Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation
Abstract One of the main drawbacks of Element Free Galerkin (EFG) method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Marcílio Alves
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| Series: | Latin American Journal of Solids and Structures |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252017000601017&lng=en&tlng=en |
| _version_ | 1818228529565794304 |
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| author | Samira Hosseini Mohammad Malekan Roque L. S. Pitangueira Ramon P. Silva |
| author_facet | Samira Hosseini Mohammad Malekan Roque L. S. Pitangueira Ramon P. Silva |
| author_sort | Samira Hosseini |
| collection | DOAJ |
| description | Abstract One of the main drawbacks of Element Free Galerkin (EFG) method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions. |
| first_indexed | 2024-12-12T10:04:09Z |
| format | Article |
| id | doaj.art-4cebd8edf7c64829a563740532de75f6 |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-12-12T10:04:09Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-4cebd8edf7c64829a563740532de75f62022-12-22T00:27:55ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-78251461017103910.1590/1679-78253607S1679-78252017000601017Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented ImplementationSamira HosseiniMohammad MalekanRoque L. S. PitangueiraRamon P. SilvaAbstract One of the main drawbacks of Element Free Galerkin (EFG) method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252017000601017&lng=en&tlng=enElement Free Galerkin methodEFG-FE CouplingLagrange MultipliersPenalty MethodObject-Oriented Programming |
| spellingShingle | Samira Hosseini Mohammad Malekan Roque L. S. Pitangueira Ramon P. Silva Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation Latin American Journal of Solids and Structures Element Free Galerkin method EFG-FE Coupling Lagrange Multipliers Penalty Method Object-Oriented Programming |
| title | Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation |
| title_full | Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation |
| title_fullStr | Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation |
| title_full_unstemmed | Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation |
| title_short | Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation |
| title_sort | imposition of dirichlet boundary conditions in element free galerkin method through an object oriented implementation |
| topic | Element Free Galerkin method EFG-FE Coupling Lagrange Multipliers Penalty Method Object-Oriented Programming |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252017000601017&lng=en&tlng=en |
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