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http://dx.doi.org/10.12989/anr.2019.7.2.109

Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method  

Emdadi, Mohsen (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Navi, Borhan Rousta (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Publication Information
Advances in nano research / v.7, no.2, 2019 , pp. 109-123 More about this Journal
Abstract
In this article, the free vibration analysis of annular sandwich plates with various functionally graded (FG) porous cores and carbon nanotubes reinforced composite (CNTRC) facesheets is investigated based on modified couple stress theory (MCST) and first order shear deformation theories (FSDT). The annular sandwich plate is composed of two face layers and a functionally graded porous core layer which contains different porosity distributions. Various approaches such as extended mixture rule (EMR), Eshelby-Mori-Tanaka (E-M-T), and Halpin-Tsai (H-T) are used to determine the effective material properties of microcomposite circular sandwich plate. The governing equations of motion are extracted by using Hamilton's principle and FSDT. A Ritz method has been utilized to calculate the natural frequency of an annular sandwich plate. The effects of material length scale parameters, boundary conditions, aspect and inner-outer radius ratios, FG porous distributions, pore compressibility and volume fractions of CNTs are considered. The results are obtained by Ritz solutions that can be served as benchmark data to validate their numerical and analytical methods in the future work and also in solid-state physics, materials science, and micro-electro-mechanical devices.
Keywords
free vibration analysis; circular annular sandwich plate; FG-porous core; CNTRC facesheets; EMR; EMT; HT approaches;
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Times Cited By KSCI : 12  (Citation Analysis)
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1 Arani, A.G., Hashemian, M., Loghman, A. and Mohammadimehr, M. (2011b), "Study of dynamic stability of the double-walled carbon nanotubes under axial loading embedded in an elastic medium by the energy method", J. Appl. Mech. Tech. Phys., 52(5), 815-824.   DOI
2 Arani, A.G., Mobarakeh, M.R., Shams, S. and Mohammadimehr, M. (2012), "The effect of CNT volume fraction on the magnetothermo- electro-mechanical behavior of smart nanocomposite cylinder", J. Mech. Sci. Technol., 26(8), 2565-2572.   DOI
3 Ashby, M.F., Evans, T., Fleck, N.A., Hutchinson, J., Wadley, H. and Gibson L. (2000), Metal Foams: A Design Guide, Butterworth-Heinemann, Boston, MA, USA.
4 Belkorissat, I., Sid Ahmed, H.M., Bedia, E.A.A., Tounsi, A. and Hassan, S. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081.   DOI
5 Ke, L.L. and Wang, Y.S. (2013), "Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory", Int. J. Eng. Sci., 64, 37-53.   DOI
6 Kong, S., Zhou, S., Nie, Z. and Wang, K. (2009), "Static and dynamic analysis of micro beams based on strain gradient elasticity theory", Int. J. Eng. Sci., 47(4), 487-498.   DOI
7 Lam, D.C.C., Yang, F. and Chong, A.C.M. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51, 1477-1508 .   DOI
8 Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2014 ), "Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method", Compos. Struct., 113, 328-338.   DOI
9 Lei, Z.X., Zhang, L.W. and Liew, K.M. (2015 ), "Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method", Compos. Struct., 127, 245-259.   DOI
10 Zhang, L.W., Huang, D. and Liew, K.M. (2015a ), "An elementfree IMLS-Ritz method for numerical solution of threedimensional wave equations", Comput. Meth. Appl. Mech. Eng., 297, 116-139.   DOI
11 Zhang, L.W., Song, Z.G. and Liew, K.M. (2015b ), "State-space Levy method for vibration analysis of FG-CNT composite plates subjected to in-plane loads based on higher-order shear deformation theory", Compos. Struct., 134, 989-1003.   DOI
12 Zhang, L.W., Song, Z.G. and Liew, K.M. (2015c ), " Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLSRitz method", Compos. Struct., 128, 165-175.   DOI
13 Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P.A., Nguyen-Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Methods Appl. Mech. Eng., 313, 904-940.   DOI
14 Lei, Z.X., Zhang, L.W. and Liew, K.M. (2016a ), "Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method", Compos. part B, 84, 211-221.   DOI
15 Lei, Z.X., Zhang, L.W. and Liew, K.M. (2016b), "Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method", Compos. part B, 85, 140-149.   DOI
16 Magnucka-Blandzi, E. (2009), "Dynamic stability of a metal foam circular plate", J. Theor. Appl. Mech., 47(2), 421-433.
17 Mohammadimehr, M., Emdadi, M. and Rousta Navi, B. (2018b), "Dynamic stability analysis of microcomposite annular sandwich plate with CNT reinforced composite facesheets based on MSGT", J. Sandw. Struct. Mater., DOI: org/10.1177/1099636218782770
18 Mojahedin, A., Jabbari, M., Khorshidvand, A.R. and Eslami, M.R. (2016), "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory", Thin-Wall. Struct., 99, 83-90.   DOI
19 Shi, D., Feng, X.Q. and Huang, Y.Y. (2004), "The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composite", J. Eng. Mater. Technol., 126, 250-257.   DOI
20 Simseka, M. and Reddy, J.N. (2014), "Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory", Compos. Struct., 115, 41-50.   DOI
21 Smith, B.H., Szyniszewski, S., Hajjar, J.F., Schafer, B.W. and Arwade, S.R. (2012), "Steel foam for structures: a review of applications, manufacturing and material properties", J. Constr. Steel Res., 117, 1-10.   DOI
22 Sun, C.H., Li, F., Cheng, H.M. and Lu, G.Q. (2005), "Axial Young's modulus prediction of single walled carbon nanotube arrays with diameters from nanometer to meter scales", Appl. Phys. Lett., 87, 193-201.
23 Zhang, L.W., Xiao, L.N., Zou, G.L. and Liew , K.M. (2016c), "Elastodynamic analysis of quadrilateral CNT-reinforced functionally graded composite plates using FSDT element-free method", Compos. Struct., 148, 144-154.   DOI
24 Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015d), "Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach", Compos. part B, 75, 36-46.   DOI
25 Zhang, L.W., Liew, K.M. and Jiang, Z. (2016a ), "An element-free analysis of CNT-reinforced composite plates with column supports and elastically restrained edges under large deformation", Compos. part B, 95, 18-28.   DOI
26 Zhang, L.W., Liew, K.M. and Reddy, J.N. (2016b ), "Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression", Comput. Meth. Appl. Mech. Eng., 298, 1-28.   DOI
27 Zhang, L.W., Zhang, Y., Zou, G.L. and Liew, K.M. (2016d), "Free vibration analysis of triangular CNT-reinforced composite plates subjected to in-plane stresses using FSDT element-free method", Compos. Struct., 149, 247-260.   DOI
28 Magnucki, K. and Stasiewicz, P. (2004), "Elastic buckling of a porous beam", J. Theor. Appl. Mech., 42(4), 859-868.
29 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Hassan, S. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. M ech., Int. J., 62(6), 695-702.
30 Magnucka-Blandzi, E. (2011), "Mathematical modeling of a rectangular sandwich plate with metal foam core", J. Theor. Appl. Mech., 49(2), 439-455.
31 Mahi, A., Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508.   DOI
32 Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., Int. J., 25(2), 157-175.
33 Meziane, A.A., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318.   DOI
34 Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., Int. J., 59(3), 431-454.   DOI
35 Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409- 423.   DOI
36 Ugale, V., Singh, K. and Mishra, N. (2015), "Comparative study of carbon fabric reinforced and glass fabric reinforced thin sandwich panels under impact and static loading", J. Compos. Mater., 49, 99-112.   DOI
37 Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2018), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position ", J. Braz. Soc. Mech. Sci. Eng., 38, 265-275 .   DOI
38 Zhang, L.W., Liew, K.M. and Reddy, J.N. (2016e), "Postbuckling analysis of bi-axially compressed laminated nanocomposite plates using the first-order shear deformation theory", Compos. Struct., 152, 418-431.   DOI
39 Betts, C. (2012), "Benefits of metal foams and developments in modeling techniques to assess their materials behavior: a review", Mater. Sci. Technol., 28, 129-143.   DOI
40 Bounouara, F., Benrahou, K.H., Belkorissat, I. and 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., Int. J., 20(2), 227-249.   DOI
41 Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61.   DOI
42 Chen, D., Kitipornchai, S. and Yang, J. (2016), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin-Wall. Struct., 107, 39-48.   DOI
43 Dukhan, N. (2013), Metal Foams: Fundamentals and Applications, DEStech Publications, Inc Lancaster USA.
44 Ghorbanpour Arani, A., Rousta Navi, B. and Mohammadimehr, M. (2016), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441.   DOI
45 Guo, J., Shi, D., Wang, Q., Pang, F. and Liang, Q. (2018), "A domain decomposition approach for static and dynamic analysis of composite laminated curved beam with general elastic restrains", Mech. Adv. Mater. Struct., 1-13. DOI: 10.1080/15376494.2018.1432810
46 Wen, P.H. (2012), "The analytical solutions of incompressible saturated poroelastic circular Mindlin's plate", J. Appl. Mech., 79(5), 203-210.
47 Wang, Z.X. and Shen, H.S. (2012), "Nonlinear vibration and bending of sandwich plates with nanotube reinforced composite", Compos. Part B, 43, 411-421.   DOI
48 Wang, B., Zhou, S., Zhao, J. and Chen, X. (2011), "A sizedependent Kirchhoff micro-plate model based on strain gradient elasticity theory", Eur. J. Mech. A-Solid, 30, 517-524.   DOI
49 Wang, Q., Shi, D., Liang, Q. and Shi, X. (2016), "A unified solution for vibration analysis of functionally graded circular, annular and sector plates with general boundary conditions", Compos. Part B-Eng., 88, 264-294.   DOI
50 Whitney, J. (1972), "Stress analysis of thick laminated composite and sandwich plates", J. Compos. Mater., 6, 426-440.   DOI
51 Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories ", Struct. Eng. Mech., Int. J., 53(6), 1143-1165.   DOI
52 Yin, L., Qian, Q., Wang, L. and Xia, W. (2010), "Vibration analysis of micro scale plates based on modified couple stress theory", Acta Mech. Solid Sin., 23, 386-393.   DOI
53 Zhong, R., Wang, Q., Tang, J., Shuai, C. and Qin, B. (2018), "Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates", Compos. Struct., 194(15), 49-67.   DOI
54 Zhang, L.W., Song, Z.G. and Liew, K.M. (2016f ), "Optimal shape control of CNT reinforced functionally graded composite plates using piezoelectric patches", Compos. part B, 85, 140-149.   DOI
55 Zhang, L.W., Song, Z.G. and Liew, K.M. (2016g), "Computation of aerothermoelastic properties and active flutter control of CNT reinforced functionally graded composite panels in supersonic airflow", Comput. Meth. Appl. Mech. Eng., 300, 427-441.   DOI
56 Zhang, L.W., Liu, W.H. and Liew, K.M. (2016h ), "Geometrically nonlinear large deformation analysis of triangular CNTreinforced composite plates", Int. J. Non-Linear Mech., 86, 122-132.   DOI
57 Zhou, D., Au, F.T.K., Cheung, Y.K. and Lo, S.H. (2003), "Threedimensional vibration analysis of circular and annular plates via the Chebyshev-Ritz method", Int. J. Solids Struct., 40, 3089-3105.   DOI
58 Zhu, P., Zhang, L.W. and Liew, K.M. (2014 ), "Geometrically nonlinear thermo mechanical analysis of moderately thick functionally graded plates using a local Petrov-Galerkin approach with moving Kriging interpolation", Compos. Struct., 107, 298-314.   DOI
59 Mohammadimehr, M. and Mehrabi, M. (2017), "Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow", Appl. Math. Model., 47, 685-709.   DOI
60 Mohammadimehr, M. and Alimirzaei, S. (2017), "Buckling and free vibration analysis of tapered FG- CNTRC micro Reddy beam under longitudinal magnetic field using FEM", Smart Struct. Syst., Int. J., 19(3), 309-322.   DOI
61 Mohammadimehr, M. and Mehrabi, M. (2018), "Electro-thermomechanical vibration and stability analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow", Appl. Math. Model., 60, 255-272.   DOI
62 Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation", Turkish J. Eng. Environ. Sci., 37(1), 1-15.
63 Mohammadimehr, M. and Salemi, M. (2014), "Bending and buckling analysis of functionally graded Mindlin nano-plate model based on strain gradient elasticity theory", Indian J. Sci. Res., 2(2), 587-598.
64 Mohammadimehr, M. and Shahedi, S. (2017) "High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM", Compos. Part B: Eng., 108, 91-107.   DOI
65 Mohammadimehr, M., Saidi, A.R., Arani, A.G., Arefmanesh, A. and Han, Q. (2010), "Torsional Buckling of a DWCNT Embedded on Winkler and Pasternak Foundations Using Nonlocal Theory", J. Mech. Sci. Tech., 24(6), 1289-1299.   DOI
66 Mohammadimehr, M., Rousta-Navi, B. and Ghorbanpour-Arani, A. (2014), "Biaxial buckling and bending of smart nanocomposite plate reinforced by CNTs using extended mixture rule approach", Mech. Adv. Compos. Struct., 1, 17-26.
67 Halpin, J.C. and Kardos, J.L. (1976), "The Halpin -Tsaiequation: a review", Polym. Eng. Sci., 16, 344-352.   DOI
68 Zeighampour, H. and Beni, Y.T. (2014), "Cylindrical thin-shell model based on modified strain gradient theory", Int. J. Eng. Sci., 78, 27-47.   DOI
69 Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710.   DOI
70 Zenkour, A. (2005), "A comprehensive analysis of functionally graded sandwich plates, Part 1 - deflection and stresses", Int. J. Solids Str., 42, 5224-5242.   DOI
71 Jalaei, M.H., Ghorbanpour, Arani, A. and Tourang, H. (2018), "On the dynamic stability of viscoelastic graphene sheets", Int. J.of En. Sci., 132, 16-29.   DOI
72 Jasion, P. and Magnucki, K. (2013), "Global buckling of a sandwich column with metal foam core", J. Sandw. Struct. Mater., 1099636213499339.
73 Jia, J., Zhao, J., Xu, G., Di, J., Yong, Z., Tao, Y., Fang, C., Zhang, Z., Zhang, X., Zheng, L. and Li, Q. (2011), "A comparison of the mechanical properties of fibers spun from different carbon nanotubes", Carbon, 49, 1333-1339.   DOI
74 Karami, B., Janghorban, M. and 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-Wall. Struct., 129, 251-264.   DOI
75 Abdel Ghafaar, M., Mazen, A.A. and El-Mahallawy, N.A. (2006), "Application of the rule of mixtures and halpin-tsai equations to woven fabric reinforced epoxy composites", J. Eng. Sci. Assiut Univ., 34(1), 227-236.
76 Ahouel, M., Sid Ahmed, H.M., Bedia, E.A.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., Int. J., 20(5), 963-981.   DOI
77 Zhang, L.W. (2017a), "Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports", J. Model. Mech. Mater., 1, 20160154. DOI: https://doi.org/10.1515/nano.0070.00001   DOI
78 Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630.   DOI
79 Arani, A.G., Mohammadimehr, M., Saidi, A.R., Shogaei, S. and Arefmanesh, A. (2011a), "Thermal buckling analysis of doublewalled carbon nanotubes considering the small-scale length effect", Proc. IMechE, Part C, J. Mech. Eng. Sci., 225(1), 248-256.   DOI
80 Zhao, C. (2012), "Review on thermal transport in high porosity cellular metal foams with open cells", Int. J. Heat Mass Transf., 55, 3618-3632.   DOI
81 Zhang, L.W. (2017b), "On the study of the effect of in-plane forces on the frequency parameters of CNT-reinforced composite skew plates", Compos. Struct., 160, 824-837.   DOI
82 Zhang, L.W. and Liew, K.M. (2016a ), "Postbuckling analysis of axially compressed CNT reinforced functionally graded composite plates resting on Pasternak foundations using an element-free approach", Compos. Struct., 138, 40-51.   DOI
83 Mohammadimehr, M., Mohammadimehr, M.A. and Dashti, P. (2016d), "Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic microplate based on surface stress and modified couple stress theories using differential quadrature method (DQM)", Appl. Math. Mech. (English Edition), 37(4), 529-554.   DOI
84 Mohammadimehr, M., Shahedi, S. and Rousta Navi, B. (2016a), "Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(20), 3866-3885.   DOI
85 Mohammadimehr, M., Navi, B.R. and Arani, A.G. (2016b), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of doublecoupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B, 87, 132-148.   DOI
86 Mohammadimehr, M., Rostami, R. and Arefi, M. (2016c), "Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., Int. J., 20(3), 513-544.   DOI
87 Mohammadimehr, M., Zarei, H.B., Parakandeh, A. and Arani, A.G. (2017), "Vibration analysis of double-bonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields", Struct. Eng. Mech., Int. J., 64(3), 361-379.
88 Mohammadimehr, M., Emdadi, M., Afshari, H. and Rousta Navi, B. (2018a), "Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo- magneto-mechanical loadings using DQM", Int. J. Smart Nano Mater., 9(4), 223-260.
89 Zhang, L.W. and Selim, B.A. (2017), "Vibration analysis of CNTreinforced thirck laminated composite plates based on Reddy's higher-order shear deformation theory", Compos. Struct., 160, 689-705.   DOI
90 Zhang, L.W. and Liew, K.M. (2016b ), "Element-free geometrically nonlinear analysis of quadrilateral functionally graded material plates with internal column supports", Compos. Struct., 147, 99-110.   DOI
91 Zhang, L.W. and Xiao, L.N. (2017) , "Mechanical behavior of laminated CNT-reinforced composite skew plates subjected to dynamic loading", Compos. part B, 122, 219-230.   DOI
92 Zhang, L.W. and Liew, K.M. (2015 ), "Large deflection analysis of FG-CNT reinforced composite skew plates resting on Pasternak foundations using an element-free approach", Compos. Struct., 132, 974-993.   DOI
93 Zhang, L.W., Zhub, P. and Liew, K.M. (2014 ), "Thermal buckling of functionally graded plates using a local Kriging meshless method", Compos. Struct., 108, 472-492.   DOI