{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T06:44:22Z","timestamp":1763102662966,"version":"3.45.0"},"reference-count":69,"publisher":"Tech Science Press","issue":"1","license":[{"start":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T00:00:00Z","timestamp":1743292800000},"content-version":"vor","delay-in-days":88,"URL":"https:\/\/doi.org\/10.32604\/TSP-CROSSMARKPOLICY"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["CMC"],"published-print":{"date-parts":[[2025]]},"DOI":"10.32604\/cmc.2025.061741","type":"journal-article","created":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T03:27:22Z","timestamp":1740626842000},"page":"79-96","update-policy":"https:\/\/doi.org\/10.32604\/tsp-crossmarkpolicy","source":"Crossref","is-referenced-by-count":0,"title":["A DFE<sup>2<\/sup>-SPCE Method for Multiscale Parametric Analysis of Heterogenous Piezoelectric Materials and Structures"],"prefix":"10.32604","volume":"83","author":[{"given":"Qingxiang","family":"Pei","sequence":"first","affiliation":[]},{"given":"Fan","family":"Li","sequence":"additional","affiliation":[]},{"given":"Ziheng","family":"Fei","sequence":"additional","affiliation":[]},{"given":"Haojie","family":"Lian","sequence":"additional","affiliation":[]},{"given":"Xiaohui","family":"Yuan","sequence":"additional","affiliation":[]}],"member":"17807","published-online":{"date-parts":[[2025]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.3390\/s21124145","article-title":"A systematic review of piezoelectric materials and energy harvesters for industrial applications","volume":"21","author":"Aabid","year":"2021","journal-title":"Sensors"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"77","DOI":"10.3390\/act4020077","article-title":"Survey of active structural control and repair using piezoelectric patches","volume":"4","author":"Abuzaid","year":"2015","journal-title":"Actuators"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"104057","DOI":"10.1016\/j.ijengsci.2024.104057","article-title":"Thermo-electro-mechanical vibration analysis for piezoelectric plates under two-parameter elastic foundation with general boundary conditions","volume":"201","author":"He","year":"2024","journal-title":"Int J Eng Sci"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"113213","DOI":"10.1016\/j.oceaneng.2022.113213","article-title":"A unified analysis model of FGM double-layered submarine type coupled structure with spectral geometry method","volume":"267","author":"He","year":"2023","journal-title":"Ocean Eng"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"6115","DOI":"10.1016\/j.jeurceramsoc.2021.06.022","article-title":"High voltage coefficient piezoelectric materials and their applications","volume":"41","author":"Hooper","year":"2021","journal-title":"J Eur Ceram Soc"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1016\/j.jeurceramsoc.2020.07.071","article-title":"Textured Mn-doped PIN-PMN-PT ceramics: harnessing intrinsic piezoelectricity for high-power transducer applications","volume":"41","author":"Watson","year":"2021","journal-title":"J Eur Ceram Soc"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"2129","DOI":"10.1177\/00219983221082492","article-title":"Implementation of multiscale mechanisms in finite element analysis of active composite structures","volume":"56","author":"Micheal","year":"2022","journal-title":"J Compos Mater"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"31259","DOI":"10.1016\/j.ceramint.2021.07.302","article-title":"Bending vibration characteristics of the piezoelectric composite double laminated vibrator","volume":"47","author":"Lv","year":"2021","journal-title":"Ceram Int"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"105145","DOI":"10.1016\/j.euromechsol.2023.105145","article-title":"A Galerkin approach for analysing coupling effects in the piezoelectric semiconducting beams","volume":"103","author":"Liu","year":"2024","journal-title":"Eur J Mech A-Solid"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"160666","DOI":"10.1016\/j.jallcom.2021.160666","volume":"881","author":"Jia","year":"2021","journal-title":"J Alloys Compd"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1109\/TDEI.2019.008291","article-title":"Increase of capacitance of thick dielectrics by fringe effect","volume":"26","author":"Chen","year":"2019","journal-title":"IEEE Trans Dielectr Electr Insul"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1021\/acsaelm.8b00107","article-title":"Large thermal-electrical response and rectifying conduction behavior in asymmetrically reduced ferroelectric ceramics","volume":"1","author":"Chen","year":"2019","journal-title":"ACS Appl Electron Mater"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"16554","DOI":"10.1007\/s10854-021-06211-y","article-title":"Effects of density inhomogeneity in green body on the structure and properties of ferroelectric ceramics","volume":"32","author":"Chen","year":"2021","journal-title":"J Mater Sci-Mater El"},{"key":"ref14","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1111\/j.1151-2916.1999.tb01840.x","article-title":"Ferroelectric ceramics: history and technology","volume":"82","author":"Haertling","year":"1999","journal-title":"J Am Ceram Soc"},{"key":"ref15","first-page":"153","article-title":"Multiscale composite analysis in Abaqus: theory and motivations","volume":"61","author":"MacKrell","year":"2017","journal-title":"Plast Compos"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"118554","DOI":"10.1016\/j.oceaneng.2024.118554","article-title":"FEM-BEM analysis of acoustic interaction with submerged thin-shell structures under seabed reflection conditions","volume":"309","author":"Chen","year":"2024","journal-title":"Ocean Eng"},{"key":"ref17","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.enganabound.2021.11.005","article-title":"Bi-material topology optimization for fully coupled structural-acoustic systems with isogeometric FEM-BEM","volume":"135","author":"Chen","year":"2022","journal-title":"Eng Anal Boundary Elem"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"5151","DOI":"10.1002\/nme.7345","article-title":"A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method\u2014application to 2D acoustic scattering problems","volume":"124","author":"Chen","year":"2023","journal-title":"Int J Numer Methods Eng"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1016\/j.enganabound.2022.11.010","article-title":"Acoustic shape optimization based on isogeometric boundary element method with subdivision surfaces","volume":"146","author":"Lu","year":"2023","journal-title":"Eng Anal Boundary Elem"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"106112","DOI":"10.1016\/j.enganabound.2024.106112","article-title":"Deep-neural-network-based framework for the accelerating uncertainty quantification of a structural-acoustic fully coupled system in a shallow sea","volume":"171","author":"Chen","year":"2025","journal-title":"Eng Anal Boundary Elem"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1007\/s00466-014-1044-y","article-title":"Multi-physics computational grains (MPCGs) for direct numerical simulation (DNS) of piezoelectric composite\/porous materials and structures","volume":"54","author":"Bishay","year":"2014","journal-title":"Comput Mech"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/S0093-6413(96)00081-X","article-title":"Homogenization of heterogeneous piezoelectric medium","volume":"24","author":"Otero","year":"1997","journal-title":"Mech Res Commun"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1121\/1.1537710","article-title":"Numerical homogenization techniques applied to piezoelectric composites","volume":"113","author":"Lenglet","year":"2003","journal-title":"J Acoust Soc Am"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.enganabound.2021.09.014","article-title":"Generalized multiscale finite element method for piezoelectric problem in heterogeneous media","volume":"135","author":"Ammosov","year":"2022","journal-title":"Eng Anal Boundary Elem"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1038\/s41563-020-00913-0","article-title":"Mesoscopic and multiscale modelling in materials","volume":"20","author":"Fish","year":"2021","journal-title":"Nat Mater"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"060802","DOI":"10.1115\/1.4025633","article-title":"Advances in developing electromechanically coupled computational methods for piezoelectrics\/ferroelectrics at multiscale","volume":"65","author":"Fang","year":"2013","journal-title":"Appl Mech Rev"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.commatsci.2014.01.059","article-title":"A hierarchical multiscale approach for predicting thermo-electro-mechanical behavior of heterogeneous piezoelectric smart materials","volume":"87","author":"Lv","year":"2014","journal-title":"Comput Mater Sci"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/j.compositesb.2010.10.010","article-title":"Comprehensive investigation on hierarchical multiscale homogenization using representative volume element for piezoelectric nanocomposites","volume":"42","author":"Jafari","year":"2011","journal-title":"Compos Part B-Eng"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1007\/s00466-015-1147-0","article-title":"Computational homogenization of fibrous piezoelectric materials","volume":"55","author":"Maruccio","year":"2015","journal-title":"Comput Mech"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.compstruct.2017.02.005","article-title":"An efficient multiscale computational formulation for geometric nonlinear analysis of heterogeneous piezoelectric composite","volume":"167","author":"Fu","year":"2017","journal-title":"Compos Struct"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"118063","DOI":"10.1016\/j.jsv.2023.118063","article-title":"Analysis of smart laminated composites integrated with piezoelectric patches using spectral element method and lamination parameters","volume":"567","author":"Motlagh","year":"2023","journal-title":"J Sound Vib"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"095023","DOI":"10.1088\/1361-665X\/aceba5","article-title":"High-fidelity dynamics of piezoelectric covered metamaterial timoshenko beams using the spectral element method","volume":"32","author":"Hu","year":"2023","journal-title":"Smart Mater Struct"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/S0927-0256(99)00077-4","volume":"16","author":"Feyel","year":"1999","journal-title":"Comput Mater Sci"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"3233","DOI":"10.1016\/S0045-7825(03)00348-7","volume":"192","author":"Feyel","year":"2003","journal-title":"Comput Methods Appl Mech Eng"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"5427","DOI":"10.1016\/S0045-7825(01)00179-7","article-title":"A class of general algorithms for multi-scale analyses of heterogeneous media","volume":"190","author":"Terada","year":"2001","journal-title":"Comput Methods Appl Mech Eng"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1080\/12506559.2001.11869262","volume":"10","author":"Feyel","year":"2001","journal-title":"Revue Europ\u00e9enne Des \u00e9l\u00e9ments Finis"},{"key":"ref37","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1016\/j.compstruct.2015.10.025","volume":"136","author":"Papadopoulos","year":"2016","journal-title":"Compos Struct"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.compstruct.2018.03.072","volume":"193","author":"Tikarrouchine","year":"2018","journal-title":"Compos Struct"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.compstruct.2018.06.033","volume":"201","author":"Herwig","year":"2018","journal-title":"Compos Struct"},{"key":"ref40","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.compstruct.2018.12.028","volume":"211","author":"Xu","year":"2019","journal-title":"Compos Struct"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"112694","DOI":"10.1016\/j.cma.2019.112694","volume":"360","author":"Tan","year":"2020","journal-title":"Comput Methods Appl Mech Eng"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"108537","DOI":"10.1016\/j.engfracmech.2022.108537","volume":"269","author":"Chen","year":"2022","journal-title":"Eng Fract Mech"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1007\/s00466-021-02012-6","article-title":"Transient multi-scale analysis with micro-inertia effects using Direct FE 2 method","volume":"67","author":"Zhi","year":"2021","journal-title":"Comput Mech"},{"key":"ref44","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.compstruct.2019.02.010","article-title":"Numerical analysis of the vibration response of skew magneto-electro-elastic plates based on the higher-order shear deformation theory","volume":"214","author":"Vinyas","year":"2019","journal-title":"Compos Struct"},{"key":"ref45","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.ijprt.2017.08.001","article-title":"Design method for piezoelectric cantilever beam structure under low frequency condition","volume":"11","author":"Zhao","year":"2018","journal-title":"Int J Pavement Res Technol"},{"key":"ref46","doi-asserted-by":"crossref","first-page":"103925","DOI":"10.1016\/j.tafmec.2023.103925","article-title":"Enhancing deep neural networks for multivariate uncertainty analysis of cracked structures by POD-RBF","volume":"125","author":"Shen","year":"2023","journal-title":"Theor Appl Fract Mech"},{"key":"ref47","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.apm.2023.08.040","article-title":"Multivariate uncertainty analysis of fracture problems through model order reduction accelerated SBFEM","volume":"125","author":"Shen","year":"2024","journal-title":"Appl Math Modell"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"115806","DOI":"10.1016\/j.apm.2024.115806","article-title":"Bayesian uncertainty analysis for underwater 3D reconstruction with neural radiance fields","volume":"138","author":"Lian","year":"2025","journal-title":"Appl Math Modell"},{"key":"ref49","doi-asserted-by":"crossref","first-page":"117388","DOI":"10.1016\/j.oceaneng.2024.117388","article-title":"Uncertainty quantification of vibro-acoustic coupling problems for robotic manta ray models based on deep learning","volume":"299","author":"Qu","year":"2024","journal-title":"Ocean Eng"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.apm.2022.09.030","article-title":"Generalized isogeometric boundary element method for uncertainty analysis of time-harmonic wave propagation in infinite domains","volume":"114","author":"Chen","year":"2023","journal-title":"Appl Math Modell"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.enganabound.2005.01.007","article-title":"Stochastic BEM with spectral approach in elastostatic and elastodynamic problems with geometrical uncertainty","volume":"29","author":"Honda","year":"2005","journal-title":"Eng Anal Boundary Elem"},{"key":"ref52","doi-asserted-by":"crossref","first-page":"1831","DOI":"10.1002\/nme.1620231004","article-title":"Random field finite elements","volume":"23","author":"Liu","year":"1986","journal-title":"Int J Numeri Methods Eng"},{"key":"ref53","doi-asserted-by":"crossref","first-page":"117464","DOI":"10.1016\/j.cma.2024.117464","article-title":"Uncertainty quantification of 3D acoustic shape sensitivities with generalized nth-order perturbation boundary element methods","volume":"433","author":"Chen","year":"2025","journal-title":"Comput Methods Appl Mech Eng"},{"key":"ref54","doi-asserted-by":"crossref","first-page":"114130","DOI":"10.1016\/j.cma.2021.114130","article-title":"A hybrid sequential sampling strategy for sparse polynomial chaos expansion based on compressive sampling and Bayesian experimental design","volume":"386","author":"Zhang","year":"2021","journal-title":"Comput Methods Appl Mech Eng"},{"key":"ref55","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.jcp.2015.01.034","article-title":"A new surrogate modeling technique combining Kriging and polynomial chaos expansions-Application to uncertainty analysis in computational dosimetry","volume":"286","author":"Kersaudy","year":"2015","journal-title":"J Comput Phys"},{"key":"ref56","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1002\/best.201800048","article-title":"Polynomial chaos expansion for surrogate modelling: theory and software","volume":"113","author":"Novak","year":"2018","journal-title":"Beton-und Stahlbetonbau"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"123783","DOI":"10.1016\/j.ijheatmasstransfer.2022.123783","article-title":"Isogeometric dual reciprocity BEM for solving non-Fourier transient heat transfer problems in FGMs with uncertainty analysis","volume":"203","author":"Cao","year":"2023","journal-title":"Int J Heat Mass Transfer"},{"key":"ref58","doi-asserted-by":"crossref","first-page":"2345","DOI":"10.1016\/j.jcp.2010.12.021","article-title":"Adaptive sparse polynomial chaos expansion based on least angle regression","volume":"230","author":"Blatman","year":"2011","journal-title":"J Comput Phys"},{"key":"ref59","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.jcp.2016.12.015","article-title":"A robust and efficient stepwise regression method for building sparse polynomial chaos expansions","volume":"332","author":"Abraham","year":"2017","journal-title":"J Comput Phys"},{"key":"ref60","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.cma.2017.01.033","article-title":"Bayesian sparse polynomial chaos expansion for global sensitivity analysis","volume":"318","author":"Shao","year":"2017","journal-title":"Comput Methods Appl Mech Eng"},{"key":"ref61","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.jcp.2019.01.035","article-title":"Some greedy algorithms for sparse polynomial chaos expansions","volume":"387","author":"Baptista","year":"2019","journal-title":"J Comput Phys"},{"key":"ref62","first-page":"17","article-title":"Sparse polynomial chaos expansion based on D-MORPH regression","volume":"323","author":"Cheng","year":"2018","journal-title":"Appl Math Comput"},{"key":"ref63","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.probengmech.2009.10.003","article-title":"An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis","volume":"25","author":"Blatman","year":"2010","journal-title":"Probab Eng Mech"},{"key":"ref64","doi-asserted-by":"crossref","first-page":"107025","DOI":"10.1016\/j.ress.2020.107025","article-title":"Active sparse polynomial chaos expansion for system reliability analysis","volume":"202","author":"Zhou","year":"2020","journal-title":"Reliab Eng Syst Saf"},{"key":"ref65","first-page":"593","article-title":"Sparse polynomial chaos expansions: literature survey and benchmark","volume":"9","author":"L\u00fcthen","year":"2021","journal-title":"SIAM-ASA J Uncertain"},{"key":"ref66","doi-asserted-by":"crossref","first-page":"116696","DOI":"10.1016\/j.cma.2023.116696","volume":"420","author":"Li","year":"2024","journal-title":"Comput Methods Appl Mech Eng"},{"key":"ref67","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.cma.2017.01.041","article-title":"Accelerating Monte Carlo estimation with derivatives of high-level finite element models","volume":"318","author":"Hauseux","year":"2017","journal-title":"Comput Methods Appl Mech Eng"},{"key":"ref68","unstructured":"Abaqus Analysis User\u2019s Guide (6.14). Abaqus. 2013."},{"key":"ref69","doi-asserted-by":"crossref","DOI":"10.1142\/6057","author":"Yang","year":"2006","journal-title":"Mechanics of piezoelectric structures"}],"container-title":["Computers, Materials & Continua"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/cdn.techscience.cn\/files\/cmc\/2025\/TSP_CMC-83-1\/TSP_CMC_61741\/TSP_CMC_61741.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T06:40:33Z","timestamp":1763102433000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.techscience.com\/cmc\/v83n1\/60125"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":69,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025]]},"published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.32604\/cmc.2025.061741","relation":{},"ISSN":["1546-2226"],"issn-type":[{"type":"electronic","value":"1546-2226"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"2024-12-02","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-02-03","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-26","order":2,"name":"published","label":"Published Online","group":{"name":"publication_history","label":"Publication History"}}]}}