{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T00:05:00Z","timestamp":1783037100495,"version":"3.54.6"},"reference-count":88,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T00:00:00Z","timestamp":1552521600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T00:00:00Z","timestamp":1552521600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s00366-019-00732-1","type":"journal-article","created":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T09:46:46Z","timestamp":1552556806000},"page":"807-821","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":92,"title":["Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT"],"prefix":"10.1007","volume":"36","author":[{"given":"Mokhtar","family":"Khiloun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdelmoumen Anis","family":"Bousahla","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdelhakim","family":"Kaci","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aicha","family":"Bessaim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdelouahed","family":"Tounsi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. R.","family":"Mahmoud","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,3,14]]},"reference":[{"key":"732_CR1","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1016\/j.compstruct.2017.10.047","volume":"184","author":"M Abualnour","year":"2018","unstructured":"Abualnour M, Houari MSA, Tounsi A, Adda Bedia EA, Mahmoud SR (2018) A novel quasi 3D trigonometric plate theory for free vibration analysis of advanced composite plates. Compos Struct 184:688\u2013697","journal-title":"Compos Struct"},{"key":"732_CR2","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1016\/j.ijmecsci.2017.06.039","volume":"130","author":"R Kolahchi","year":"2017","unstructured":"Kolahchi R, Zarei MS, Hajmohammad MH, Nouri A (2017) Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory. Int J Mech Sci 130:534\u2013545","journal-title":"Int J Mech Sci"},{"issue":"6","key":"732_CR3","first-page":"695","volume":"62","author":"H Bellifa","year":"2017","unstructured":"Bellifa H, Benrahou KH, Bousahla AA, Tounsi A, Mahmoud SR (2017) A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams. Struct Eng Mech 62(6):695\u2013702","journal-title":"Struct Eng Mech"},{"issue":"3","key":"732_CR4","first-page":"257","volume":"25","author":"H Bellifa","year":"2017","unstructured":"Bellifa H, Bakora A, Tounsi A, Bousahla AA, Mahmoud SR (2017) An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates. Steel Compos Struct 25(3):257\u2013270","journal-title":"Steel Compos Struct"},{"key":"732_CR5","doi-asserted-by":"publisher","DOI":"10.1177\/1099636217720373","author":"MH Hajmohammad","year":"2017","unstructured":"Hajmohammad MH, Zarei MS, Nouri A, Kolahchi R (2017) Dynamic buckling of sensor\/functionally graded-carbon nanotube-reinforced laminated plates\/actuator based on sinusoidal-visco-piezoelasticity theories. J Sandw Struct Mater. \nhttps:\/\/doi.org\/10.1177\/1099636217720373","journal-title":"J Sandw Struct Mater"},{"key":"732_CR6","doi-asserted-by":"crossref","first-page":"489","DOI":"10.12989\/sem.2016.60.3.489","volume":"60","author":"AA Ghorbanpour","year":"2016","unstructured":"Ghorbanpour AA, Cheraghbak A, Kolahchi R (2016) Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory. Struct Eng Mech 60:489\u2013505","journal-title":"Struct Eng Mech"},{"issue":"5","key":"732_CR7","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1080\/15376494.2016.1191095","volume":"24","author":"AMA Neves","year":"2017","unstructured":"Neves AMA, Ferreira AJM, Carrera E, Cinefra M, Jorge RMN, Mota Soares CM et al (2017) Influence of zig-zag and warping effects on buckling of functionally graded sandwich plates according to sinusoidal shear deformation theories. Mech Adv Mater Struct 24(5):360\u2013376","journal-title":"Mech Adv Mater Struct"},{"issue":"4","key":"732_CR8","first-page":"453","volume":"65","author":"A Attia","year":"2018","unstructured":"Attia A, Bousahla AA, Tounsi A, Mahmoud SR, Alwabli AS (2018) \u201cA refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations\u201d. Struct Eng Mech 65(4):453\u2013464","journal-title":"Struct Eng Mech"},{"key":"732_CR9","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.compositesb.2013.11.022","volume":"59","author":"R Gunes","year":"2014","unstructured":"Gunes R, Aydin M, Apalak MK, Reddy JN (2014) Experimental and numerical investigations of low velocity impact on functionally graded circular plates. Compos Part B 59:21\u201332","journal-title":"Compos Part B"},{"issue":"2","key":"732_CR10","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.compositesb.2010.10.005","volume":"42","author":"E Carrera","year":"2011","unstructured":"Carrera E, Brischetto S, Cinefra M, Soave M (2011) Effects of thickness stretching in functionally graded plates and shells. Compos Part B 42(2):123\u2013133","journal-title":"Compos Part B"},{"key":"732_CR11","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.compstruct.2008.09.006","volume":"89","author":"AJM Ferreira","year":"2009","unstructured":"Ferreira AJM, Castro LM, Bertoluzza S (2009) A high order collocation method for the static and vibration analysis of composite plates using a first-order theory. Compos Struct 89:424\u2013432","journal-title":"Compos Struct"},{"issue":"4","key":"732_CR12","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1115\/1.3167719","volume":"51","author":"JN Reddy","year":"1984","unstructured":"Reddy JN (1984) A simple higher-order theory for laminated composite plates. J Appl Mech 51(4):745\u2013752","journal-title":"J Appl Mech"},{"issue":"16","key":"732_CR13","doi-asserted-by":"crossref","first-page":"2295","DOI":"10.1016\/0020-7683(94)00258-X","volume":"32","author":"PF Pai","year":"1995","unstructured":"Pai PF (1995) A new look at shear correction factors and warping functions of anisotropic laminates. Int J Solids Struct 32(16):2295\u20132313","journal-title":"Int J Solids Struct"},{"issue":"2","key":"732_CR14","doi-asserted-by":"crossref","first-page":"227","DOI":"10.12989\/scs.2016.20.2.227","volume":"20","author":"F Bounouara","year":"2016","unstructured":"Bounouara F, Benrahou KH, Belkorissat I, Tounsi A (2016) A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation. Steel Compos Struct 20(2):227\u2013249","journal-title":"Steel Compos Struct"},{"issue":"8","key":"732_CR15","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1016\/0020-7225(91)90165-Y","volume":"29","author":"M Touratier","year":"1991","unstructured":"Touratier M (1991) An efficient standard plate theory. Int J Eng Sci 29(8):901\u2013916","journal-title":"Int J Eng Sci"},{"issue":"3","key":"732_CR16","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF01176650","volume":"94","author":"KP Soldatos","year":"1992","unstructured":"Soldatos KP (1992) A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mech 94(3):195\u2013220","journal-title":"Acta Mech"},{"issue":"2","key":"732_CR17","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s10999-010-9110-x","volume":"6","author":"H Ait Atmane","year":"2010","unstructured":"Ait Atmane H, Tounsi A, Mechab I, Adda Bedia EA (2010) Free vibration analysis of functionally graded plates resting on Winkler\u2013Pasternak elastic foundations using a new shear deformation theory. Int J Mech Mater Des 6(2):113\u2013121","journal-title":"Int J Mech Mater Des"},{"issue":"6","key":"732_CR18","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1016\/S0020-7683(02)00647-9","volume":"40","author":"M Karama","year":"2003","unstructured":"Karama M, Afaq KS, Mistou S (2003) Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. Int J Solids Struct 40(6):1525\u20131546","journal-title":"Int J Solids Struct"},{"issue":"2","key":"732_CR19","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1061\/(ASCE)EM.1943-7889.0000665","volume":"140","author":"H Hebali","year":"2014","unstructured":"Hebali H, Tounsi A, Houari MSA, Bessaim A, Adda Bedia EA (2014) New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. J Eng Mech (ASCE) 140(2):374\u2013383","journal-title":"J Eng Mech (ASCE)"},{"issue":"3","key":"732_CR20","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1016\/j.jsv.2005.02.031","volume":"289","author":"J Woo","year":"2006","unstructured":"Woo J, Meguid SA, Ong LS (2006) Nonlinear free vibration behavior of functionally graded plates. J Sound Vib 289(3):595\u2013611","journal-title":"J Sound Vib"},{"issue":"4","key":"732_CR21","doi-asserted-by":"crossref","first-page":"1450043","DOI":"10.1142\/S1758825114500434","volume":"6","author":"S Chakraverty","year":"2014","unstructured":"Chakraverty S, Pradhan KK (2014) Free vibration of functionally graded thin rectangular plates resting on Winkler elastic foundation with general boundary conditions using Rayleigh\u2013Ritz method. Int J Appl Mech 6(4):1450043","journal-title":"Int J Appl Mech"},{"issue":"1","key":"732_CR22","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0263-8223(97)00038-X","volume":"38","author":"E Feldman","year":"1997","unstructured":"Feldman E, Aboudi J (1997) Buckling analysis of functionally graded plates subjected to uniaxial loading. Compos Struct 38(1):29\u201336","journal-title":"Compos Struct"},{"key":"732_CR23","doi-asserted-by":"crossref","first-page":"3657","DOI":"10.1016\/j.ijsolstr.2005.04.011","volume":"43","author":"S-H Chi","year":"2006","unstructured":"Chi S-H, Chung Y-L (2006) Mechanical behavior of functionally graded material plates under transverse load-Part I: analysis. Int J Solids Struct 43:3657\u20133674","journal-title":"Int J Solids Struct"},{"key":"732_CR24","doi-asserted-by":"crossref","first-page":"3675","DOI":"10.1016\/j.ijsolstr.2005.04.010","volume":"43","author":"S-H Chi","year":"2006","unstructured":"Chi S-H, Chung Y-L (2006) Mechanical behavior of functionally graded material plates under transverse load-Part II: numerical results. Int J Solids Struct 43:3675\u20133691","journal-title":"Int J Solids Struct"},{"key":"732_CR25","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.ijmecsci.2017.06.044","volume":"131","author":"PV Joshi","year":"2017","unstructured":"Joshi PV, Gupta A, Jain NK, Salhotra R, Rawani AM, Ramtekkar GD (2017) Effect of thermal environment on free vibration and buckling of partially cracked isotropic and FGM micro plates based on a non classical Kirchhoff\u2019s plate theory: an analytical approach. Int J Mech Sci 131:155\u2013170","journal-title":"Int J Mech Sci"},{"issue":"4\u20136","key":"732_CR26","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1016\/j.cma.2006.08.002","volume":"196","author":"JR Xiao","year":"2007","unstructured":"Xiao JR, Batra RC, Gilhooley DF, Gillespie Jr JW, McCarthy MA (2007) Analysis of thick plates by using a higher-order shear and normal deformable plate theory and MLPG method with radial basis functions. Comput Methods Appl Mech Eng 196(4\u20136):979\u2013987","journal-title":"Comput Methods Appl Mech Eng"},{"key":"732_CR27","doi-asserted-by":"crossref","first-page":"4457","DOI":"10.1016\/S0020-7683(97)00253-9","volume":"35","author":"GV Praveen","year":"1998","unstructured":"Praveen GV, Reddy JN (1998) Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int J Solids Struct 35:4457\u20134476","journal-title":"Int J Solids Struct"},{"key":"732_CR28","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1016\/j.apm.2009.08.008","volume":"34","author":"S Hosseini-Hashemi","year":"2010","unstructured":"Hosseini-Hashemi S, Taher HRD, Akhavan H, Omidi M (2010) Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl Math Model 34:1276\u20131291","journal-title":"Appl Math Model"},{"issue":"1\u20132","key":"732_CR29","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.jsv.2005.01.031","volume":"289","author":"JS Park","year":"2006","unstructured":"Park JS, Kim JH (2006) Thermal postbuckling and vibration analyses of functionally graded plates. J Sound Vib 289(1\u20132):77\u201393","journal-title":"J Sound Vib"},{"issue":"6","key":"732_CR30","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.12989\/sem.2015.53.6.1215","volume":"53","author":"A Meksi","year":"2015","unstructured":"Meksi A, Benyoucef S, Houari MSA, Tounsi A (2015) A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations. Struct Eng Mech 53(6):1215\u20131240","journal-title":"Struct Eng Mech"},{"issue":"6","key":"732_CR31","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0093-6413(80)90049-X","volume":"7","author":"M Levinson","year":"1980","unstructured":"Levinson M (1980) An accurate simple theory of the statics and dynamics of elastic plates. Mech Res Commun 7(6):343\u2013350","journal-title":"Mech Res Commun"},{"key":"732_CR32","unstructured":"Murthy MV (1981) An improved transverse shear deformation theory for laminated anisotropic plates. NASA Technical Paper, 1903"},{"key":"732_CR33","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.compstruct.2016.08.020","volume":"157","author":"VK Singh","year":"2016","unstructured":"Singh VK, Mahapatra TR, Panda SK (2016) Nonlinear transient analysis of smart laminated composite plate integrated with PVDF sensor and AFC actuator. Compos Struct 157:121\u2013130","journal-title":"Compos Struct"},{"key":"732_CR34","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.ast.2016.05.009","volume":"54","author":"CK Hirwani","year":"2016","unstructured":"Hirwani CK, Patil RK, Panda SK, Mahapatra SS, Mandal SK, Srivastava L et al (2016) Experimental and numerical analysis of free vibration of delaminated curved panel. Aerosp Sci Technol 54:353\u2013370","journal-title":"Aerosp Sci Technol"},{"key":"732_CR35","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.euromechsol.2016.03.014","volume":"59","author":"SS Sahoo","year":"2016","unstructured":"Sahoo SS, Panda SK, Mahapatra TR (2016) Static, free vibration and transient response of laminated composite curved shallow panel\u2014an experimental approach. Eur J Mech A\/Solids 59:95\u2013113","journal-title":"Eur J Mech A\/Solids"},{"issue":"3","key":"732_CR36","doi-asserted-by":"crossref","first-page":"1450105","DOI":"10.1142\/S0219455414501053","volume":"16","author":"TR Mahapatra","year":"2016","unstructured":"Mahapatra TR, Kar VR, Panda SK (2016) Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment. Int J Struct Stab Dyn 16(3):1450105","journal-title":"Int J Struct Stab Dyn"},{"key":"732_CR37","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.ijmecsci.2017.08.057","volume":"133","author":"K Mehar","year":"2017","unstructured":"Mehar K, Panda SK, Mahapatra TR (2017) Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure. Int J Mech Sci 133:319\u2013329","journal-title":"Int J Mech Sci"},{"issue":"5","key":"732_CR38","first-page":"463","volume":"231","author":"SS Sahoo","year":"2017","unstructured":"Sahoo SS, Panda SK, Singh VK (2017) Experimental and numerical investigation of static and free vibration responses of woven glass\/epoxy laminated composite plate. J Proc Inst Mech Eng Part L J Mater Des Appl 231(5):463\u2013478","journal-title":"J Proc Inst Mech Eng Part L J Mater Des Appl"},{"issue":"4","key":"732_CR39","doi-asserted-by":"crossref","first-page":"04016008","DOI":"10.1061\/(ASCE)EM.1943-7889.0001040","volume":"142","author":"SS Sahoo","year":"2016","unstructured":"Sahoo SS, Singh VK, Panda SK (2016) Nonlinear flexural analysis of shallow carbon\/epoxy laminated composite curved panels: experimental and numerical investigation. J Eng Mech 142(4):04016008","journal-title":"J Eng Mech"},{"issue":"2","key":"732_CR40","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1177\/1056789516676515","volume":"27","author":"CK Hirwani","year":"2018","unstructured":"Hirwani CK, Panda SK, Mahapatra SS, Mandal SK, Srivastava L, Buragohain MK (2018) Flexural strength of delaminated composite plate\u2014an experimental validation. Int J Damage Mech 27(2):296\u2013329","journal-title":"Int J Damage Mech"},{"issue":"6","key":"732_CR41","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.1002\/adv.21821","volume":"37","author":"K Mehar","year":"2018","unstructured":"Mehar K, Panda SK (2018) Elastic bending and stress analysis of carbon nanotube reinforced composite plate: experimental, numerical, and simulation. Adv Polym Technol 37(6):1643\u20131657","journal-title":"Adv Polym Technol"},{"issue":"04","key":"732_CR42","doi-asserted-by":"crossref","first-page":"1850027","DOI":"10.1142\/S0219876218500275","volume":"15","author":"CK Hirwani","year":"2018","unstructured":"Hirwani CK, Panda SK, Mandal SK, Mahapatra SS et al (2018) Delamination effect on flexural responses of layered curved shallow shell panel-experimental and numerical analysis. Int J Comput Methods 15(04):1850027","journal-title":"Int J Comput Methods"},{"key":"732_CR43","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.apacoust.2017.12.013","volume":"133","author":"N Sharma","year":"2018","unstructured":"Sharma N, Mahapatra SS, Panda SK, Hirwani CK (2018) Acoustic radiation and frequency response of higher-order shear deformable multilayered composite doubly curved shell panel-An experimental validation. Appl Acoust 133:38\u201351","journal-title":"Appl Acoust"},{"key":"732_CR44","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.oceaneng.2018.04.035","volume":"159","author":"CK Hirwani","year":"2018","unstructured":"Hirwani CK, Panda SK (2018) Numerical and experimental validation of nonlinear deflection and stress responses of pre-damaged glass-fibre reinforced composite structure. Ocean Eng 159:237\u2013252","journal-title":"Ocean Eng"},{"key":"732_CR45","doi-asserted-by":"publisher","DOI":"10.1177\/0954410018761192","author":"K Mehar","year":"2018","unstructured":"Mehar K, Panda SK, Mahapatra TR (2018) Large deformation bending responses of nanotube-reinforced polymer composite panel structure: numerical and experimental analyses. Proc Inst Mech Eng Part G J Aerosp Eng. \nhttps:\/\/doi.org\/10.1177\/0954410018761192","journal-title":"Proc Inst Mech Eng Part G J Aerosp Eng"},{"key":"732_CR46","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.compositesb.2018.12.058","volume":"167","author":"K Mehar","year":"2019","unstructured":"Mehar K, Panda SK (2019) Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification. Compos Part B: Eng 167:317\u2013328","journal-title":"Compos Part B: Eng"},{"issue":"2","key":"732_CR47","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1016\/j.compositesb.2011.08.009","volume":"43","author":"AMA Neves","year":"2012","unstructured":"Neves AMA, Ferreira AJM, Carrera E, Roque CMC, Cinefra M, Jorge RMN et al (2012) A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos B Eng 43(2):711\u2013725","journal-title":"Compos B Eng"},{"issue":"5","key":"732_CR48","doi-asserted-by":"crossref","first-page":"1814","DOI":"10.1016\/j.compstruct.2011.12.005","volume":"94","author":"AMA Neves","year":"2012","unstructured":"Neves AMA, Ferreira AJM, Carrera E, Cinefra M, Roque CMC, Jorge RMN et al (2012) A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos Struct 94(5):1814\u20131825","journal-title":"Compos Struct"},{"issue":"9","key":"732_CR49","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1002\/zamm.201100186","volume":"92","author":"AMA Neves","year":"2012","unstructured":"Neves AMA, Ferreira AJM, Carrera E, Cinefra M, Jorge RMN, Soares CMM (2012) Buckling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear deformation theory and collocation with radial basis functions. ZAMM J Appl Math Mech 92(9):749\u2013766","journal-title":"ZAMM J Appl Math Mech"},{"issue":"2","key":"732_CR50","first-page":"147","volume":"6","author":"A Bouadi","year":"2018","unstructured":"Bouadi A, Bousahla AA, Houari MSA, Heireche H, Tounsi A (2018) A new nonlocal HSDT for analysis of stability of single layer graphene sheet. Adv Nano Res 6(2):147\u2013162","journal-title":"Adv Nano Res"},{"issue":"6","key":"732_CR51","first-page":"661","volume":"68","author":"F Bourada","year":"2018","unstructured":"Bourada F, Amara K, Bousahla AA, Tounsi A, Mahmoud SR (2018) A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates. Struct Eng Mech 68(6):661\u2013675","journal-title":"Struct Eng Mech"},{"issue":"4","key":"732_CR52","first-page":"391","volume":"64","author":"H Khetir","year":"2017","unstructured":"Khetir H, Bachir Bouiadjra M, Houari MSA, Tounsi A, Mahmoud SR (2017) A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates. Struct Eng Mech 64(4):391\u2013402","journal-title":"Struct Eng Mech"},{"issue":"4","key":"732_CR53","first-page":"397","volume":"21","author":"Y Mokhtar","year":"2018","unstructured":"Mokhtar Y, Heireche H, Bousahla AA, Houari MSA, Tounsi A, Mahmoud SR (2018) A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory. Smart Struct Syst 21(4):397\u2013405","journal-title":"Smart Struct Syst"},{"issue":"3","key":"732_CR54","doi-asserted-by":"crossref","first-page":"289","DOI":"10.12989\/sss.2017.19.3.289","volume":"19","author":"A Chikh","year":"2017","unstructured":"Chikh A, Tounsi A, Hebali H, Mahmoud SR (2017) Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT. Smart Struct Syst 19(3):289\u2013297","journal-title":"Smart Struct Syst"},{"issue":"1","key":"732_CR55","first-page":"109","volume":"27","author":"H Fourn","year":"2018","unstructured":"Fourn H, Ait Atmane H, Bourada M, Bousahla AA, Tounsi A, Mahmoud SR (2018) A novel four variable refined plate theory for wave propagation in functionally graded material plates. Steel Compos Struct 27(1):109\u2013122","journal-title":"Steel Compos Struct"},{"issue":"2","key":"732_CR56","doi-asserted-by":"crossref","first-page":"257","DOI":"10.12989\/scs.2016.22.2.257","volume":"22","author":"MSA Houari","year":"2016","unstructured":"Houari MSA, Tounsi A, Bessaim A, Mahmoud SR (2016) A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates. Steel Compos Struct 22(2):257\u2013276","journal-title":"Steel Compos Struct"},{"issue":"2","key":"732_CR57","first-page":"103","volume":"14","author":"Z Belabed","year":"2018","unstructured":"Belabed Z, Bousahla AA, Houari MSA, Tounsi A, Mahmoud SR (2018) A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate. Earthq Struct 14(2):103\u2013115","journal-title":"Earthq Struct"},{"issue":"6","key":"732_CR58","first-page":"717","volume":"25","author":"H Hachemi","year":"2017","unstructured":"Hachemi H, Kaci A, Houari MSA, Bourada A, Tounsi A, Mahmoud SR (2017) A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations. Steel Compos Struct 25(6):717\u2013726","journal-title":"Steel Compos Struct"},{"issue":"5","key":"732_CR59","first-page":"621","volume":"65","author":"A Kaci","year":"2018","unstructured":"Kaci A, Houari MSA, Bousahla AA, Tounsi A, Mahmoud SR (2018) \u201cPost-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory\u201d. Struct Eng Mech 65(5):621\u2013631","journal-title":"Struct Eng Mech"},{"issue":"3","key":"732_CR60","first-page":"369","volume":"20","author":"A Mouffoki","year":"2017","unstructured":"Mouffoki A, Adda Bedia EA, Houari MSA, Tounsi A, Mahmoud SR (2017) Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory. Smart Struct Syst 20(3):369\u2013383","journal-title":"Smart Struct Syst"},{"issue":"2","key":"732_CR61","first-page":"145","volume":"64","author":"M Zidi","year":"2017","unstructured":"Zidi M, Houari MSA, Tounsi A, Bessaim A, Mahmoud SR (2017) A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams. Struct Eng Mech 64(2):145\u2013153","journal-title":"Struct Eng Mech"},{"issue":"1","key":"732_CR62","first-page":"61","volume":"66","author":"A Bouhadra","year":"2018","unstructured":"Bouhadra A, Tounsi A, Bousahla AA, Benyoucef S, Mahmoud SR (2018) Improved HSDT accounting for effect of thickness stretching in advanced composite plates. Struct Eng Mech 66(1):61\u201373","journal-title":"Struct Eng Mech"},{"issue":"2","key":"732_CR63","first-page":"201","volume":"27","author":"B Karami","year":"2018","unstructured":"Karami B, Janghorban M, Tounsi A (2018) Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles. Steel Compos Struct 27(2):201\u2013216","journal-title":"Steel Compos Struct"},{"key":"732_CR64","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.tws.2018.02.025","volume":"129","author":"B Karami","year":"2018","unstructured":"Karami B, Janghorban M, Tounsi A (2018) Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory. Thin-Walled Struct 129:251\u2013264","journal-title":"Thin-Walled Struct"},{"key":"732_CR65","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.compositesb.2018.09.051","volume":"159","author":"FZ Zaoui","year":"2019","unstructured":"Zaoui FZ, Ouinas D, Tounsi A (2019) New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations. Compos Part B 159:231\u2013247","journal-title":"Compos Part B"},{"issue":"2","key":"732_CR66","doi-asserted-by":"crossref","first-page":"409","DOI":"10.12989\/scs.2015.18.2.409","volume":"18","author":"M Bourada","year":"2015","unstructured":"Bourada M, Kaci A, Houari MSA, Tounsi A (2015) A new simple shear and normal deformations theory for functionally graded beams. Steel Compos Struct 18(2):409\u2013423","journal-title":"Steel Compos Struct"},{"issue":"1","key":"732_CR67","doi-asserted-by":"crossref","first-page":"9","DOI":"10.12989\/gae.2017.12.1.009","volume":"12","author":"A Benahmed","year":"2017","unstructured":"Benahmed A, Houari MSA, Benyoucef S, Belakhdar K, Tounsi. A (2017) A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation. Geomech Eng 12(1):9\u201334","journal-title":"Geomech Eng"},{"key":"732_CR68","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.compositesb.2013.12.057","volume":"60","author":"Z Belabed","year":"2014","unstructured":"Belabed Z, Houari MSA, Tounsi A, Mahmoud SR, Anwar B\u00e9g O (2014) An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates. Compos Part B 60:274\u2013283","journal-title":"Compos Part B"},{"issue":"1","key":"732_CR69","doi-asserted-by":"crossref","first-page":"235","DOI":"10.12989\/scs.2015.18.1.235","volume":"18","author":"A Hamidi","year":"2015","unstructured":"Hamidi A, Houari MSA, Mahmoud SR, Tounsi A (2015) A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates. Steel Compos Struct 18(1):235\u2013253","journal-title":"Steel Compos Struct"},{"key":"732_CR70","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.nucengdes.2012.05.001","volume":"250","author":"DK Jha","year":"2012","unstructured":"Jha DK, Kant T, Singh RK (2012) Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates. Nucl Eng Des 250:8\u201313","journal-title":"Nucl Eng Des"},{"key":"732_CR71","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.compositesb.2016.04.035","volume":"96","author":"SS Akavci","year":"2016","unstructured":"Akavci SS (2016) Mechanical behavior of functionally graded sandwich plates on elastic foundation. Compos B 96:136\u2013152","journal-title":"Compos B"},{"key":"732_CR72","volume-title":"Energy principles and variational methods in applied mechanics","author":"JN Reddy","year":"2002","unstructured":"Reddy JN (2002) Energy principles and variational methods in applied mechanics. Wiley, New York"},{"issue":"11","key":"732_CR73","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1016\/0020-7683(70)90076-4","volume":"6","author":"S Srinivas","year":"1970","unstructured":"Srinivas S, Rao AK (1970) Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. Int J Solids Struct 6(11):1463\u20131481","journal-title":"Int J Solids Struct"},{"issue":"18","key":"732_CR74","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1177\/073168403027618","volume":"22","author":"RP Shimpi","year":"2003","unstructured":"Shimpi RP, Arya H, Naik NK (2003) A higher order displacement model for the plate analysis. J Reinf Plast Compos 22(18):1667\u20131688","journal-title":"J Reinf Plast Compos"},{"issue":"2","key":"732_CR75","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0022-460X(70)90089-1","volume":"12","author":"S Srinivas","year":"1970","unstructured":"Srinivas S, Joga CV, Rao AK (1970) An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates. J Sound Vib 12(2):187\u2013199","journal-title":"J Sound Vib"},{"issue":"2","key":"732_CR76","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0022-460X(85)90383-9","volume":"98","author":"JN Reddy","year":"1985","unstructured":"Reddy JN, Phan ND (1985) Stability and vibration of isotropic, orthotropic and laminated plates according to a shear deformation higher-order theory. J Sound Vib 98(2):157\u2013170","journal-title":"J Sound Vib"},{"issue":"11","key":"732_CR77","doi-asserted-by":"crossref","first-page":"4549","DOI":"10.1007\/s00707-018-2247-7","volume":"229","author":"D Shahsavari","year":"2018","unstructured":"Shahsavari D, Karami B, Fahham HR, Li L (2018) On the shear buckling of porous nanoplates using a new size-dependent quasi-3D shear deformation theory. Acta Mech 229(11):4549\u20134573","journal-title":"Acta Mech"},{"issue":"1","key":"732_CR78","first-page":"99","volume":"28","author":"B Karami","year":"2018","unstructured":"Karami B, Janghorban M, Shahsavari D, Tounsi A (2018) A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates. Steel Compos Struct 28(1):99\u2013110","journal-title":"Steel Compos Struct"},{"key":"732_CR79","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.ast.2017.11.004","volume":"72","author":"D Shahsavari","year":"2018","unstructured":"Shahsavari D, Shahsavari M, Li L, Karami B (2018) A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler\/Pasternak\/Kerr foundation. Aerosp Sci Technol 72:134\u2013149","journal-title":"Aerosp Sci Technol"},{"key":"732_CR80","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ijengsci.2018.11.005","volume":"135","author":"GL She","year":"2019","unstructured":"She GL, Yuan FG, Karami B, Ren YR, Xiao WS (2019) On nonlinear bending behavior of FG porous curved nanotubes. Int J Eng Sci 135:58\u201374","journal-title":"Int J Eng Sci"},{"issue":"12","key":"732_CR81","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1080\/15376494.2017.1323143","volume":"25","author":"B Karami","year":"2018","unstructured":"Karami B, Shahsavari D, Janghorban M (2018) Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory. Mech Adv Mater Struct 25(12):1047\u20131057","journal-title":"Mech Adv Mater Struct"},{"key":"732_CR82","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1016\/j.actaastro.2017.12.011","volume":"143","author":"B Karami","year":"2018","unstructured":"Karami B, Janghorban M, Li L (2018) On guided wave propagation in fully clamped porous functionally graded nanoplates. Acta Astronaut 143:380\u2013390","journal-title":"Acta Astronaut"},{"issue":"4","key":"732_CR83","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1080\/01495739.2017.1393781","volume":"41","author":"B Karami","year":"2018","unstructured":"Karami B, Shahsavari D, Li L (2018) Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field. J Therm Stress 41(4):483\u2013499","journal-title":"J Therm Stress"},{"key":"732_CR84","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.ast.2018.10.001","volume":"82","author":"B Karami","year":"2018","unstructured":"Karami B, Shahsavari D, Janghorban M (2018) A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates. Aerosp Sci Technol 82:499\u2013512","journal-title":"Aerosp Sci Technol"},{"issue":"1","key":"732_CR85","first-page":"53","volume":"29","author":"D Shahsavari","year":"2018","unstructured":"Shahsavari D, Karami B, Li L (2018) A high-order gradient model for wave propagation analysis of porous FG nanoplates. Steel Compos Struct 29(1):53\u201366","journal-title":"Steel Compos Struct"},{"issue":"3","key":"732_CR86","first-page":"349","volume":"29","author":"B Karami","year":"2018","unstructured":"Karami B, Shahsavari D, Nazemosadat SMR, Li L, Ebrahimi A (2018) Thermal buckling of smart porous functionally graded nanobeam rested on kerr foundation. Steel Compos Struct 29(3):349\u2013362.","journal-title":"Steel Compos Struct"},{"key":"732_CR87","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.euromechsol.2017.09.004","volume":"67","author":"D Shahsavari","year":"2018","unstructured":"Shahsavari D, Karami B, Mansouri S (2018) Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories. Eur J Mech A\/Solids 67:200\u2013214","journal-title":"Eur J Mech A\/Solids"},{"key":"732_CR88","doi-asserted-by":"publisher","DOI":"10.1007\/s00366-018-0664-9","author":"B Karami","year":"2018","unstructured":"Karami B, Janghorban M, Tounsi A (2018) Galerkin\u2019s approach for buckling analysis of functionally graded anisotropic nanoplates\/different boundary conditions. Eng Comput. \nhttps:\/\/doi.org\/10.1007\/s00366-018-0664-9","journal-title":"Eng Comput"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-019-00732-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00366-019-00732-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-019-00732-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T20:23:44Z","timestamp":1589833424000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00366-019-00732-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,14]]},"references-count":88,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["732"],"URL":"https:\/\/doi.org\/10.1007\/s00366-019-00732-1","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,14]]},"assertion":[{"value":"18 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 March 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}