Genre: Mathematik
Anzahl Seiten: 176
Gewicht: 277g
Größe: H219mm x B150mm x T15mm
Jahr: 2015