{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T13:37:32Z","timestamp":1762004252512},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2010,7,22]],"date-time":"2010-07-22T00:00:00Z","timestamp":1279756800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Mech"],"published-print":{"date-parts":[[2010,11]]},"DOI":"10.1007\/s00466-010-0518-9","type":"journal-article","created":{"date-parts":[[2010,7,21]],"date-time":"2010-07-21T04:48:24Z","timestamp":1279687704000},"page":"791-803","source":"Crossref","is-referenced-by-count":38,"title":["Analysis of plates on Pasternak foundations by radial basis functions"],"prefix":"10.1007","volume":"46","author":[{"given":"A. J. M.","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"C. M. C.","family":"Roque","sequence":"additional","affiliation":[]},{"given":"A. M. A.","family":"Neves","sequence":"additional","affiliation":[]},{"given":"R. M. N.","family":"Jorge","sequence":"additional","affiliation":[]},{"given":"C. M. M.","family":"Soares","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,7,22]]},"reference":[{"key":"518_CR1","unstructured":"Pasternak PL (1954) On a new method of analysis of an elastic foundation by means of two foundation constants. Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR, pp 1\u201356 (in Russian)"},{"key":"518_CR2","volume-title":"Die Lehre von der Elasticitaet und Festigkeit","author":"E Winkler","year":"1867","unstructured":"Winkler E (1867) Die Lehre von der Elasticitaet und Festigkeit. Prag, Dominicus"},{"key":"518_CR3","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/S0022-460X(73)80371-2","volume":"31","author":"AW Leissa","year":"1973","unstructured":"Leissa AW (1973) The free vibration of plates. J Sound Vib 31: 257\u2013293","journal-title":"J Sound Vib"},{"key":"518_CR4","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/S0141-0296(98)00116-3","volume":"22","author":"KY Lam","year":"2000","unstructured":"Lam KY, Wang CM, He XQ (2000) Canonical exact solutions for levy-plates on two-parameter foundation using green\u2019s functions. Eng Struct 22: 364\u2013378","journal-title":"Eng Struct"},{"key":"518_CR5","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/0020-7403(94)90037-X","volume":"36","author":"Y Xiang","year":"1994","unstructured":"Xiang Y, Wang CM, Kitipornchai S (1994) Exact vibration solution for initially stressed Mindlin plates on pasternak foundation. Int J Mech Sci 36: 311\u2013316","journal-title":"Int J Mech Sci"},{"key":"518_CR6","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1002\/(SICI)1097-0207(19970130)40:2<295::AID-NME66>3.0.CO;2-2","volume":"40","author":"MH Omurtag","year":"1997","unstructured":"Omurtag MH, Ozutok A, Akoz AY (1997) Free vibration analysis of kirchhoff plates resting on elastic foundation by mixed finite element formulation based on gateaux differential. Int J Numer Methods Eng 40: 295\u2013317","journal-title":"Int J Numer Methods Eng"},{"key":"518_CR7","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1061\/(ASCE)0733-9399(2000)126:1(27)","volume":"126","author":"H Matsunaga","year":"2000","unstructured":"Matsunaga H (2000) Vibration and stability of thick plates on elastic foundations. J Eng Mech ASCE 126: 27\u201334","journal-title":"J Eng Mech ASCE"},{"key":"518_CR8","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1006\/jsvi.2000.3501","volume":"244","author":"HS Shen","year":"2001","unstructured":"Shen HS, Yang J, Zhang L (2001) Free and forced vibration of Reissner\u2013Mindlin plates with free edges resting on elastic foundations. J Sound Vib 244: 299\u2013320","journal-title":"J Sound Vib"},{"key":"518_CR9","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1006\/jsvi.1997.1394","volume":"212","author":"Y Ayvaz","year":"1998","unstructured":"Ayvaz Y, Daloglu A, Dogangun A (1998) Application of a modified Vlasov model to earthquake analysis of plates resting on elastic foundations. J Sound Vib 212: 499\u2013509","journal-title":"J Sound Vib"},{"key":"518_CR10","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1016\/S0020-7403(02)00034-6","volume":"44","author":"KM Liew","year":"2002","unstructured":"Liew KM, Teo TM (2002) Differential cubature method for analysis of shear deformable rectangular plates on pasternak foundations. Int J Mech Sci 44: 1179\u20131194","journal-title":"Int J Mech Sci"},{"key":"518_CR11","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/0020-7403(95)00062-3","volume":"38","author":"KM Liew","year":"1996","unstructured":"Liew KM, Han JB, Xiao ZM, Du H (1996) Differential quadrature method for Mindlin plates on winkler foundations. Int J Mech Sci 38: 405\u2013421","journal-title":"Int J Mech Sci"},{"key":"518_CR12","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1016\/S0020-7403(97)00001-5","volume":"39","author":"JB Han","year":"1997","unstructured":"Han JB, Liew KM (1997) Numerical differential quadrature method for Reissner\u2013Mindlin plates on two-parameter foundations. Int J Mech Sci 39: 977\u2013989","journal-title":"Int J Mech Sci"},{"key":"518_CR13","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1002\/nme.915","volume":"59","author":"D Zhou","year":"2004","unstructured":"Zhou D, Cheung YK, Lo SH, Au FTK (2004) Three-dimensional vibration analysis of rectangular thick plates on pasternak foundation. Int J Numer Methods Eng 59: 1313\u20131334","journal-title":"Int J Numer Methods Eng"},{"key":"518_CR14","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/j.ijpvp.2007.07.001","volume":"84","author":"O Civalek","year":"2007","unstructured":"Civalek O, Acar MH (2007) Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations. Int J Pres Vessel Pip 84: 527\u2013535","journal-title":"Int J Pres Vessel Pip"},{"key":"518_CR15","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/S0955-7997(02)00007-3","volume":"26","author":"S Chucheepsakul","year":"2002","unstructured":"Chucheepsakul S, Chinnaboom B (2002) An alternative domainboundary element technique for analyzing plates on two-parameter elastic foundations. Eng Anal Bound Elem 26: 547\u2013555","journal-title":"Eng Anal Bound Elem"},{"issue":"8\/9","key":"518_CR16","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0898-1221(90)90270-T","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa EJ (1990) Multiquadrics\u2014a scattered data approximation scheme with applications to computational fluid dynamics. i: Surface approximations and partial derivative estimates. Comput Math Appl 19(8\/9): 127\u2013145","journal-title":"Comput Math Appl"},{"key":"518_CR17","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S0096-3003(96)00309-8","volume":"88","author":"YC Hon","year":"1997","unstructured":"Hon YC, Lu MW, Xue WM, Zhu YM (1997) Multiquadric method for the numerical solution of byphasic mixture model. Appl Math Comput 88: 153\u2013175","journal-title":"Appl Math Comput"},{"issue":"5","key":"518_CR18","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1061\/(ASCE)0733-9429(1999)125:5(524)","volume":"125","author":"YC Hon","year":"1999","unstructured":"Hon YC, Cheung KF, Mao XZ, Kansa EJ (1999) A multiquadric solution for the shallow water equation. J Hydr Eng ASCE 125(5): 524\u2013533","journal-title":"J Hydr Eng ASCE"},{"issue":"6","key":"518_CR19","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1016\/S0020-7683(02)00005-7","volume":"39","author":"JG Wang","year":"2002","unstructured":"Wang JG, Liu GR, Lin P (2002) Numerical analysis of biot\u2019s consolidation process by radial point interpolation method. Int J Solids Struct 39(6): 1557\u20131573","journal-title":"Int J Solids Struct"},{"issue":"1","key":"518_CR20","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1006\/jsvi.2000.3626","volume":"246","author":"GR Liu","year":"2001","unstructured":"Liu GR, Gu YT (2001) A local radial point interpolation method (LRPIM) for free vibration analyses of 2-d solids. J Sound Vib 246(1): 29\u201346","journal-title":"J Sound Vib"},{"key":"518_CR21","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1002\/nme.489","volume":"54","author":"GR Liu","year":"2002","unstructured":"Liu GR, Wang JG (2002) A point interpolation meshless method based on radial basis functions. Int J Numer Methods Eng 54: 1623\u20131648","journal-title":"Int J Numer Methods Eng"},{"key":"518_CR22","doi-asserted-by":"crossref","first-page":"2611","DOI":"10.1016\/S0045-7825(01)00419-4","volume":"191","author":"JG Wang","year":"2002","unstructured":"Wang JG, Liu GR (2002) On the optimal shape parameters of radial basis functions used for 2-d meshless methods. Comput Meth Appl Mech Eng 191: 2611\u20132630","journal-title":"Comput Meth Appl Mech Eng"},{"key":"518_CR23","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/S0263-8223(02)00034-X","volume":"59","author":"XL Chen","year":"2003","unstructured":"Chen XL, Liu GR, Lim SP (2003) An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape. Compos Struct 59: 279\u2013289","journal-title":"Compos Struct"},{"key":"518_CR24","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/S0022-460X(03)00089-0","volume":"269","author":"KY Dai","year":"2004","unstructured":"Dai KY, Liu GR, Lim SP, Chen XL (2004) An element free Galerkin method for static and free vibration analysis of shear-deformable laminated composite plates. J Sound Vib 269: 633\u2013652","journal-title":"J Sound Vib"},{"key":"518_CR25","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1142\/S0219455402000634","volume":"2","author":"GR Liu","year":"2002","unstructured":"Liu GR, Chen XL (2002) Buckling of symmetrically laminated composite plates using the element-free Galerkin method. Int J Struct Stabil Dyn 2: 281\u2013294","journal-title":"Int J Struct Stabil Dyn"},{"key":"518_CR26","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.cma.2003.10.002","volume":"193","author":"KM Liew","year":"2004","unstructured":"Liew KM, Chen XL, Reddy JN (2004) Mesh-free radial basis function method for buckling analysis of non-uniformity loaded arbitrarily shaped shear deformable plates. Comput Meth Appl Mech Eng 193: 205\u2013225","journal-title":"Comput Meth Appl Mech Eng"},{"key":"518_CR27","doi-asserted-by":"crossref","first-page":"3471","DOI":"10.1016\/j.cma.2003.12.039","volume":"193","author":"YQ Huang","year":"2004","unstructured":"Huang YQ, Li QS (2004) Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method. Comput Meth Appl Mech Eng 193: 3471\u20133492","journal-title":"Comput Meth Appl Mech Eng"},{"key":"518_CR28","doi-asserted-by":"crossref","first-page":"5923","DOI":"10.1016\/S0045-7825(02)00504-2","volume":"191","author":"L Liu","year":"2002","unstructured":"Liu L, Liu GR, Tan VCB (2002) Element free method for static and free vibration analysis of spatial thin shell structures. Comput Meth Appl Mech Eng 191: 5923\u20135942","journal-title":"Comput Meth Appl Mech Eng"},{"key":"518_CR29","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/S0263-8223(02)00239-8","volume":"59","author":"AJM Ferreira","year":"2003","unstructured":"Ferreira AJM (2003) A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Compos Struct 59: 385\u2013392","journal-title":"Compos Struct"},{"key":"518_CR30","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1080\/15376490306743","volume":"10","author":"AJM Ferreira","year":"2003","unstructured":"Ferreira AJM (2003) Thick composite beam analysis using a global meshless approximation based on radial basis functions. Mech Adv Mater Struct 10: 271\u2013284","journal-title":"Mech Adv Mater Struct"},{"key":"518_CR31","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1016\/S1359-8368(03)00083-0","volume":"34","author":"AJM Ferreira","year":"2003","unstructured":"Ferreira AJM, Roque CMC, Martins PALS (2003) Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method. Compos Part B Eng 34: 627\u2013636","journal-title":"Compos Part B Eng"},{"issue":"189","key":"518_CR32","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1090\/S0025-5718-1990-0993931-7","volume":"54","author":"WR Madich","year":"1990","unstructured":"Madich WR, Nelson SA (1990) Multivariate interpolation and conditionally positive definite functions. ii. Math Comp 54(189): 211\u2013230","journal-title":"Math Comp"},{"issue":"4","key":"518_CR33","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1137\/S0036141000373811","volume":"33","author":"J Yoon","year":"2001","unstructured":"Yoon J (2001) Spectral approximation orders of radial basis function interpolation on the sobolev space. SIAM J Math Anal 33(4): 946\u2013958","journal-title":"SIAM J Math Anal"},{"key":"518_CR34","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1029\/JB076i008p01905","volume":"176","author":"RL Hardy","year":"1971","unstructured":"Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 176: 1905\u20131915","journal-title":"J Geophys Res"},{"key":"518_CR35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492900000015","volume":"9","author":"MD Buhmann","year":"2000","unstructured":"Buhmann MD (2000) Radial basis functions. Acta Numer 9: 1\u201338","journal-title":"Acta Numer"},{"key":"518_CR36","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1016\/j.camwa.2003.08.007","volume":"48","author":"RB Platte","year":"2004","unstructured":"Platte RB, Driscoll TA (2004) Computing eigenmodes of elliptic operators using radial basis functions. Comput Math Appl 48: 561\u2013576","journal-title":"Comput Math Appl"},{"key":"518_CR37","volume-title":"Mechanics of laminated composite plates: theory and analysis","author":"JN Reddy","year":"1997","unstructured":"Reddy JN (1997) Mechanics of laminated composite plates: theory and analysis. CRC Press, Boca Raton"},{"key":"518_CR38","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.1016\/S0045-7825(03)00238-X","volume":"192","author":"KM Liew","year":"2003","unstructured":"Liew KM, Huang YQ, Reddy JN (2003) Vibration analysis of symmetrically laminated plates based on fsdt using the moving least squares differential quadrature method. Comput Meth Appl Mech Eng 192: 2203\u20132222","journal-title":"Comput Meth Appl Mech Eng"},{"issue":"9","key":"518_CR39","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/S0020-7403(89)80003-7","volume":"31","author":"H Kobayashi","year":"1989","unstructured":"Kobayashi H, Sonoda K (1989) Rectangular Mindlin plates on elastic foundation. Int J Mech Sci 31(9): 679\u2013692","journal-title":"Int J Mech Sci"}],"container-title":["Computational Mechanics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00466-010-0518-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00466-010-0518-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00466-010-0518-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T06:33:19Z","timestamp":1685687599000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00466-010-0518-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,22]]},"references-count":39,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,11]]}},"alternative-id":["518"],"URL":"https:\/\/doi.org\/10.1007\/s00466-010-0518-9","relation":{},"ISSN":["0178-7675","1432-0924"],"issn-type":[{"value":"0178-7675","type":"print"},{"value":"1432-0924","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,22]]}}}