{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T11:33:18Z","timestamp":1768995198466,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2011,11,8]],"date-time":"2011-11-08T00:00:00Z","timestamp":1320710400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Meccanica"],"published-print":{"date-parts":[[2012,6]]},"DOI":"10.1007\/s11012-011-9501-6","type":"journal-article","created":{"date-parts":[[2011,11,7]],"date-time":"2011-11-07T10:33:03Z","timestamp":1320661983000},"page":"1157-1171","source":"Crossref","is-referenced-by-count":11,"title":["Analysis of thick plates by local radial basis functions-finite differences method"],"prefix":"10.1007","volume":"47","author":[{"given":"C. M. C.","family":"Roque","sequence":"first","affiliation":[]},{"given":"J. D.","family":"Rodrigues","sequence":"additional","affiliation":[]},{"given":"A. J. M.","family":"Ferreira","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,11,8]]},"reference":[{"issue":"7","key":"9501_CR1","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1115\/1.3424154","volume":"44","author":"KH Lo","year":"1977","unstructured":"Lo KH, Christensen RM, Wu EM (1977) A high-order theory of plate deformation, part 1: homogeneous plates. J\u00a0Appl Mech 44(7):663\u2013668","journal-title":"J\u00a0Appl Mech"},{"issue":"4","key":"9501_CR2","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1115\/1.3424155","volume":"44","author":"KH Lo","year":"1977","unstructured":"Lo KH, Christensen RM, Wu EM (1977) A high-order theory of plate deformation, part 2: laminated plates. J Appl Mech 44(4):669\u2013676","journal-title":"J Appl Mech"},{"key":"9501_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0045-7825(82)90043-3","volume":"31","author":"T Kant","year":"1982","unstructured":"Kant T (1982) Numerical analysis of thick plates. Comput Methods Appl Mech Eng 31:1\u201318","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"2","key":"9501_CR4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0045-7949(82)90065-7","volume":"15","author":"T Kant","year":"1982","unstructured":"Kant T, Owen DRJ, Zienkiewicz OC (1982) A refined higher-order c o plate element. Comput Struct 15(2):177\u2013183","journal-title":"Comput Struct"},{"key":"9501_CR5","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/0020-7683(88)90090-X","volume":"24","author":"BN Pandya","year":"1988","unstructured":"Pandya BN, Kant T (1988) Higher-order shear deformable theories for flexure of sandwich plates-finite element evaluations. Int J Solids Struct 24:419\u2013451","journal-title":"Int J Solids Struct"},{"key":"9501_CR6","doi-asserted-by":"crossref","first-page":"91","DOI":"10.2514\/2.1618","volume":"40","author":"RC Batra","year":"2002","unstructured":"Batra RC, Vidoli S (2002) Higher order piezoelectric plate theory derived from a three-dimensional variational principle. AIAA J 40:91\u2013104","journal-title":"AIAA J"},{"key":"9501_CR7","doi-asserted-by":"crossref","first-page":"1797","DOI":"10.1002\/(SICI)1097-0207(19960615)39:11<1797::AID-NME928>3.0.CO;2-W","volume":"39","author":"E Carrera","year":"1996","unstructured":"Carrera E (1996) C0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity. Int J Numer Methods Eng 39:1797\u20131820","journal-title":"Int J Numer Methods Eng"},{"key":"9501_CR8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1080\/10759419708945875","volume":"4","author":"E Carrera","year":"1997","unstructured":"Carrera E, Kroplin B (1997) Zig-zag and interlaminar equilibria effects in large deflection and post-buckling analysis of multilayered plates. Mech Compos Mater Struct 4:69\u201394","journal-title":"Mech Compos Mater Struct"},{"key":"9501_CR9","doi-asserted-by":"crossref","first-page":"830","DOI":"10.2514\/2.444","volume":"36","author":"E Carrera","year":"1998","unstructured":"Carrera E (1998) Evaluation of layer-wise mixed theories for laminated plate analysis. AIAA J 36:830\u2013839","journal-title":"AIAA J"},{"key":"9501_CR10","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF01174647","volume":"70","author":"L Librescu","year":"1987","unstructured":"Librescu L, Khdeir AA, Reddy JN (1987) A comprehensive analysis of the state of stress of elastic anisotropic flat plates using refined theories. Acta Mech 70:57\u201381","journal-title":"Acta Mech"},{"key":"9501_CR11","volume-title":"Mechanics of laminated composite plates","author":"JN Reddy","year":"1997","unstructured":"Reddy JN (1997) Mechanics of laminated composite plates. CRC Press, New York"},{"key":"9501_CR12","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s00707-009-0142-y","volume":"209","author":"L Fiedler","year":"2010","unstructured":"Fiedler L, Vestroni F, Lacarbonara W (2010) A generalized higher-order theory for multi-layered, shear-deformable composite plates. Acta Mech 209:85\u201398","journal-title":"Acta Mech"},{"key":"9501_CR13","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"},{"issue":"4","key":"9501_CR14","first-page":"321","volume":"35","author":"RL Hardy","year":"1975","unstructured":"Hardy RL (1975) Research results in the application of multiquadric equations to surveying and mapping problems. Surv Mapp 35(4):321\u2013332","journal-title":"Surv Mapp"},{"issue":"8\u20139","key":"9501_CR15","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 a scattered data approximation scheme with applications to computational fluid-dynamics. i. surface approximations and partial derivative estimates. Comput Math Appl 19(8\u20139):127\u2013145","journal-title":"Comput Math Appl"},{"issue":"8\u20139","key":"9501_CR16","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0898-1221(90)90271-K","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa EJ (1990) Multiquadrics a scattered data approximation scheme with applications to computational fluid-dynamics. ii. solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 19(8\u20139):147\u2013161","journal-title":"Comput Math Appl"},{"issue":"3\u20135","key":"9501_CR17","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1016\/j.jsv.2006.08.037","volume":"300","author":"CMC Roque","year":"2007","unstructured":"Roque CMC, Ferreira AJM, Jorge RMN (2007) A radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory. J Sound Vib 300(3\u20135):1048\u20131070","journal-title":"J Sound Vib"},{"issue":"3","key":"9501_CR18","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.compstruct.2005.07.009","volume":"77","author":"AJM Ferreira","year":"2007","unstructured":"Ferreira AJM, Roque CMC, Jorge RMN (2007) Natural frequencies of fsdt cross-ply composite shells by multiquadrics. Compos Struct 77(3):296\u2013305","journal-title":"Compos Struct"},{"issue":"1","key":"9501_CR19","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.compfluid.2010.08.005","volume":"46","author":"N Flyer","year":"2011","unstructured":"Flyer N, Fornberg B (2011) Radial basis functions: Developments and applications to planetary scale flows. Comput Fluids 46(1):23\u201332","journal-title":"Comput Fluids"},{"issue":"5\u20136","key":"9501_CR20","first-page":"531","volume":"55","author":"AI Tolstykh","year":"2003","unstructured":"Tolstykh AI, Lipavskii MV, Shirobokov DA (2003) High-accuracy discretization methods for solid mechanics. Arch Mech 55(5\u20136):531\u2013553","journal-title":"Arch Mech"},{"issue":"7\u20138","key":"9501_CR21","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1016\/S0045-7825(02)00618-7","volume":"192","author":"C Shu","year":"2003","unstructured":"Shu C, Ding H, Yeo KS (2003) Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 192(7\u20138):941\u2013954","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"1","key":"9501_CR22","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.jcp.2003.11.010","volume":"196","author":"T Cecil","year":"2004","unstructured":"Cecil T, Qian J, Osher S (2004) Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions. J Comput Phys 196(1):327\u2013347","journal-title":"J Comput Phys"},{"issue":"1","key":"9501_CR23","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.jcp.2005.05.030","volume":"212","author":"GB Wright","year":"2006","unstructured":"Wright GB, Fornberg B (2006) Scattered node compact finite difference-type formulas generated from radial basis functions. J Comput Phys 212(1):99\u2013123","journal-title":"J Comput Phys"},{"issue":"5","key":"9501_CR24","doi-asserted-by":"crossref","first-page":"615","DOI":"10.4208\/aamm.09-m0942","volume":"1","author":"YY Shan","year":"2009","unstructured":"Shan YY, Shu C, Qin N (2009) Multiquadric finite difference (mq-fd) methods and its application. Adv Appl Math Mech 1(5):615\u2013638","journal-title":"Adv Appl Math Mech"},{"issue":"22","key":"9501_CR25","doi-asserted-by":"crossref","first-page":"8281","DOI":"10.1016\/j.jcp.2010.07.008","volume":"229","author":"V Bayona","year":"2010","unstructured":"Bayona V, Moscoso M, Carretero M, Kindelan M (2010) Rbf-fd formulas and convergence properties. J Comput Phys 229(22):8281\u20138295","journal-title":"J Comput Phys"},{"issue":"6","key":"9501_CR26","doi-asserted-by":"crossref","first-page":"2270","DOI":"10.1016\/j.jcp.2010.12.014","volume":"230","author":"B Fornberg","year":"2011","unstructured":"Fornberg B, Lehto E (2011) Stabilization of rbf-generated finite difference methods for convective pdes. J Comput Phys 230(6):2270\u20132285","journal-title":"J Comput Phys"},{"issue":"1","key":"9501_CR27","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01893414","volume":"2","author":"CA Micchelli","year":"1986","unstructured":"Micchelli CA (1986) Interpolation of scattered data distance matrices and conditionally positive definite functions. Constr Approx 2(1):11\u201322","journal-title":"Constr Approx"},{"key":"9501_CR28","volume-title":"Topics in multivariate approximation and interpolation","author":"H Wendland","year":"2005","unstructured":"Wendland H (2005) Computational aspects of radial basis function approximation. In: Jetter K, Buhmann M, Haussmann W, Schaback R, Stoeckler J (eds) Topics in multivariate approximation and interpolation. Elsevier, Amsterdam"},{"key":"9501_CR29","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S0898-1221(04)90004-1","volume":"47","author":"B Fornberg","year":"2004","unstructured":"Fornberg B, Wright G, Larsson E (2004) Some observations regarding interpolants in the limit of flat radial basis functions. Comput Math Appl 47:37\u201355","journal-title":"Comput Math Appl"},{"key":"9501_CR30","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1115\/1.4010217","volume":"18","author":"RD Mindlin","year":"1951","unstructured":"Mindlin RD (1951) Influence of rotary inertia and shear in flexural motions of isotropic elastic plates. J Appl Mech 18:31\u201338","journal-title":"J Appl Mech"},{"key":"9501_CR31","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.cma.2006.02.009","volume":"196","author":"AJM Ferreira","year":"2006","unstructured":"Ferreira AJM, Fasshauer GE (2006) Computation of natural frequencies of shear deformable beams and plates by a rbf-pseudospectral method. Comput Methods Appl Mech Eng 196:134\u2013146","journal-title":"Comput Methods Appl Mech Eng"},{"key":"9501_CR32","volume-title":"MATLAB codes for finite element analysis: solids and structures","author":"AJM Ferreira","year":"2008","unstructured":"Ferreira AJM (2008) MATLAB codes for finite element analysis: solids and structures. Springer, Berlin"},{"issue":"3","key":"9501_CR33","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0022-460X(80)90477-0","volume":"69","author":"DJ Dawe","year":"1980","unstructured":"Dawe DJ, Roufaeil OL (1980) Rayleigh-Ritz vibration analysis of Mindlin plates. J Sound Vib 69(3):345\u2013359","journal-title":"J Sound Vib"},{"key":"9501_CR34","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1016\/j.jsv.2003.08.026","volume":"276","author":"KM Liew","year":"2004","unstructured":"Liew KM, Wang J, Ng TY, Tan MJ (2004) Free vibration and buckling analyses of shear-deformable plates based on fsdt meshfree method. J Sound Vib 276:997\u20131017","journal-title":"J Sound Vib"},{"key":"9501_CR35","volume-title":"Numerical methods and software for dynamic analysis of plates and shells","author":"E Hinton","year":"1988","unstructured":"Hinton E (1988) Numerical methods and software for dynamic analysis of plates and shells. Pineridge, Swansea"},{"issue":"2","key":"9501_CR36","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1006\/jsvi.2000.3232","volume":"241","author":"T Kant","year":"2001","unstructured":"Kant T, Swaminathan K (2001) Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories. J Sound Vib 241(2):319\u2013327","journal-title":"J Sound Vib"}],"container-title":["Meccanica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11012-011-9501-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11012-011-9501-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11012-011-9501-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,15]],"date-time":"2021-12-15T04:09:44Z","timestamp":1639541384000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11012-011-9501-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11,8]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2012,6]]}},"alternative-id":["9501"],"URL":"https:\/\/doi.org\/10.1007\/s11012-011-9501-6","relation":{},"ISSN":["0025-6455","1572-9648"],"issn-type":[{"value":"0025-6455","type":"print"},{"value":"1572-9648","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,11,8]]}}}