NEW TREATMENT OF ESSENTIAL BOUNDARY CONDITIONS IN EFG METHOD BY COUPLING WITH RPIM
One of major difficulties in the implementation of meshfree methods using the moving least square (MLS) approximation, such as element-free Galerkin method (EFG), is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of...
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| Published in | Acta mechanica solida Sinica Vol. 26; no. 3; pp. 302 - 316 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
Elsevier Ltd
01.06.2013
Springer Singapore School of Urban Rail Transportation, Soochow University, Suzhou 215006, China School of Mathematical Sciences, Soochow University, Suzhou 215006, China%School of Mathematical Sciences, Soochow University, Suzhou 215006, China |
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| Online Access | Get full text |
| ISSN | 0894-9166 1860-2134 |
| DOI | 10.1016/S0894-9166(13)60028-2 |
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| Abstract | One of major difficulties in the implementation of meshfree methods using the moving least square (MLS) approximation, such as element-free Galerkin method (EFG), is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpolation can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin(EFG)-radial point interpolation method (RPIM) is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory. |
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| AbstractList | One of major difficulties in the implementation of meshfree methods using the moving least square (MLS) approximation, such as element-free Galerkin method (EFG), is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpolation can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin(EFG)-radial point interpolation method (RPIM) is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory. One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpola- tion can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin（EFG）-radial point interpola- tion method （RPIM） is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory. |
| Author | Yin, Yu Cao, Yang Yao, Linquan |
| AuthorAffiliation | School of Mathematical Sciences, Soochow University, Suzhou 215006, China School of Urban Rail Transportation, Soochow University, Suzhou 215006, China |
| AuthorAffiliation_xml | – name: School of Mathematical Sciences, Soochow University, Suzhou 215006, China%School of Mathematical Sciences, Soochow University, Suzhou 215006, China;School of Urban Rail Transportation, Soochow University, Suzhou 215006, China |
| Author_xml | – sequence: 1 givenname: Yang surname: Cao fullname: Cao, Yang organization: School of Mathematical Sciences, Soochow University, Suzhou 215006, China – sequence: 2 givenname: Linquan surname: Yao fullname: Yao, Linquan email: lqyao@suda.edu.cn organization: School of Mathematical Sciences, Soochow University, Suzhou 215006, China – sequence: 3 givenname: Yu surname: Yin fullname: Yin, Yu organization: School of Mathematical Sciences, Soochow University, Suzhou 215006, China |
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| CitedBy_id | crossref_primary_10_1142_S0219876218300015 crossref_primary_10_1016_j_enganabound_2013_11_007 crossref_primary_10_1007_s11071_022_07238_4 crossref_primary_10_1007_s40996_020_00407_8 crossref_primary_10_52547_nmce_5_4_46 crossref_primary_10_1002_nla_2362 crossref_primary_10_1016_j_enganabound_2020_11_005 crossref_primary_10_1007_s40997_021_00471_z crossref_primary_10_1080_02533839_2016_1203735 crossref_primary_10_1155_2014_528082 crossref_primary_10_3390_app13042366 crossref_primary_10_1016_j_enganabound_2023_02_022 crossref_primary_10_1007_s40430_018_1459_z |
| Cites_doi | 10.1016/S0965-9978(02)00069-8 10.1007/s00466-009-0411-6 10.1002/1097-0207(20010210)50:4<937::AID-NME62>3.0.CO;2-X 10.1002/cnm.395 10.1016/0377-0427(96)00020-9 10.1007/s00466-003-0477-5 10.1007/s004660050296 10.1016/S0898-1221(01)00293-0 10.1006/jath.1997.3137 10.1007/BF00364252 10.1016/S0045-7825(01)00419-4 10.1090/S0025-5718-1981-0616367-1 10.1016/0045-7825(94)90056-6 10.1016/0045-7825(95)00804-A 10.1016/S0045-7825(98)00014-0 10.1016/0045-7825(95)00954-X 10.1007/s004660050346 10.1007/s004660000181 10.1007/s004660050175 10.1007/BF00364080 10.1007/s004660050403 10.1002/nme.489 10.1007/BF02824850 10.1002/nme.1620370205 10.1016/S0045-7825(00)00324-8 10.1016/0045-7825(96)00994-2 |
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| Keywords | meshfree method coupled method radial point interpolation method (rpim) collocation approach moving least-squares (mls) approximation |
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| Notes | meshfree method, moving least-squares （ntis） approximation, radial point inter-polation method （rpim）, coupled method, collocation approach One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpola- tion can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin（EFG）-radial point interpola- tion method （RPIM） is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory. 42-1121/O3 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 ObjectType-Article-1 ObjectType-Feature-2 |
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| PublicationTitle | Acta mechanica solida Sinica |
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| PublicationYear | 2013 |
| Publisher | Elsevier Ltd Springer Singapore School of Urban Rail Transportation, Soochow University, Suzhou 215006, China School of Mathematical Sciences, Soochow University, Suzhou 215006, China%School of Mathematical Sciences, Soochow University, Suzhou 215006, China |
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| SubjectTerms | Approximation Boundary conditions Classical Mechanics collocation approach coupled method EFG Engineering Galerkin methods Interpolation Joining Mathematical analysis Mathematical models meshfree method Meshless methods moving least-squares (mls) approximation radial point interpolation method (rpim) Surfaces and Interfaces Theoretical and Applied Mechanics Thin Films 无网格伽辽金法 无网格方法 本质边界条件 治疗 移动最小二乘 耦合 逼近函数 |
| Title | NEW TREATMENT OF ESSENTIAL BOUNDARY CONDITIONS IN EFG METHOD BY COUPLING WITH RPIM |
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