An efficient methodology for complementary finite element approximations in three‐dimensional elasticity

We present a methodology for the definition of the matrices involved in stress based finite element approximations in three‐dimensional problems. In order to handle the increased complexity of the 3D case, a rotation of the global reference frame is used, which greatly simplifies the expressions inv...

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Veröffentlicht in:International journal for numerical methods in engineering Jg. 124; H. 19; S. 4405 - 4421
Hauptverfasser: Moitinho de Almeida, J. P., Reis, Jonatha
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hoboken, USA John Wiley & Sons, Inc 15.10.2023
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Schlagworte:
Approximation
elasticity
equilibrium finite elements
error bounds
hybrid finite elements
Methodology
Rotation
solid mechanics
stress approximation
ISSN:0029-5981, 1097-0207
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Zusammenfassung:We present a methodology for the definition of the matrices involved in stress based finite element approximations in three‐dimensional problems. In order to handle the increased complexity of the 3D case, a rotation of the global reference frame is used, which greatly simplifies the expressions involved. This rotation is also applicable to the 2D case. The main focus of this work concerns the matrices used in the implementation of the hybrid equilibrium approach. However, a similar complementary methodology (displacement based) is also presented, allowing for an efficient definition of the matrices required for dual analysis, wherein bounds of the solution error are obtained from pairs of complementary solutions, one compatible and the other equilibrated.
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.7313