메뉴 건너뛰기




Volumn 89, Issue 6, 2012, Pages 513-551

A new and simple meshless LBIE-RBF numerical scheme in linear elasticity

Author keywords

Linear elasticity; Local Boundary Integral Equation (LBIE); Local Radial Basis Functions (LRBF); Meshless methods

Indexed keywords

INTEGRAL REPRESENTATION; LINEAR ELASTICITY; LOCAL BOUNDARY INTEGRAL EQUATION METHODS; LOCAL BOUNDARY INTEGRAL EQUATIONS; LOCAL RADIAL BASIS FUNCTION; MESH-LESS METHODS; MESHLESS INTERPOLATION; THREE-DIMENSIONAL PROBLEMS;

EID: 84875156230     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (18)

References (47)
  • 1
    • 0029778570 scopus 로고    scopus 로고
    • Some studies on dual reciprocity BEM for elastodynamic analysis
    • Agnantiaris, J.; Polyzos, D.; Beskos, D. (1996): Some Studies on Dual Reciprocity BEM for Elastodynamic Analysis. Computational Mechanics, vol. 17, pp. 270-277. (Pubitemid 126708340)
    • (1996) Computational Mechanics , vol.17 , Issue.4 , pp. 270-277
    • Agnantiaris, J.P.1    Polyzos, D.2    Beskos, D.E.3
  • 3
    • 0242346713 scopus 로고    scopus 로고
    • Meshless local Petrov-Galerkin (MLPG) approaches for solving the weakly singular traction and displacement boundary integral equations
    • Atluri, S. N.; Han, Z. D.; Shen, S. (2003): Meshless local Petrov-Galerkin (MLPG) approaches for solving the weakly singular traction and displacement boundary integral equations. CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 507-517.
    • (2003) CMES: Computer Modeling in Engineering & Sciences , vol.4 , pp. 507-517
    • Atluri, S.N.1    Han, Z.D.2    Shen, S.3
  • 5
    • 0033885238 scopus 로고    scopus 로고
    • Local boundary integral equation (LBIE) and it's meshless implementation for linear elasticity
    • Atluri, S. N.; Sladek, J.; Sladek, V.; Zhu, T. (2000): The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity. Computational Mechanics, vol. 25, pp. 180-198. (Pubitemid 30593734)
    • (2000) Computational Mechanics , vol.25 , Issue.2 , pp. 180-198
    • Atluri, S.N.1    Sladek, J.2    Sladek, V.3    Zhu, T.4
  • 6
    • 33746175316 scopus 로고    scopus 로고
    • A meshless integral method based on regularized boundary integral equation
    • DOI 10.1016/j.cma.2005.12.005, PII S004578250600020X
    • Bodin, A.; Ma, J.; Xin, X. J.; Krishnaswami, P. (2006): A meshless integral method based on regularized boundary integral equation. Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 6258-6286. (Pubitemid 44081047)
    • (2006) Computer Methods in Applied Mechanics and Engineering , vol.195 , Issue.44-47 , pp. 6258-6286
    • Bodin, A.1    Ma, J.2    Xin, X.J.3    Krishnaswami, P.4
  • 7
    • 77957577505 scopus 로고    scopus 로고
    • Numerical solution of non-isothermal fluid flows using Local Radial Basis Functions (LRBF) interpolation and a velocity-correction method
    • Bourantas, G. C.; Skouras, E. D.; Loukopoulos, V. C.; Nikiforidis, G. C. (2010): Numerical solution of non-isothermal fluid flows using Local Radial Basis Functions (LRBF) interpolation and a velocity-correction method. CMES: Computer Modeling in Engineering & Sciences, vol. 64(2), pp. 187-212.
    • (2010) CMES: Computer Modeling in Engineering & Sciences , vol.64 , Issue.2 , pp. 187-212
    • Bourantas, G.C.1    Skouras, E.D.2    Loukopoulos, V.C.3    Nikiforidis, G.C.4
  • 8
    • 38649087922 scopus 로고    scopus 로고
    • Two-dimensional stress analysis of functionally graded solids using the MLPG method with radial basis functions
    • DOI 10.1016/j.commatsci.2007.05.003, PII S0927025607001346
    • Gilhooley, D. F.; Xiao, J. R.; Batra, M. A.; McCarthy, M. A.; Gillespie, J.W. J. (2008): Two dimensional stress analysis of functional graded solids using the MLPG method with radial basis functions. Computational Materials Science, vol. 41, pp. 467-481. (Pubitemid 351173679)
    • (2008) Computational Materials Science , vol.41 , Issue.4 , pp. 467-481
    • Gilhooley, D.F.1    Xiao, J.R.2    Batra, R.C.3    McCarthy, M.A.4    Gillespie Jr., J.W.5
  • 9
    • 0030415105 scopus 로고    scopus 로고
    • Admissible approximations for essential boundary conditions in the reproducing kernel particle method
    • Gosz, S.; Liu, W. K. (1996): Admissible approximations for essential boundary conditions in the reproducing kernel particle method. Computational Mechanics, vol. 19, pp. 120-135. (Pubitemid 126541079)
    • (1996) Computational Mechanics , vol.19 , Issue.2 , pp. 120-135
    • Gosz, J.1    Liu, W.K.2
  • 10
    • 0242285518 scopus 로고    scopus 로고
    • On simple formulations of weakly-singular traction & displacement BIE, and their solutions through Petrov-Galerkin approaches
    • Han, Z. D.; Atluri, S. N. (2003): On simple formulations of weakly singular traction & displacement BIE, and their solutions through Petrov Galerkin approaches. CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 5-20. (Pubitemid 37360199)
    • (2003) CMES - Computer Modeling in Engineering and Sciences , vol.4 , Issue.1 , pp. 5-20
    • Han, Z.D.1    Atluri, S.N.2
  • 11
    • 0242285518 scopus 로고    scopus 로고
    • On simple formulations of weakly-singular traction & displacement BIE, and their solutions through Petrov-Galerkin approaches
    • Han, Z. D.; Atluri, S. N. (2003): On Simple Formulations of Weakly-Singular Traction & Displacement BIE,and Their Solutions through Petrov-Galerkin Approaches. CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 5-20. (Pubitemid 37360199)
    • (2003) CMES - Computer Modeling in Engineering and Sciences , vol.4 , Issue.1 , pp. 5-20
    • Han, Z.D.1    Atluri, S.N.2
  • 12
    • 35348954889 scopus 로고    scopus 로고
    • A systematic approach for the development of weakly-singular BIEs
    • Han, Z. D.; Atluri, S. N. (2007): A Systematic Approach for the Development of Weakly-Singular BIEs. CMES: Computer Modeling in Engineering & Sciences, vol. 21, pp. 41-52. (Pubitemid 47606860)
    • (2007) CMES - Computer Modeling in Engineering and Sciences , vol.21 , Issue.1 , pp. 41-52
    • Han, Z.D.1    Atluri, S.N.2
  • 13
    • 0025206382 scopus 로고
    • Theory and applications of the multiquadric-biharmonic method. 20 Years of discovery 1968-1988
    • Hardy, R. L. (1990): Theory and applications of the multiquadrics- biharmonic method (20 years of discovery 1968-1988). Computers and Mathematics with Applications, vol. 19, pp. 163-208. (Pubitemid 20668366)
    • (1990) Computers & mathematics with applications , vol.19 , Issue.8-9 , pp. 163-208
    • Hardy, R.L.1
  • 14
    • 84875160549 scopus 로고    scopus 로고
    • ISoBEM (2012): BEM package. www.bemsands.com.
    • (2012) BEM Package
  • 17
    • 0001476575 scopus 로고
    • A new approach to free vibration analysis using boundary elements
    • Brebbia CA (ed), Springer, Berlin
    • Nardini, D.; Brebbia, C. (1982): A new approach to free vibration analysis using boundary elements. In: Brebbia CA (ed) Boundary Element Methods in Engineering, Springer, Berlin, vol. 50, pp. 313-326.
    • (1982) Boundary Element Methods in Engineering , vol.50 , pp. 313-326
    • Nardini, D.1    Brebbia, C.2
  • 18
    • 0242315239 scopus 로고
    • A novel displacement gradient boundary element method for elastic stress analysis with high accuracy
    • Okada, H.; Rajiyah, H.; Atluri, S. N. (1989): A Novel Displacement Gradient Boundary Element Method for Elastic Stress Analysis with High Accuracy. J. Applied Mech., pp. 1-9.
    • (1989) J. Applied Mech. , pp. 1-9
    • Okada, H.1    Rajiyah, H.2    Atluri, S.N.3
  • 19
    • 34250092203 scopus 로고
    • Non-hyper-singular integral representations for velocity (displacement) gradients in elastic/plastic solids (small or finite deformations)
    • Okada, H.; Rajiyah, H.; Atluri, S. N. (1989): Non-hyper-singular integral representations for velocity (displacement) gradients in elastic/plastic solids (small or finite deformations). Comp. Mech., vol. 4, pp. 165-175.
    • (1989) Comp. Mech. , vol.4 , pp. 165-175
    • Okada, H.1    Rajiyah, H.2    Atluri, S.N.3
  • 20
    • 0032058003 scopus 로고    scopus 로고
    • Static and dynamic boundary element analysis in incompressible linear elasticity
    • Polyzos, D.; Tsinopoulos, S. V.; Beskos, D. E. (1998): Static and dynamic boundary element analysis in incompressible linear elasticity. European. J. Mech. A/Solids, vol. 17, pp. 515-536. (Pubitemid 128431787)
    • (1998) European Journal of Mechanics, A/Solids , vol.17 , Issue.3 , pp. 515-536
    • Polyzos, D.1    Tsinopoulos, S.V.2    Beskos, D.E.3
  • 23
    • 13944263278 scopus 로고    scopus 로고
    • A meshless local boundary integral equation method for solving transient elastodynamic problems
    • DOI 10.1007/s00466-004-0584-y
    • Sellountos, E. J.; Polyzos, D. (2005): A meshless local boundary integral equation method for solving transient elastodynamic problems. Computational Mechanics, vol. 35 (4), pp. 265-276. (Pubitemid 40266350)
    • (2005) Computational Mechanics , vol.35 , Issue.4 , pp. 265-276
    • Sellountos, E.J.1    Polyzos, D.2
  • 24
    • 10644276384 scopus 로고    scopus 로고
    • A MLPG(LBIE) approach in combination with BEM
    • DOI 10.1016/j.cma.2004.06.007, PII S0045782504003044
    • Sellountos, E. J.; Polyzos, D. (2005): A MLPG (LBIE) approach in combination with BEM. Computer Methods in Applied Mechanics and Engineering, vol. 194, pp. 859-875. (Pubitemid 39660449)
    • (2005) Computer Methods in Applied Mechanics and Engineering , vol.194 , Issue.6-8 , pp. 859-875
    • Sellountos, E.J.1    Polyzos, D.2
  • 25
    • 38549103229 scopus 로고    scopus 로고
    • An advanced meshless LBIE/RBF method for solving two-dimensional incompressible fluid flows
    • DOI 10.1007/s00466-007-0219-1
    • Sellountos, E. J.; Sequeira, A. (2008a): An advanced meshless LBIE/RBF method for solving two-dimensional incompressible fluid flows. Computational Mechanics, vol. 41, pp. 617-631. (Pubitemid 351161452)
    • (2008) Computational Mechanics , vol.41 , Issue.5 , pp. 617-631
    • Sellountos, E.J.1    Sequeira, A.2
  • 26
    • 39349099929 scopus 로고    scopus 로고
    • A hybrid multi-region BEM / LBIE-RBF velocity-vorticity scheme for the two-dimensional Navier-Stokes equations
    • Sellountos, E. J.; Sequeira, A. (2008b): A HybridMulti-Region BEM / LBIERBF Velocity-Vorticity Scheme for the Two-Dimensional Navier-Stokes Equations. CMES: Computer Modelling in Engineering & Sciences, vol. 23, pp. 127- 147. (Pubitemid 351262051)
    • (2008) CMES - Computer Modeling in Engineering and Sciences , vol.23 , Issue.2 , pp. 127-147
    • Sellountos, E.J.1    Sequeira, A.2
  • 28
    • 77951958652 scopus 로고    scopus 로고
    • Solving Elastic Problems with Local Boundary Integral Equations (LBIE) and Radial Basis Functions (RBF) Cells
    • Sellountos, E. J.; Sequeira, A.; Polyzos, D. (2010): Solving Elastic Problems with Local Boundary Integral Equations (LBIE) and Radial Basis Functions (RBF) Cells. CMES: Computer Modelling in Engineering & Sciences, vol. 57, pp. 109- 135.
    • (2010) CMES: Computer Modelling in Engineering & Sciences , vol.57 , pp. 109-135
    • Sellountos, E.J.1    Sequeira, A.2    Polyzos, D.3
  • 31
    • 77955471289 scopus 로고    scopus 로고
    • Local integral equations implemented by MLSapproximation and analytical integrations
    • Sladek, J.; Sladek, V. (2010): Local integral equations implemented by MLSapproximation and analytical integrations. Engineering Analysis with Boundary Elements, vol. 34, pp. 904-913.
    • (2010) Engineering Analysis with Boundary Elements , vol.34 , pp. 904-913
    • Sladek, J.1    Sladek, V.2
  • 32
    • 0036937131 scopus 로고    scopus 로고
    • Application of the local boundary integral equation method to boundary value problems
    • Sladek, J.; Sladek, V.; Atluri, S. N. (2002): Application of the local boundary integral equation method to boundary value problems. International Journal of Applied Mechanics, vol. 38, pp. 1025-1043.
    • (2002) International Journal of Applied Mechanics , vol.38 , pp. 1025-1043
    • Sladek, J.1    Sladek, V.2    Atluri, S.N.3
  • 33
    • 0000557479 scopus 로고    scopus 로고
    • Numerical integration of singularities of local boundary integral equations
    • Sladek, J.; Sladek, V.; Keer, R. V. V. (2000): Numerical integration of singularities of local boundary integral equations. Computational Mechanics, vol. 25, pp. 394-403.
    • (2000) Computational Mechanics , vol.25 , pp. 394-403
    • Sladek, J.1    Sladek, V.2    Keer, R.V.V.3
  • 34
    • 0038741912 scopus 로고    scopus 로고
    • Meshless local boundary integral equation method for 2D elastodynamic problems
    • DOI 10.1002/nme.675
    • Sladek, J.; Sladek, V.; Keer, R. V. V. (2003): Meshless local boundary integral equation method for 2D elastodynamic problems. International Journal of Numerical Methods in Engineering, vol. 57, pp. 235-249. (Pubitemid 36586570)
    • (2003) International Journal for Numerical Methods in Engineering , vol.57 , Issue.2 , pp. 235-249
    • Sladek, J.1    Sladek, V.2    Van Keer, R.3
  • 37
    • 58149501149 scopus 로고    scopus 로고
    • A local hypersingular integral equation method using triangular background mesh
    • Vavourakis, V. (2008): A local hypersingular integral equation method using triangular background mesh. CMES: Computer Modelling in Engineering & Sciences, vol. 36, pp. 119-146.
    • (2008) CMES: Computer Modelling in Engineering & Sciences , vol.36 , pp. 119-146
    • Vavourakis, V.1
  • 38
    • 70349604307 scopus 로고    scopus 로고
    • A meshless local boundary integral equation method for two-dimensional steady elliptic problems
    • Vavourakis, V. (2009): A meshless local boundary integral equation method for two-dimensional steady elliptic problems. Computational Mechanics, vol. 44, pp. 777-790.
    • (2009) Computational Mechanics , vol.44 , pp. 777-790
    • Vavourakis, V.1
  • 39
    • 34250221149 scopus 로고    scopus 로고
    • A new MLPG(LBIE) method for solving 2D elastostatic problems
    • Vavourakis, V.; Polyzos, D. (2007): A new MLPG(LBIE) method for solving 2D elastostatic problems. Computers Materials and Continua, vol. 5 (3), pp. 185-196.
    • (2007) Computers Materials and Continua , vol.5 , Issue.3 , pp. 185-196
    • Vavourakis, V.1    Polyzos, D.2
  • 40
    • 42149184844 scopus 로고    scopus 로고
    • A MLPG(LBIE) numerical method for solving 2D incompressible and nearly incompressible elastostatic problems
    • DOI 10.1002/cnm.965
    • Vavourakis, V.; Polyzos, D. (2008): A MLPG(LBIE) numerical method for solving 2D incompressible and nearly incompressible elastostatic problems. Communications in Numerical Methods in Engineering, vol. 24, pp. 281-296. (Pubitemid 351523394)
    • (2008) Communications in Numerical Methods in Engineering , vol.24 , Issue.4 , pp. 281-296
    • Vavourakis, V.1    Polyzos, D.2
  • 41
    • 55849144005 scopus 로고    scopus 로고
    • Numerical determination of modal dispersion and AE signals characterization in waveguides through LBIE/BEM and time-frequency analysis
    • Vavourakis, V.; Protopappas, V. I. C.; Fotiadis, D.; Polyzos, D. (2009): Numerical determination of modal dispersion and AE signals characterization in waveguides through LBIE/BEM and time-frequency analysis. Computational Mechanics, vol. 43, pp. 431-441.
    • (2009) Computational Mechanics , vol.43 , pp. 431-441
    • Vavourakis, V.1    Protopappas, V.I.C.2    Fotiadis, D.3    Polyzos, D.4
  • 43
    • 0037143775 scopus 로고    scopus 로고
    • A point interpolation meshless method based on radial basis functions
    • DOI 10.1002/nme.489
    • Wang, J. G.; Liu, G. R. (2002): A point interpolation meshless method based on radial basis functions. International Journal of Numerical Methods in Engineering, vol. 54 (11), pp. 1623-1648. (Pubitemid 34842350)
    • (2002) International Journal for Numerical Methods in Engineering , vol.54 , Issue.11 , pp. 1623-1648
    • Wang, J.G.1    Liu, G.R.2
  • 44
    • 0037192730 scopus 로고    scopus 로고
    • On the optimal shape parameters of radial basis functions used for 2-D meshless methods
    • DOI 10.1016/S0045-7825(01)00419-4, PII S0045782501004194
    • Wang, J. G.; Liu, G. R. (2002): On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Computer Methods in Applied Mechanics and Engineering, vol. 191, pp. 2611-2630. (Pubitemid 34452176)
    • (2002) Computer Methods in Applied Mechanics and Engineering , vol.191 , Issue.23-24 , pp. 2611-2630
    • Wang, J.G.1    Liu, G.R.2
  • 45
    • 84870242115 scopus 로고    scopus 로고
    • Analytical formulation of meshless local integral equation method
    • Wen, P. H.; Aliabadi, M. H. (2012): Analytical formulation of meshless local integral equation method. Applied Mathematical Modelling, vol. http://dx.doi.org/10.1016/j.apm.2012.05.006.
    • (2012) Applied Mathematical Modelling
    • Wen, P.H.1    Aliabadi, M.H.2
  • 46
    • 34547525447 scopus 로고    scopus 로고
    • A meshless local Petrov-Galerkin (MLPG) approach based on the regular local boundary integral equation for linear elasticity
    • DOI 10.1080/15502280701471434, PII 780912487
    • Zhu, T.; Zhang, J.;Wang, D. (2007): A meshless Local Petrov-Galerkin (MLPG) approach based on the regular local boundary integral equation for linear elasticity. Int. J. Comput. Methods in Enng Sci. and Mechanics, vol. 8, pp. 373-382. (Pubitemid 47185131)
    • (2007) International Journal of Computational Methods in Engineering Science and Mechanics , vol.8 , Issue.5 , pp. 373-382
    • Zhu, T.-L.1    Zhang, J.2    Wang, D.3
  • 47
    • 0032047472 scopus 로고    scopus 로고
    • A local boundary integral equation (LBIE) method in computational mechanics, and ameshless discretization approach
    • Zhu, T.; Zhang, J. D.; Atluri, S. N. (1998): A local boundary integral equation (LBIE) method in computational mechanics and a meshless discretization approach. Computational Mechanics, vol. 21, pp. 223-235. (Pubitemid 128566412).
    • (1998) Computational Mechanics , vol.21 , Issue.3 , pp. 223-235
    • Zhu, T.1    Zhang, J.-D.2    Atluri, S.N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.