The GDQ method for the free vibration analysis of arbitrarily shaped laminated composite shells using a NURBS-based isogeometric approach

Composite Structures - Tập 154 - Trang 190-218 - 2016
Francesco Tornabene1, Nicholas Fantuzzi1, Michele Bacciocchi1
1DICAM Department, School of Engineering and Architecture, University of Bologna, Italy

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Tài liệu tham khảo

Kraus, 1967

Reddy, 2004

Tornabene, 2016

Tornabene, 2016

Dozio, 2011, A variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness, J. Sound Vib., 330, 4611, 10.1016/j.jsv.2011.04.022

Dozio, 2012, Ritz analysis of vibrating rectangular and skew multilayered plates based on advanced variable-kinematic models, Compos. Struct., 94, 2118, 10.1016/j.compstruct.2012.02.008

Brischetto, 2014, An exact 3d solution for free vibrations of multilayered cross-ply composite and sandwich plates and shells, Int. J. Appl. Mech., 6, 1450076, 10.1142/S1758825114500768

Brischetto, 2016, Convergence analysis of the exponential matrix method for the solution of 3D equilibrium equations for free vibration analysis of plates and shells, Compos. Part B-Eng., 98, 453, 10.1016/j.compositesb.2016.05.047

Groh, 2015, Static inconsistencies in certain axiomatic higher-order shear deformation theories for beams, plates and shells, Compos. Struct., 120, 231, 10.1016/j.compstruct.2014.10.006

Groh, 2015, On displacement-based and mixed-variational equivalent single layer theories for modelling highly heterogeneous laminated beams, Int. J. Solids Struct., 59, 147, 10.1016/j.ijsolstr.2015.01.020

Dozio, 2016, Variable kinematic finite element models of multilayered composite plates coupled with acoustic fluid, Mech. Adv. Mater. Struct., 23, 981, 10.1080/15376494.2015.1121558

Dozio, 2016, A hierarchical formulation of the state-space Levy’s method for vibration analysis of thin and thick multilayered shells, Compos. Part B-Eng., 98, 97, 10.1016/j.compositesb.2016.05.022

Vescovini, 2016, A variable-kinematic model for variable stiffness plates: vibration and buckling analysis, Compos. Struct., 142, 15, 10.1016/j.compstruct.2016.01.068

Zucco, 2016, Mixed shell element for static and buckling analysis of variable angle tow composite plates, Compos. Struct., 152, 324, 10.1016/j.compstruct.2016.05.030

Barbero, 2014, Koiter asymptotic analysis of folded laminated composite plates, Compos. Part B-Eng., 61, 267, 10.1016/j.compositesb.2014.01.045

Carpentieri, 2015, An accurate one-dimensional theory for the dynamics of laminated composite curved beams, J. Sound Vib., 336, 96, 10.1016/j.jsv.2014.09.041

Mahapatra, 2016, Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model, Mech. Adv. Mater. Struct., 23, 1343, 10.1080/15376494.2015.1085606

Sahoo, 2016, Static, free vibration and transient response of laminated composite curved shallow panel – an experimental approach, Eur. J. Mech. A-Solids, 59, 95, 10.1016/j.euromechsol.2016.03.014

Biswal, 2016, Vibration of composite cylindrical shallow shells subjected to hygrothermal loading-experimental and numerical results, Compos. Part B-Eng., 98, 108, 10.1016/j.compositesb.2016.05.037

Xin, 2016, Free vibration analysis of laminated cylindrical panels using discrete singular convolution, Compos. Struct., 149, 362, 10.1016/j.compstruct.2016.04.027

Javed, 2016, Vibration analysis of a shear deformed anti-symmetric angle-ply conical shells with varying sinusoidal thickness, Struct. Eng. Mech., 58, 1001, 10.12989/sem.2016.58.6.1001

Wang, 2016, Static analysis of sandwich panels with non-homogeneous soft-cores by novel weak form quadrature element method, Compos. Struct., 146, 207, 10.1016/j.compstruct.2016.03.017

Kulikov, 2016, Three-dimensional vibration analysis of layered and functionally graded plates through sampling surfaces formulation, Compos. Struct., 152, 349, 10.1016/j.compstruct.2016.05.043

Kulikov, 2016, Exact geometry solid-shell element based on a sampling surfaces technique for 3D stress analysis of doubly-curved composite shells, Curved Layer. Struct., 3, 1

Viola, 2013, General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels, Compos. Struct., 95, 639, 10.1016/j.compstruct.2012.08.005

Viola, 2013, Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories, Compos. Struct., 101, 59, 10.1016/j.compstruct.2013.01.002

Tornabene, 2013, General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels, Compos. Struct., 104, 94, 10.1016/j.compstruct.2013.04.009

Viola, 2013, Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape, Compos. Struct., 106, 815, 10.1016/j.compstruct.2013.07.034

Fantuzzi, 2014, Strong formulation finite element method for arbitrarily shaped laminated plates – II. Numerical analysis, Adv. Aircraft Space. Sci., 1, 143

Fantuzzi, 2014, Strong formulation finite element method for arbitrarily shaped laminated plates – I. Theoretical analysis, Adv. Aircraft Space. Sci., 1, 124

Tornabene, 2015, Accurate inter-laminar recovery for plates and doubly-curved shells with variable radii of curvature using layer-wise theories, Compos. Struct., 124, 368, 10.1016/j.compstruct.2014.12.062

Tornabene, 2015, Dynamic analysis of thick and thin elliptic shell structures made of laminated composite materials, Compos. Struct., 133, 278, 10.1016/j.compstruct.2015.06.052

Tornabene, 2015, Higher-order theories for the free vibration of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method, Compos. Part B-Eng., 81, 196, 10.1016/j.compositesb.2015.07.012

Tornabene, 2015, Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels, Compos. Part B-Eng., 81, 231, 10.1016/j.compositesb.2015.07.015

Tornabene, 2015, Free vibrations of composite oval and elliptic cylinders by the generalized differential quadrature method, Thin-Wall. Struct., 97, 114, 10.1016/j.tws.2015.08.023

Tornabene, 2015, A new approach for treating concentrated loads in doubly-curved composite deep shells with variable radii of curvature, Compos. Struct., 131, 433, 10.1016/j.compstruct.2015.05.049

Fantuzzi, 2015, Radial basis functions based on differential quadrature method for the free vibration of laminated composite arbitrary shaped plates, Compos. Part B-Eng., 78, 65, 10.1016/j.compositesb.2015.03.027

Tornabene, 2016, The local GDQ method for the natural frequencies of doubly-curved shells with variable thickness: a general formulation, Compos. Part B-Eng., 92, 265, 10.1016/j.compositesb.2016.02.010

Tornabene, 2016, General higher order layer-wise theory for free vibrations of doubly-curved laminated composite shells and panels, Mech. Adv. Mat. Struct., 23, 1046, 10.1080/15376494.2015.1121522

Tornabene, 2016, Higher-order structural theories for the static analysis of doubly-curved laminated composite panels reinforced by curvilinear fibers, Thin-Wall. Struct., 102, 222, 10.1016/j.tws.2016.01.029

Tornabene, 2016, Inter-laminar stress recovery procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method, Mech. Adv. Mat. Struct., 23, 1019, 10.1080/15376494.2015.1121521

Tornabene, 2016, MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells, Compos. Part B-Eng., 99, 30, 10.1016/j.compositesb.2016.05.049

Tornabene, 2016, Transient dynamic response of generally-shaped arches based on a GDQ-time-stepping method, Int. J. Mech. Sci., 10.1016/j.ijmecsci.2016.05.005

Bacciocchi, 2016, Vibration analysis of variable thickness plates and shells by the generalized differential quadrature method, Compos. Struct., 10.1016/j.compstruct.2015.12.004

Tornabene, 2009, Free vibration analysis of functionally graded panels and shells of revolution, Meccanica, 44, 255, 10.1007/s11012-008-9167-x

Tornabene, 2013, Static analysis of functionally graded doubly-curved shells and panels of revolution, Meccanica, 48, 901, 10.1007/s11012-012-9643-1

Viola, 2014, Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery, Compos. Struct., 112, 44, 10.1016/j.compstruct.2014.01.039

Tornabene, 2014, Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories, Compos. Part B-Eng., 67, 490, 10.1016/j.compositesb.2014.08.012

Tornabene, 2015, Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory, Compos. Struct., 119, 67, 10.1016/j.compstruct.2014.08.005

Fantuzzi, 2016, Four-parameter functionally graded cracked plates of arbitrary shape: a GDQFEM solution for free vibrations, Mech. Adv. Mat. Struct., 23, 89, 10.1080/15376494.2014.933992

Brischetto, 2016, 3D exact and 2D generalized differential quadrature models for free vibration analysis of functionally graded plates and cylinders, Meccanica, 10.1007/s11012-016-0361-y

Viola, 2016, Generalized stress-strain recovery formulation applied to functionally graded spherical shells and panels under static loading, Compos. Struct., 10.1016/j.compstruct.2015.12.060

Ranganathan, 2016, Buckling of slender columns with functionally graded microstructures, Mech. Adv. Mater. Struct., 23, 1360, 10.1080/15376494.2015.1086452

Lanc, 2016, Nonlinear buckling behaviours of thin-walled functionally graded open section beams, Compos. Struct., 152, 829, 10.1016/j.compstruct.2016.06.023

Sofiyev, 2016, Thermoelastic stability of freely supported functionally graded conical shells within the shear deformation theory, Compos. Struct., 152, 74, 10.1016/j.compstruct.2016.05.027

Sofiyev, 2016, Nonlinear free vibration of shear deformable orthotropic functionally graded cylindrical shells, Compos. Struct., 142, 35, 10.1016/j.compstruct.2016.01.066

Akavci, 2016, Mechanical behavior of functionally graded sandwich plates on elastic foundation, Compos. Part B-Eng., 96, 136, 10.1016/j.compositesb.2016.04.035

Jooybar, 2016, Thermal effect on free vibration of functionally graded truncated conical shell panels, Thin Wall. Struct., 103, 45, 10.1016/j.tws.2016.01.032

Demir, 2016, Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel, Compos. Part B-Eng., 94, 1, 10.1016/j.compositesb.2016.03.031

Fazzolari, 2015, Natural frequencies and critical temperatures of functionally graded sandwich plates subjected to uniform and non-uniform temperature distributions, Compos. Struct., 121, 197, 10.1016/j.compstruct.2014.10.039

Fazzolari, 2016, Reissner’s mixed variational theorem and variable kinematics in the modelling of laminated composite and FGM doubly-curved shells, Compos. Part B-Eng., 89, 408, 10.1016/j.compositesb.2015.11.031

Fazzolari, 2016, Stability analysis of FGM sandwich plates by using variable-kinematics Ritz models, Mech. Adv. Mater. Struct., 23, 1104, 10.1080/15376494.2015.1121559

Tornabene, 2016, Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells, Compos. Part B-Eng., 89, 187, 10.1016/j.compositesb.2015.11.016

Kamarian, 2016, Free vibration analysis of conical shells reinforced with agglomerated carbon nanotubes, Int. J. Mech. Sci., 108–109, 157, 10.1016/j.ijmecsci.2016.02.006

Tahouneh, 2016, 3D free vibration analysis of elastically supported thick nanocomposite curved panels with finite length and different boundary conditions via 2D GDQ method, Mech. Adv. Mater. Struct., 23, 1216, 10.1080/15376494.2015.1068402

Mehralian, 2016, Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell, Compos. Struct., 152, 45, 10.1016/j.compstruct.2016.05.024

Tarlton, 2016, A stochastic approach towards a predictive model on charge transport properties in carbon nanotube composites, Compos. Part B-Eng., 100, 56, 10.1016/j.compositesb.2016.06.021

Viet, 2016, Effective Young’s modulus of carbon nanotube/epoxy composites, Compos. Part B-Eng., 94, 160, 10.1016/j.compositesb.2016.03.060

Mareishi, 2015, Nonlinear forced vibration response of smart two-phase nano-composite beams to external harmonic excitations, Curved Layer. Struct., 2, 150

Ray, 2005, Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites, Compos. Sci. Technol., 65, 1226, 10.1016/j.compscitech.2004.12.027

Raney, 2011, Modeling and in situ identification of material parameters for layered structures based on carbon nanotube arrays, Compos. Struct., 93, 3013, 10.1016/j.compstruct.2011.04.034

Brischetto, 2013, Static analysis of multilayered smart shells subjected to mechanical, thermal and electrical loads, Meccanica, 48, 1263, 10.1007/s11012-012-9666-7

Hadjiloizi, 2014, Analysis of smart piezo-magneto-thermo-elastic composite and reinforced plates: part I – model development, Curved Layer. Struct., 1, 11

Hadjiloizi, 2014, Analysis of smart piezo-magneto-thermo-elastic composite and reinforced plates: part II – applications, Curved Layer. Struct., 1, 32

Hariri, 2015, A two dimensions modeling of non-collocated piezoelectric patches bonded on thin structure, Curved Layer. Struct., 2, 15

Carrera, 2002, Theories and finite elements for multilayered, anisotropic, composite plates and shells, Arch. Comput. Methods Eng., 9, 87, 10.1007/BF02736649

Carrera, 2003, Historical review of zig-zag theories for multilayered plates and shells, Appl. Mech. Rev., 56, 287, 10.1115/1.1557614

Carrera, 2004, On the use of the Murakami’s zig-zag function in the modeling of layered plates and shells, Comput. Struct., 82, 541, 10.1016/j.compstruc.2004.02.006

Hughes, 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Eng., 194, 4135, 10.1016/j.cma.2004.10.008

Piegl, 1997

Cottrell, 2009

Piegl, 1991, On NURBS: a survey, IEEE Comput. Graph. Appl., 10, 55, 10.1109/38.67702

Rogers, 2001

Zhao, 2016, Injectivity of NURBS curves, J. Comput. Appl. Math., 302, 129, 10.1016/j.cam.2016.01.046

Borden, 2011, Isogeometric finite element data structures based on Bézier extraction of NURBS, Int. J. Numer. Meth. Eng., 87, 15, 10.1002/nme.2968

Askari, 2015, A unified approach for nonlinear vibration analysis of curved structures using non-uniform rational B-spline representation, J. Sound Vib., 353, 292, 10.1016/j.jsv.2015.05.022

Luu, 2015, NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature, Compos. Struct., 119, 150, 10.1016/j.compstruct.2014.08.014

Luu, 2015, Bending and buckling of general laminated curved beams using NURBS-based isogeometric analysis, Eur. J. Mech. A/Solids, 54, 218, 10.1016/j.euromechsol.2015.07.006

Lezgy-Nazargah, 2015, NURBS-based isogeometric analysis of laminated composite beams using refined sinus model, Eur. J. Mech. A/Solids, 53, 34, 10.1016/j.euromechsol.2015.03.004

Marino, 2016, Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams, Comput. Methods Appl. Mech. Eng., 307, 383, 10.1016/j.cma.2016.04.016

Zhang, 2016, Analysis of three-dimensional curved beams using isogeometric approach, Eng. Struct., 117, 560, 10.1016/j.engstruct.2016.03.035

Chiozzi, 2016, ArchNURBS: NURBS-based tool for the structural safety assessment of masonry arches in MATLAB, J. Comput. Civil Eng., 30, 04015010, 10.1061/(ASCE)CP.1943-5487.0000481

Thai, 2012, Static, free vibration, and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach, Int. J. Numer. Methods Eng., 91, 571, 10.1002/nme.4282

Thai, 2013, Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory, Compos. Struct., 104, 196, 10.1016/j.compstruct.2013.04.002

Tran, 2014, Isogeometric analysis of functionally graded plates using higher-order shear deformation theory, Compos. Part B Eng., 51, 368, 10.1016/j.compositesb.2013.02.045

Thai, 2014, Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory, Eur. J. Mech. A/Solids, 43, 89, 10.1016/j.euromechsol.2013.09.001

Natarajan, 2014, Analysis of cross-ply laminated plates using isogeometric analysis and unified formulation, Curved Layer. Struct., 1, 1

Jari, 2015, Nonlinear thermal analysis of functionally graded material plates using a NURBS based isogeometric approach, Compos. Struct., 119, 333, 10.1016/j.compstruct.2014.09.006

Adam, 2015, Selective and reduced numerical integrations for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Eng., 284, 732, 10.1016/j.cma.2014.11.001

Klinkel, 2015, A NURBS based hybrid collocation–Galerkin method for the analysis of boundary represented solids, Comput. Methods Appl. Mech. Eng., 284, 689, 10.1016/j.cma.2014.10.029

Nguyen, 2015, An isogeometric finite element approach for three-dimensional static and dynamic analysis of functionally graded material plate structures, Compos. Struct., 132, 423, 10.1016/j.compstruct.2015.04.063

Phung-Van, 2015, Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory, Compos. Struct., 123, 137, 10.1016/j.compstruct.2014.12.021

Yin, 2015, A cutout isogeometric analysis for thin laminated composite plates using level sets, Compos. Struct., 127, 152, 10.1016/j.compstruct.2015.03.016

Ansari, 2016, Nonlocal and surface effects on the buckling behavior of functionally graded nanoplates: an isogeometric analysis, Phys. E, 84, 84, 10.1016/j.physe.2016.05.036

Thai, 2016, A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis, Compos. Struct., 139, 77, 10.1016/j.compstruct.2015.11.066

Yu, 2016, NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method, Thin Wall. Struct., 101, 141, 10.1016/j.tws.2015.12.008

Breitenberger, 2015, Analysis in computer aided design: nonlinear isogeometric B-Rep analysis of shell structures, Comput. Methods Appl. Mech. Eng., 284, 401, 10.1016/j.cma.2014.09.033

Guo, 2015, A layerwise isogeometric approach for NURBS-derived laminate composite shells, Compos. Struct., 124, 300, 10.1016/j.compstruct.2015.01.012

Kang, 2015, Isogeometric analysis of topologically complex shell structures, Finite Elem. Anal. Des., 99, 68, 10.1016/j.finel.2015.02.002

Kang, 2016, Isogeometric topology optimization of shell structures using trimmed NURBS surfaces, Finite Elem. Anal. Des., 120, 18, 10.1016/j.finel.2016.06.003

Riffnaller-Schiefer, 2016, Isogeometric shell analysis with NURBS compatible subdivision surfaces, Appl. Math. Comput., 272, 139, 10.1016/j.amc.2015.06.113

Choi, 2015, Isogeometric analysis of stress intensity factors for curved crack problems, Theor. Appl. Fract. Mech., 75, 89, 10.1016/j.tafmec.2014.11.003

Ghorashi, 2015, T-spline based XIGA for fracture analysis of orthotropic media, Comput. Struct., 147, 138, 10.1016/j.compstruc.2014.09.017

Shojaee, 2015, Crack analysis in media with orthotropic Functionally Graded Materials using extended Isogeometric analysis, Eng. Fract. Mech., 147, 203, 10.1016/j.engfracmech.2015.08.025

Tran, 2015, Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach, Int. J. Mech. Sci., 96–97, 65, 10.1016/j.ijmecsci.2015.03.003

Nguyen, 2016, An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems, Comput. Methods Appl. Mech. Eng., 306, 252, 10.1016/j.cma.2016.04.002

Fantuzzi, 2016, A SFEM-based evaluation of mode-I stress intensity factor in composite structures, Compos. Struct., 145, 162, 10.1016/j.compstruct.2016.02.076

Dimitri, 2014, Isogeometric large deformation frictionless contact using T-splines, Comput. Methods Appl. Mech. Eng., 269, 394, 10.1016/j.cma.2013.11.002

Dimitri, 2014, NURBS- and T-spline-based isogeometric cohesive zone modeling of interface debonding, Comput. Mech., 54, 369, 10.1007/s00466-014-0991-7

Dimitri, 2015, T-splines discretizations for large deformation contact problems, Proc. Appl. Math. Mech. (PAMM), 15, 183, 10.1002/pamm.201510082

Dimitri, 2015, Isogeometric treatment of large deformation contact and debonding problems with T-splines: a review, Curved Layer. Struct., 2, 59

Tornabene, 2015, Strong formulation finite element method based on differential quadrature: a survey, Appl. Mech. Rev., 67, 55, 10.1115/1.4028859

Fantuzzi, 2016, Strong formulation isogeometric analysis (SFIGA) for laminated composite arbitrarily shaped plates, Compos. Part B-Eng., 96, 173, 10.1016/j.compositesb.2016.04.034

Viola E., Tornabene F., Fantuzzi N., Bacciocchi M., DiQuMASPAB Software, DICAM Department, Alma Mater Studiorum – University of Bologna (http://software.dicam.unibo.it/diqumaspab-project).

Wang, 1997, Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory, Comput. Struct., 63, 525, 10.1016/S0045-7949(96)00357-4

Garg, 2006, Free vibration of skew fiber-reinforced composite and sandwich laminates using a shear deformable finite element method, J. Sandwich Struct. Mater., 8, 33, 10.1177/1099636206056457