Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains

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The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality ... continued below

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N.M. Ferraro, S.C. Jardin, X. Luo February 19, 2010.

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The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.

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1.71MB

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  • Report No.: PPPL-4497
  • Grant Number: DE-ACO2-09CH11466
  • DOI: 10.2172/973199 | External Link
  • Office of Scientific & Technical Information Report Number: 973199
  • Archival Resource Key: ark:/67531/metadc926997

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  • February 19, 2010

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 8:53 p.m.

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N.M. Ferraro, S.C. Jardin, X. Luo. Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains, report, February 19, 2010; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc926997/: accessed September 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.