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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Vydáno v:International journal for numerical methods in engineering Ročník 124; číslo 19; s. 4405 - 4421
Hlavní autoři: Moitinho de Almeida, J. P., Reis, Jonatha
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hoboken, USA John Wiley & Sons, Inc 15.10.2023
Wiley Subscription Services, Inc
Témata:
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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Abstract 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.
AbstractList 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.
Author Reis, Jonatha
Moitinho de Almeida, J. P.
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  organization: Universitat Politecnica de Catalunya
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10.1186/s40323‐016‐0073‐9
10.1002/nme.6458
10.3166/reef.13.547‐558
10.1002/nme.5695
10.1002/nme.3180
10.1002/9781118925782
10.1002/nme.2579
10.1002/nme.2703
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StartPage 4405
SubjectTerms Approximation
elasticity
equilibrium finite elements
error bounds
hybrid finite elements
Methodology
Rotation
solid mechanics
stress approximation
Title An efficient methodology for complementary finite element approximations in three‐dimensional elasticity
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