×

Efficient modeling of smart piezoelectric composite laminates: a review. (English) Zbl 1397.74046

Summary: Current research issues in the development of efficient analysis models and their efficient numerical implementation for smart piezoelectric laminated structures are discussed in this paper. The improved zigzag theories with a layerwise quadratic variation of electric potential have emerged as the best compromise between accuracy and cost for hybrid composite, sandwich and FGM beams and plates. The concept of associating surface potentials to electric nodes and internal potentials to physical nodes is very effective in modeling the equipotential electroded surfaces. Unified formulations for shear and extension mode actuation, and modeling of piezoelectric composite actuators and sensors are discussed. Future challenge lies in developing efficient theories capable of predicting the interlaminar transverse shear stresses in hybrid laminates directly from the constitutive equations.

MSC:

74E30 Composite and mixture properties
74F15 Electromagnetic effects in solid mechanics
74M05 Control, switches and devices (“smart materials”) in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Altus A., Rotem A., Shmueli M.: Free edge effect in angle-ply laminates-A new three dimensional finite difference solution. J. Compos. Mater. 14, 21–30 (1980)
[2] Artel J., Becker W.: Coupled and uncoupled analyses of piezoelectric free-edge effect in laminated plates. Compos. Struct. 69, 329–339 (2005) · doi:10.1016/j.compstruct.2004.07.015
[3] Attallah K.M.Z., Ye J.Q., Sheng H.Y.: Three-dimensional finite strip analysis of laminated panels. Comput. Struct. 85, 1769–1781 (2007) · doi:10.1016/j.compstruc.2007.04.003
[4] Bailey T., Hubbard J.E.: Distributed piezoelectric-polymer active vibration control of a cantilever beam. J. Guiding Control 8, 605–611 (1985) · Zbl 0633.93047 · doi:10.2514/3.20029
[5] Becker W.: Free-edge stress concentration in angle-ply laminates. Arch. Appl. Mech. 65, 38–43 (1995) · Zbl 0819.73007
[6] Becker W.: The influence of clamping on uniaxial laminate tensile tests. Zeitschrift Angewandte Mathematik Mechanik 77, 513–514 (1997) · Zbl 0900.73471
[7] Benjeddou A.: Advances in piezoelectric finite element modelling of adaptive structural elements: a survey. Comput. Struct. 76, 347–363 (2000) · doi:10.1016/S0045-7949(99)00151-0
[8] Benjeddou A., Trindade M.A., Ohayon R.: New shear actuated smart structure beam finite element. AIAA J. 37, 378–383 (1999) · doi:10.2514/2.719
[9] Benjeddou A., Trindade M.A., Ohayon R.: Piezoelctric actuation mechanisms for intelligent sandwich structures. Smart Mater. Struct. 9, 328–335 (2000) · doi:10.1088/0964-1726/9/3/313
[10] Bent A.A.: Piezoelectric fiber composites for structural actuation: MS Thesis. Massachusetts Institute of Technology, USA (1994)
[11] Bent A.A., Hagood N.W.: Piezoelectric fiber composites with interdigitated electrodes. J. Intell. Mater. Syst. Struct. 8, 903–919 (1997) · doi:10.1177/1045389X9700801101
[12] Bent A.A., Hagood N.W., Rodgers J.P.: Anisotropic actuation with piezoelectric fiber composites. J. Intell. Mater. Syst. Struct. 6, 338–349 (1995) · doi:10.1177/1045389X9500600305
[13] Bhattacharyya M., Kapuria S., Kumar A.N.: On the stress to strain transfer ratio and elastic deflection behaviour for AlSiC functionally graded material. Mech. Adv. Mater. Struct. 14, 295–302 (2007) · doi:10.1080/15376490600817917
[14] Bhattacharyya M., Kumar A.N., Kapuria S.: Synthesis and characterization of Al/SiC and Ni/Al2O3 functionally graded materials. Mater. Sci. Eng. A Struct. Mater. 487, 524–535 (2008) · doi:10.1016/j.msea.2007.10.040
[15] Bhimaraddi A.: Free vibration analysis of doubly-curved shallow shells on rectangular plan form using three-dimensional elasticity theory. Int. J. Solids Struct. 27, 897–913 (1991) · Zbl 0734.73048 · doi:10.1016/0020-7683(91)90023-9
[16] Bisegna P., Maceri F.: An exact three-dimensional solution for simply supported rectangular piezoelectric plates. J. Appl. Mech. Trans. ASME 63, 628–638 (1996) · Zbl 0886.73054 · doi:10.1115/1.2823343
[17] Burton W.S., Noor A.K.: Three dimensional solutions for thermomechanical stresses in sandwich panels and shells. J. Eng. Mech.ASCE 120, 2044–2071 (1994) · doi:10.1061/(ASCE)0733-9399(1994)120:10(2044)
[18] Cady W.G.: Piezoelectricity. Dover, New York (1964)
[19] Chakraborty A., Gopalakrishnan S., Reddy J.N.: A new beam finite element for the analysis of functionally graded materials. Int. J. Mech. Sci. 45, 519–539 (2003) · Zbl 1035.74053 · doi:10.1016/S0020-7403(03)00058-4
[20] Chan H.L.W., Unsworth J.: Simple model for piezoelectric ceramic/polymer 1–3 composites used in ultrasonic transducer applications. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 36, 434–441 (1989) · doi:10.1109/58.31780
[21] Chandrashekhara K., Agarwal A.N.: Active vibration control of laminated composite plates using piezoelectric devices: a finite element approach. J. Int. Mater. Syst. Struct. 4, 496–508 (1993) · doi:10.1177/1045389X9300400409
[22] Chattopadhyay A., Seely E.: A higher order theory for modeling laminates with induced strain actuators. Compos. Part B 28, 243–252 (1997) · doi:10.1016/S1359-8368(96)00043-1
[23] Chattopadhyay A., Li J., Gu H.: Coupled piezoelectric mechanical model for smart composite laminates. AIAA J. 37, 1633–1638 (1999) · doi:10.2514/2.645
[24] Chen W.Q., Lee K.Y.: On free vibration of cross-ply laminates in cylindrical bending. J. Sound. Vib. 273, 667–676 (2004) · doi:10.1016/j.jsv.2003.08.003
[25] Chen W.Q., Lüe C.F.: 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported. Compos. Struct. 69, 77–87 (2005) · doi:10.1016/j.compstruct.2004.05.015
[26] Chen W.Q., Lv C.F., Bian Z.G.: Elasticity solution for free vibration of laminated beams. Compos. Struct. 62, 75–82 (2003) · doi:10.1016/S0263-8223(03)00086-2
[27] Cheng Z.Q., Lim C.W., Kitpornchai S.: Three-dimensional exact solution for inhomogeneous and laminated piezoelectric plates. Int. J. Eng. Sci. 37, 1425–1439 (1999) · doi:10.1016/S0020-7225(98)00125-6
[28] Cho J.R., Ha D.Y.: Averaging and finite element discretisation approaches in numerical analysis of functionally graded materials. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 302, 187–196 (2001)
[29] Cho M., Kim H.S.: Iterative free-edge stress analysis of composite laminates under extension, bending, twisting and thermal loading. Int. J. Solids Struct. 37, 435–459 (2000) · Zbl 1090.74553 · doi:10.1016/S0020-7683(99)00014-1
[30] Cho M., Kim H.S.: Iterative free-edge stress analysis of composite laminates under extension, bending, twisting and thermal loadings. Int. J. Solids Struct. 37, 435–459 (2000) · Zbl 1090.74553 · doi:10.1016/S0020-7683(99)00014-1
[31] Cho M., Oh J.: Higher order zigzag theory for fully coupled thermo-electro-mechanical smart composite plates. Int. J. Solids Struct. 41, 1331–1356 (2004) · Zbl 1106.74366 · doi:10.1016/j.ijsolstr.2003.10.020
[32] Cho M., Parmerter R.R.: Efficient higher order composite plate theory for general lamination configurations. AIAA J. 31, 1299–1306 (1993) · Zbl 0781.73036 · doi:10.2514/3.11767
[33] Crawley E.F., Lazarus K.B.: Induced strain actuation of isotropic and anisotropic plates. AIAA J. 29, 944–951 (1991) · doi:10.2514/3.10684
[34] Crawley, E.F., Luis de, J.: Use of piezo-ceramics as distributed actuators in large space structures. In: Proceeding of AIAA/ASME/ASCE/AHS 26th structures, structural dynamics and materials conference, pp. 126–133 (1985)
[35] Dube G.P., Upadhyay M.M., Dumir P.C., Kapuria S.: Piezothermoelastic solution for angle-ply laminated plate in cylindrical. Struct. Eng. Mech. 6, 529–554 (1998)
[36] Dumir P.C., Dube G.P., Kumar S.: Piezothermoelastic solution for angle-ply laminated cylindrical panel. J. Int. Mater. Syst. Struct. 8, 452–464 (1997) · doi:10.1177/1045389X9700800508
[37] Dunn M.L., Taya M.: Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites. Int. J. Solids Struct. 30, 161–175 (1993) · Zbl 0772.73068 · doi:10.1016/0020-7683(93)90058-F
[38] Fan J.R.: Exact theory of laminated thick plates and shells. Science Press, Beijing (1996)
[39] Fan J.R., Sheng H.Y.: Exact solution for thick laminates with clamped edges. Acta. Mechanica. Sinica. 24, 574–583 (1992)
[40] Fernandes A., Pouget J.: Structural response of composite plates equipped with piezoelectric actuators. Comput. Struct. 84, 1459–1470 (2006) · doi:10.1016/j.compstruc.2006.01.014
[41] Flanagan G.: An efficient stress function approximation for free-edge stresses in laminates. Int. J. Solids Struct. 31, 941–952 (1994) · Zbl 0946.74513 · doi:10.1016/0020-7683(94)90004-3
[42] Franco Correia V.M., Aguiar Gomes M.A., Suleman A., Mota Soares C.M., Mota Soares C.A.: Modeling and design of adaptive composite structures. Comput. Methods Appl. Mech. Eng. 185, 325–346 (2000) · Zbl 0981.74010 · doi:10.1016/S0045-7825(99)00265-0
[43] Gandhi M.V., Thompson B.S.: Smart materials and structures. Chapman and Hall, London (1992)
[44] Gu H., Chattopadhyay A., Li J., Zhou X.: A higher order temperature theory for coupled thermo-piezoelectro-mechanical modeling of smart composites. Int. J. Solids Struct. 37, 6479–6497 (2002) · Zbl 1026.74021 · doi:10.1016/S0020-7683(99)00283-8
[45] Guiping Z., Limin T.: A semi-analytical solution for thermal stress analysis of laminated composite plates in the Hamiltonian system. Comput. Struct. 55, 113–118 (1995) · Zbl 0894.73058 · doi:10.1016/0045-7949(94)00419-4
[46] Hayashi T.: Analytical study of interlaminar shear stresses in a laminated composite plate. Trans. Jpn. Soc. Aeronaut. Space Sci. 10, 43–48 (1967)
[47] Herakovich C.T.: On thermal edge effects in composite laminates. Int. J. Mech. Sci. 18, 129–138 (1976) · doi:10.1016/0020-7403(76)90062-X
[48] Heyliger P.: Static behaviour of laminated elastic/piezoelectric plates. AIAA J. 32, 2481–2484 (1994) · Zbl 0824.73056 · doi:10.2514/3.12321
[49] Heyliger P.: Exact solution for simply supported laminated piezoelectric plates. J. Appl. Mech. Trans. ASME 64, 299–306 (1997) · Zbl 0890.73052 · doi:10.1115/1.2787307
[50] Heyliger P., Saravanos D.A.: Exact free-vibration analysis of laminated plates with embedded piezoelectric layers. J. Acoust. Soc. Am. 98, 1547–1557 (1995) · doi:10.1121/1.413420
[51] Hill R.: A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213–222 (1965) · doi:10.1016/0022-5096(65)90010-4
[52] Hwang W.S., Park H.C.: Finite element modelling of piezoelectric sensors and actuators. AIAA J. 31, 930–937 (1993) · doi:10.2514/3.11707
[53] Icardi U., Bertetto A.M.: An evaluation of the influence of geometry and of material properties at free edges and at the corners of composite laminates. Comput. Struct. 57, 555–571 (1995) · Zbl 0924.73146 · doi:10.1016/0045-7949(95)00069-S
[54] Ishihara M., Noda N.: Piezothermoelastic analysis of a cross-ply laminate considering the effects of transverse shear and coupling. J. Ther. Stress. 23, 441–461 (2000) · doi:10.1080/014957300403932
[55] Jeychandrabose C., Kirkhope J., Meekisho L.: An improved discrete Kirchhoff quadrilateral thin-plate bending element. Int. J. Numer. Methods Eng. 24, 635–654 (1987) · Zbl 0602.73074 · doi:10.1002/nme.1620240312
[56] Jonnalagadda K.D., Blandford G.E., Tauchert T.R.: Piezothermoelastic composite plate analysis using first-order shear deformation theory. Comput. Struct. 51, 79–89 (1994) · Zbl 0900.73297 · doi:10.1016/0045-7949(94)90038-8
[57] Kant T., Swaminathan K.: Estimation of transverse/interlaminar stresses in laminated composites - a selective review and survey of current developments. Compos. Struct. 49, 65–75 (2000) · doi:10.1016/S0263-8223(99)00126-9
[58] Kant T., Pendhari S.S., Desai Y.M.: A general partial discretization methodology for interlaminar stress computation in composite laminates. Comput. Model. Eng. Sci. 17, 135–161 (2007) · Zbl 1184.74076
[59] Kapuria S.: An efficient coupled theory for multilayered beams with embedded piezoelectric sensory and active layers. Int. J. Solids Struct. 38, 9179–9199 (2001) · Zbl 1090.74635 · doi:10.1016/S0020-7683(01)00112-3
[60] Kapuria S.: A coupled zig-zag third-order theory for piezoelectric hybrid cross-ply plates. ASME J. Appl. Mech. 71, 604–614 (2004) · Zbl 1111.74470 · doi:10.1115/1.1767170
[61] Kapuria S., Achary G.G.S.: A coupled consistent third-order theory for hybrid piezoelectric plates. Compos. Struct. 70, 120–133 (2005) · Zbl 1119.74349 · doi:10.1016/j.compstruct.2004.08.018
[62] Kapuria S., Achary G.G.S.: A coupled zigzag theory for the dynamics of piezoelectric hybrid cross-ply plates. Arch. Appl. Mech. 75, 42–57 (2005) · Zbl 1119.74349 · doi:10.1007/s00419-005-0386-5
[63] Kapuria S., Achary G.G.S.: Exact 3D piezoelasticity solution of hybrid cross-ply plates with damping under harmonic electro-mechanical loads. J. Sound Vib. 282, 617–634 (2005) · doi:10.1016/j.jsv.2004.03.030
[64] Kapuria S., Achary G.G.S.: Electromechanically coupled zigzag third-order theory for thermally loaded hybrid piezoelectric plates. AIAA J. 44, 160–170 (2006) · doi:10.2514/1.12296
[65] Kapuria S., Achary G.G.S.: Nonlinear zigzag theory for electrothermomechanical buckling of piezoelectric composite and sandwich plates. Acta. Mech. 184, 61–76 (2006) · Zbl 1126.74017 · doi:10.1007/s00707-006-0318-7
[66] Kapuria S., Dumir P.C.: Coupled FSDT for piezothermoelastic hybrid rectangular plate. Int. J. Solids Struct. 37, 6131–6153 (2000) · Zbl 0963.74034 · doi:10.1016/S0020-7683(99)00248-6
[67] Kapuria S., Hagedorn P.: Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors. J. Mech. Mater. Struct. 2, 1267–1298 (2007) · doi:10.2140/jomms.2007.2.1267
[68] Kapuria S., Kulkarni S.D.: An improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory for static analysis of composite and sandwich plates. Int. J. Numer. Methods Eng. 69, 1948–1981 (2007) · Zbl 1194.74416 · doi:10.1002/nme.1836
[69] Kapuria S., Kulkarni S.D.: An efficient quadrilateral element based on improved zigzag theory for dynamic analysis of hybrid plates with electroded piezoelectric actuators and sensors. J. Sound Vib. 315, 118–145 (2008) · doi:10.1016/j.jsv.2008.01.053
[70] Kapuria S., Kulkarni S.D.: Static electromechanical response of smart composite/sandwich plates using an efficient finite element with physical and electric nodes. Int. J. Mech. Sci. 51, 1–20 (2009) · Zbl 1264.74166 · doi:10.1016/j.ijmecsci.2008.11.005
[71] Kapuria, S., Nath, J.K.: A new efficient laminate theory for improved prediction of transverse shear stresses in piezoelectric composite plates. AIAA J., In Press (2009)
[72] Kapuria S., Sengupta S., Dumir P.C.: Three-dimensional piezothermoelastic solution for shape control of cylindrical panel. J. Ther. Stress. 20, 67–85 (1997) · Zbl 0899.73445 · doi:10.1080/01495739708956092
[73] Kapuria S., Sengupta S., Dumir P.C.: Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load. Arch. Appl. Mech. 67, 320–330 (1997) · Zbl 0879.73038 · doi:10.1007/s004190050120
[74] Kapuria S., Dumir P.C., Sengupta S.: Three dimensional solution for shape control of a simply supported rectangular hybrid plate. J. Ther. Stress. 22, 159–176 (1999) · doi:10.1080/014957399280940
[75] Kapuria S., Bhattacharyya M., Kumar A.N.: Assessment of coupled 1D models for hybrid piezoelectric layered functionally graded beams. Compos. Struct. 72, 455–468 (2006) · doi:10.1016/j.compstruct.2005.01.015
[76] Kapuria S., Bhattacharyya M., Kumar A.N.: Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Compos. Struct. 82, 390–402 (2008) · doi:10.1016/j.compstruct.2007.01.019
[77] Kapuria S., Bhattacharyya M., Kumar A.N.: Theoretical modeling and experimental validation of thermal response of metal-ceramic functionally graded beams. J. Ther. Stress. 31, 759–787 (2008) · doi:10.1080/01495730802194292
[78] Kapuria S., Kumari P., Nath J.K.: Analytical piezoelasticity solution for vibration of piezoelectric laminated angle-ply circular cylindrical panels. J. Sound Vib. 324, 832–849 (2009) · doi:10.1016/j.jsv.2009.02.035
[79] Kassapoglou C.: Determination of interlaminar stresses in composite laminates under combined loads. J. Reinforced Plast. Compos. 9, 33–58 (1990) · doi:10.1177/073168449000900103
[80] Kerner E.H.: The elastic and thermoelastic properties of composite media. Proc. Phys. Sci. 69, 808–813 (1956) · doi:10.1088/0370-1301/69/8/305
[81] Kim H.S., Xu Z., Chattopadhyay A.: Interlaminar stress analysis of shell structures with piezoelectric patch including thermal loading. AIAA J. 40, 2517–2525 (2002) · doi:10.2514/2.1596
[82] Kreyszig E.: Advanced Engineering Mathematics. Wiley India (P) Ltd, New Delhi (1999) · Zbl 0103.27803
[83] Krishnamurty A.V., Kumar H.K.H.: Modelling of symmetric laminates under extension. Compos. Struct. 11, 15–32 (1989) · doi:10.1016/0263-8223(89)90028-7
[84] Krommer M.: On the correction of the Bernoulli-Euler beam theory for smart piezoelecric beams. Smart Mater. Struct. 10, 668–680 (2001) · doi:10.1088/0964-1726/10/4/310
[85] Krommer V.M., Irschik H.: A Reissner-Mindlin type plate theory including the direct piezoelectric and the pyroelectric effect. Acta Mech. 141, 51–69 (2000) · Zbl 0994.74043 · doi:10.1007/BF01176807
[86] Kulkarni S.D., Kapuria S.: Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory. Comput. Mech. 42, 803–824 (2008) · Zbl 1163.74508 · doi:10.1007/s00466-008-0285-z
[87] Kumar A., Chakraborty D.: Effective properties of thermo-electro-mechanically coupled piezoelectric fiber reinforced composites. Mater. Des. 30, 1216–1222 (2009) · doi:10.1016/j.matdes.2008.06.009
[88] Kumari P., Nath J.K., Dumir P.C., Kapuria S.: 2D exact solutions for flat hybrid piezoelectric and magnetoelastic angle-ply panels under harmonic load. Smart Mater. Struct. 16, 1651–1661 (2007) · doi:10.1088/0964-1726/16/5/018
[89] Lee C.K.: Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part 1: Governing equations and reciprocal relationships. J. Acoust. Soc. Am. 87, 1144–1158 (1990) · doi:10.1121/1.398788
[90] Lee J.S., Jiang L.Z.: Exact electroelastic analysis of piezoelectric laminae via state space approach. Int. J. Solids Struct. 33, 977–990 (1996) · Zbl 0919.73291 · doi:10.1016/0020-7683(95)00083-6
[91] Leguillon D.: A method based on singularity theory to predict edge delamination of laminates. Int. J. Fract. 100, 105–120 (1999) · doi:10.1023/A:1018382422833
[92] Lessard L.B., Schmidt A.S., Shokrieh M.M.: Three-dimensional stress analysis of free-edge effects in a simple composite cross-ply laminate. Int. J. Solids Struct. 33, 2243–2259 (1996) · Zbl 0900.73460 · doi:10.1016/0020-7683(95)00054-2
[93] Levin V.M., Michelitsch T., Sevostianov I.: Spheroidal inhomogeneity in a transversely isotropic piezoelectric medium. Arch. Appl. Mech. 70, 673–693 (2000) · Zbl 1013.74027 · doi:10.1007/s004190000115
[94] Levin V.M., Sabina F.J., Bravo-Castillero J., Guinovart-Diaz R., Rodriguez-Ramos R., Valdiviezo-Mijangos O.C.: Analysis of effective properties of electroelastic composites using the self consistent and asymptotic homogenization methods. Int. J. Eng. Sci. 46, 818–834 (2008) · Zbl 1213.74257 · doi:10.1016/j.ijengsci.2008.01.017
[95] Li X., Liu D.: Generalised laminate theories based on double superposition hypothesis. Int. J. Numer. Methods Eng. 40, 1197–1212 (1997) · Zbl 0905.73040 · doi:10.1002/(SICI)1097-0207(19970415)40:7<1197::AID-NME109>3.0.CO;2-B
[96] Lin Y.: Some characteristics of distributions of free-edge interlaminar stresses in composite laminates. Int. J. Solids Struct. 26, 331–351 (1990) · doi:10.1016/0020-7683(90)90044-V
[97] Lu C.F., Huang Z.Y., Chen W.Q.: Semi-analytical solutions for free vibration of anisotropic laminated plates in cylindrical bending. J. Sound Vib. 304, 987–995 (2007) · doi:10.1016/j.jsv.2007.03.023
[98] Lu C.F., Chen W.Q., Shao J.W.: Semi-analytical three-dimensional elasticity solutions for generally laminated composite plates. Eur. J. Mech. A Solids 27, 899–917 (2008) · Zbl 1146.74029 · doi:10.1016/j.euromechsol.2007.12.002
[99] Mackerle J.: Smart materials and structures-a finite element approach-an addendum: a bibliography (1997–2002). Model. Simul. Mater. Sci. Eng. 11, 707–744 (2003) · doi:10.1088/0965-0393/11/5/302
[100] Mallik N., Ray M.C.: Effective coefficients of piezoelectric fiber-reinforced composites. AIAA J. 41, 704–710 (2003) · doi:10.2514/2.2001
[101] Mannini A., Gaudenzi P.: Multi-layer higher-order finite elements for the analysis of free-edge stresses in piezoelectric actuated laminates. Compos. Struct. 63, 263–270 (2004) · doi:10.1016/S0263-8223(03)00173-9
[102] Mitchell J.A., Reddy J.N.: A refined hybrid plate theory for composite laminates with piezoelectric laminae. Int. J. Solids Struct. 32, 2345–2367 (1995) · Zbl 0869.73038 · doi:10.1016/0020-7683(94)00229-P
[103] Mittelstedt C., Becker W.: Interlaminar stress concentrations in layered structures: Part I-A selective literature survey on the free-edge effect since 1967. J. Compos. Mater. 38, 1037–1062 (2004) · doi:10.1177/0021998304040566
[104] Mittelstedt C., Becker W.: Free-edge effects in composite laminates. Appl. Mech. Rev. 60, 217–244 (2007) · doi:10.1115/1.2777169
[105] Mori T., Tanaka K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta. Mater. 21, 571–574 (1973) · doi:10.1016/0001-6160(73)90064-3
[106] Nosier A., Bahrami A.: Free edge stresses in antisymmetric angle-ply laminates in extension and torsion. Int. J. Solids Struct. 43, 6800–6816 (2006) · Zbl 1120.74429 · doi:10.1016/j.ijsolstr.2006.02.006
[107] Oh J., Cho M.: A finite element based on cubic zigzag plate theory for the prediction of thermo-electric-mechanical behaviours. Int. J. Solids Struct. 41, 1357–1375 (2004) · Zbl 1045.74606 · doi:10.1016/j.ijsolstr.2003.10.019
[108] Pagano N.J.: Exact solutions for rectangular bidirectional composites and sandwich plates. J. Compos. Mater. 4, 20–34 (1970)
[109] Parton, V.Z, Kudryavstev, B.A.: Electromagnetoelasticity: piezoelectrics and electrically conductive solids: translated from Russian. In: Strelchenko, E.G. (eds.) Gordon and Breach Science Publ, New York (1988)
[110] Phillips E.A., Herakovich C.T., Graham L.L.: Damage development in composites with large stress gradients. Compos. Sci. Technol. 61, 2169–2182 (2001) · doi:10.1016/S0266-3538(01)00112-9
[111] Pipes R.B., Pagano N.J.: Interlaminar stresses in composite laminates under uniform axial extension. J. Compos. Mater. 4, 538–548 (1970)
[112] Plagianakos T.S., Saravanos D.A.: Coupled high-order shear layerwise analysis of adaptive sandwich piezoelctric composite beams. AIAA J. 43, 885–893 (2005) · doi:10.2514/1.12269
[113] Polit O., Bruant I.: Electric potential approximations for an eight node plate finite element. Comput. Struct. 84, 1480–1493 (2006) · doi:10.1016/j.compstruc.2006.01.032
[114] Praveen G.N., Reddy J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int. J. Solids Struct. 35, 4457–4476 (1998) · Zbl 0930.74037 · doi:10.1016/S0020-7683(97)00253-9
[115] Preumont A.: Vibration control of active structures: an introduction. Kluwer Academic Publishers, Dordrecht (2002) · Zbl 1011.74001
[116] Qing G., Qiu J., Liu Y.: A semi-analytical solution for static and dynamic analysis of plates with piezoelectric patches. Int. J. Solids Struct. 43, 1388–1403 (2006) · Zbl 1120.74604 · doi:10.1016/j.ijsolstr.2005.03.048
[117] Raja S., Prathap G., Sinha P.K.: Active vibration control of composite sandwich beams with piezoelctric extension-bending and shear actuators. Smart Mater. Struct. 11, 63–71 (2002) · doi:10.1088/0964-1726/11/1/307
[118] Raja S., Sreedeep R., Prathap G.: Bending behavior of hybrid-actuated piezoelectric sandwich beams. J. Int. Mater. Syst. Struct. 15, 611–619 (2004) · doi:10.1177/1045389X04042790
[119] Raju I.S., Crews J.H.: Interlaminar stress singularities at a straight free edge in composite laminates. Comput. Struct. 14, 21–28 (1981) · doi:10.1016/0045-7949(81)90079-1
[120] Rao S.S., Sunar M.: Analysis of distributed thermopiezoelectric sensors and actuators in advanced intelligent structures. AIAA J. 31, 1280–1286 (1993) · doi:10.2514/3.11764
[121] Ravichandran K.S.: Thermal residual stresses in a functionally graded material system. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 201, 269–276 (1995)
[122] Ray M.C., Bhattacharyya R., Samanta B.: Exact solutions for static analysis of intelligent structures. AIAA J. 31, 1684–1691 (1993) · Zbl 0783.73044 · doi:10.2514/3.11831
[123] Reddy J.N.: A refined nonlinear theory of plates with transverse shear deformation. Int. J. Solids. Struct. 20, 881–896 (1984) · Zbl 0556.73064 · doi:10.1016/0020-7683(84)90056-8
[124] Reddy J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000) · Zbl 0970.74041 · doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
[125] Reddy J.N., Wang C.M., Kitipornchai S.: Axisymmetric bending of functionally graded circular annular plate. Eur. J. Mech. A Solids 18, 185–199 (1999) · Zbl 0942.74044 · doi:10.1016/S0997-7538(99)80011-4
[126] Robaldo A., Carrera E., Benjeddou A.: A unified formulation for finite element analysis of piezoelectric adaptive plates. Comput. Struct. 84, 1494–1505 (2006) · doi:10.1016/j.compstruc.2006.01.029
[127] Rogacheva N.N.: The theory of piezoelectric shells and plates. CRC Press, Boca Raton (1994) · Zbl 1330.74122
[128] Sabina F.J., Rodriguez-Ramos R., Bravo-Castillero J., Guinovart-Diaz R.: Closed-form expressions for the effective coefficients of a fiber-reinforced composite with transversely isotropic constituents II: piezoelectric and hexagonal symmetry. J. Mech. Phys. Solids 49, 1463–1479 (2001) · Zbl 1017.74056 · doi:10.1016/S0022-5096(01)00006-0
[129] Salamon N.J.: Interlaminar stresses in a layered composite laminate in bending. Fiber Sci. Technol. 11, 305–317 (1978) · doi:10.1016/0015-0568(78)90020-9
[130] Saravanos D.A.: Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. Int. J. Solids Struct. 34, 359–378 (1997) · Zbl 0946.74519 · doi:10.1016/S0020-7683(96)00012-1
[131] Schapery R.A.: Thermal expansion coefficients of composite materials based on energy principles. J. Compos. Mater. 2, 380–404 (1968) · doi:10.1177/002199836800200308
[132] Sekouri E.M., Hu Y.R., Ngo A.D.: Modeling of a circular plate with piezoelectric actuators. Mechatronics 14, 1007–1020 (2004)
[133] Shen S., Kuang Z.B.: An active control model of laminated piezothermoelastic plate. Int. J. Solids Struct. 36, 1925–1947 (1999) · Zbl 0942.74051 · doi:10.1016/S0020-7683(98)00068-7
[134] Sheng H.Y., Ye J.Q.: A semi-analytical finite element for laminated composite plates. Compos. Struct. 57, 117–123 (2002) · doi:10.1016/S0263-8223(02)00075-2
[135] Sheng H.Y., Ye J.Q.: A state space finite element for laminated composite plates. Comput. Methods Appl. Mech. Eng. 191, 4276–4295 (2002) · Zbl 1083.74592 · doi:10.1016/S0045-7825(02)00379-1
[136] Shu X., Sun L.: An improved simple higher-order theory for laminated composite plates. Comput. Struct. 50, 231–236 (1994) · Zbl 0800.73144 · doi:10.1016/0045-7949(94)90298-4
[137] Smith W.A., Auld B.A.: Modelling 1-3 composite piezoelectrics: thickness-mode oscillations. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 40–47 (1991) · doi:10.1109/58.67833
[138] Soldatos K.P., Hadjigeorgiou V.P.: Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels. J. Sound Vib. 137, 369–384 (1990) · Zbl 1235.74121 · doi:10.1016/0022-460X(90)90805-A
[139] Stolarski H.K., Chiang M.Y.M.: On the significance of the logarithmic term in the free edge stress singularity of composite laminates. Int. J. Solids Struct. 25, 75–93 (1989) · Zbl 0669.73049 · doi:10.1016/0020-7683(89)90105-4
[140] Suleman A., Venkayya V.B.: A simple finite element formulation for a laminated composite plate with piezoelectric layers. J. Intell. Mater. Syst. Struct. 6, 776–782 (1995) · doi:10.1177/1045389X9500600605
[141] Sun C.T., Zhang X.D.: Use of thickness shear-mode in adaptive sandwich structures. Smart Mater. Struct. 4, 202–206 (1995) · doi:10.1088/0964-1726/4/3/007
[142] Sunar M., Rao S.S.: Thermopiezoelectric control design and actuator placement. AIAA J. 35, 534–539 (1997) · Zbl 0898.73048 · doi:10.2514/2.127
[143] Sze K.Y., Yao L.Q.: Modelling smart structures with segmented piezoelectric sensors and actuators. J. Sound Vib. 235, 495–520 (2000) · doi:10.1006/jsvi.2000.2944
[144] Sze K.Y., Yang X.M., Fan H.: Electric assumptions for piezoelectric laminated analysis. Int. J. Solids Struct. 41, 2363–2382 (2004) · Zbl 1179.74041 · doi:10.1016/j.ijsolstr.2003.11.018
[145] Tahani M., Nosier A.: Free edge stress analysis of general cross-ply composite laminates under extension and thermal loading. Compos. Struct. 60, 91–103 (2003) · doi:10.1016/S0263-8223(02)00290-8
[146] Tang Y.Y., Noor A.K., Xu K.: Assessment of computational models for thermoelectroelastic multilayered plates. Comput. Struct. 61, 915–933 (1996) · doi:10.1016/0045-7949(96)00037-5
[147] Tauchert T.R.: Piezothermoelastic behavior of a laminated plate. J. Ther. Stress. 15, 25–37 (1992) · doi:10.1080/01495739208946118
[148] Thornburgh R.P., Chattopadhyay A., Ghosal A.: Transient vibration of smart structures using a coupled piezoelectric-mechanical theory. J. Sound Vib. 274, 53–72 (2004) · doi:10.1016/S0022-460X(03)00648-5
[149] Tiersten H.F.: Linear piezoelectric plate vibrations. Plenum Press, New York (1969)
[150] Tomota Y., Kuroki K., Mori T., Tamura I.: Tensile deformation of two-ductile-phase alloys: flow curves of {\(\alpha\)} Fe-Cr-Ni alloys. Mater. Sci. Eng. 24, 85–94 (1976) · doi:10.1016/0025-5416(76)90097-5
[151] Topdar P., Chakraborti A., Sheikh A.H.: An efficient hybrid plate model for analysis and control of smart sandwich laminates. Comput. Methods Appl. Mech. Eng. 193, 4591–4610 (2004) · Zbl 1112.74442 · doi:10.1016/j.cma.2004.03.008
[152] Trindade, M.A., Benjeddou, A.: Refined sandwich finite element model for smart beams with shear piezoceramic actuators and sensors. In: Proceedings of II eccomas thematic conference on smart structures and materials, pp. 1–20. (2005)
[153] Turner P.S.: Thermal expansion stresses in reinforced plastics. J. Res. Nat. Bureau Stand. 37, 239–250 (1946)
[154] Tzou H.S.: Distributed sensing and controls of flexible plates and shells using distributed piezoelectric element. J. Wave. Mater. Interact. 4, 11–29 (1989)
[155] Tzou H.S.: Piezoelectric shells: distributed Sensing and Control of Continua. Kluwer Academic Publishers, Dordrecht (1993)
[156] Tzou H.S., Anderson G.L.: Intelligent structural systems. Kluwer Academic Publishers, Dordrecht (1992)
[157] Tzou H.S., Howard R.V.: A piezothermoelastic thin shell theory applied to active structures. ASME J. Vib. Acoust. 116, 295–302 (1994) · doi:10.1115/1.2930428
[158] Tzou H.S., Ye R.: Piezothermoelasticity and precision control of piezoelectric systems: theory and finite element analysis. ASME J. Vib. Acoust. 116, 489–495 (1994) · doi:10.1115/1.2930454
[159] Uchino K.: Ferroelectric devices. Marcel Dekker Inc, New York (2000)
[160] Vasques C.M.A., Rodrigues J.D.: Coupled three-layered analysis of smart piezoelectric beams with different electric boundary conditions. Int. J. Numer. Methods Eng. 62, 1488–1518 (2005) · Zbl 1078.74664 · doi:10.1002/nme.1237
[161] Vel S.S., Batra R.C.: Analytical solution for rectangular thick laminated plates subjected to arbitrary boundary conditions. AIAA J. 37, 1464–1473 (1999) · doi:10.2514/2.624
[162] Vel S.S., Batra R.C.: Cylindrical bending of laminated plates with distributed and segmented piezoelectric actuators/sensors. AIAA J. 38, 857–867 (2000) · doi:10.2514/2.1040
[163] Vel S.S., Batra R.C.: The generalized plane strain deformations of thick anisotropic composite laminated plates. Int. J. Solids Struct. 37, 715–733 (2000) · Zbl 0955.74043 · doi:10.1016/S0020-7683(99)00040-2
[164] Vel S.S., Batra R.C.: Three-dimensional analytical solution for hybrid multilayered piezoelectric plates. J. Appl. Mech. Trans. ASME 67, 558–567 (2000) · Zbl 1110.74727 · doi:10.1115/1.1311274
[165] Vel S.S., Batra R.C.: Exact solution for rectangular sandwich plates with embedded piezoelectric shear actuators. AIAA J. 39, 1363–1373 (2001) · doi:10.2514/2.1455
[166] Wakashima K., Tsukamoto H.: Mean-field micromechanics model and its application to the analysis of thermomechanical behaviour of composite materials. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. A 146, 291–316 (1991)
[167] Wang A.S.D., Crossman F.W.: Some new results on edge effect in symmetric composite laminates. J. Compos. Mater. 11, 92–106 (1977) · doi:10.1177/002199837701100110
[168] Wang B.T., Rogers C.A.: Laminate plate theory for spatially distributed induced strain actuators. J. Compos. Mater. 25, 433–452 (1991)
[169] Wang J., Yang J.: Higher-order theories of piezoelectric plates and applications. Appl. Mech. Rev. 53, 87–99 (2000) · doi:10.1115/1.3097341
[170] Wang S.S., Yuan F.G.: A singular hybrid finite element analysis of boundary-layer stresses in composite laminates. Int. J. Solids Struct. 19, 825–837 (1983) · Zbl 0516.73079 · doi:10.1016/0020-7683(83)90075-6
[171] Williamson R.L., Robin B.H., Drake J.T.: Finite element analysis of thermal residual stresses at graded ceramic-metal interfaces Part-1 model description and geometrical effects. J. Appl. Phys. 74, 1310–1320 (1993) · doi:10.1063/1.354910
[172] Woo J., Meguid S.A.: Nonlinear analysis of functionally graded plates and shallow shells. Int. J. Solids Struct. 38, 7409–7421 (2001) · Zbl 1010.74034 · doi:10.1016/S0020-7683(01)00048-8
[173] Wu C.P., Chiu K.H., Wang Y.M.: A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells. Comput. Mater. Continua 8, 93–132 (2008)
[174] Xu K., Noor A.K.: Three-dimensional analytical solution for coupled thermoelectroelastic response of multilayered cylindrical shell. AIAA J. 34, 802–812 (1996) · doi:10.2514/3.13143
[175] Xu K., Noor A.K., Tang Y.Y.: Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates. Comput. Methods Appl. Mech. Eng. 126, 355–371 (1995) · doi:10.1016/0045-7825(95)00825-L
[176] Yang J., Shen H.S.: Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions. Compos. Part-B 34, 103–115 (2003) · doi:10.1016/S1359-8368(02)00083-5
[177] Yang J.S.: Equations for elastic plates with partially electroded piezoelectric actuators in flexure with shear deformation and rotory inertia. J. Int. Mater. Syst. Struct. 8, 444–451 (1997) · doi:10.1177/1045389X9700800507
[178] Yang Y., Shen H.S.: Dynamic response of initially stressed functionally graded rectangular thin plates. Compos. Struct. 54, 497–508 (2001) · doi:10.1016/S0263-8223(01)00122-2
[179] Ye J.Q.: A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges. Comput. Methods Appl. Mech. Eng. 140, 383–392 (1997) · Zbl 0894.73078 · doi:10.1016/S0045-7825(96)01112-7
[180] Ye J.Q.: Laminated composite plates and shells: 3D modelling. Springer, Great Britain (2003)
[181] Ye J.Q., Soldatos K.P.: Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up. Compos. Eng. 4, 429–444 (1994) · doi:10.1016/S0961-9526(09)80016-6
[182] Yi S., Hilton H.H.: Finite element analysis of free edges stresses in non-linear viscoelastic composites under uniaxial extension bending and twisting loadings. Int. J. Numer. Methods Eng. 40, 4225–4238 (1997) · Zbl 0898.73067 · doi:10.1002/(SICI)1097-0207(19971130)40:22<4225::AID-NME256>3.0.CO;2-T
[183] Yin W.L.: The effect of temperature gradient on the free-edge interlaminar stresses in multi-layered structures. J. Compos. Mater. 31, 2460–2477 (1997)
[184] Zhang D., Ye J.Q., Sheng H.Y.: Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos. Struct. 76, 314–325 (2006) · doi:10.1016/j.compstruct.2005.04.021
[185] Zhang D., Ye J.Q., Sheng H.Y.: Free-edge and ply cracking effect in angle-ply laminated composites subjected to in plane loads. J. Eng. Mech. ASCE 133, 1268–1277 (2007) · doi:10.1061/(ASCE)0733-9399(2007)133:12(1268)
[186] Zhen W., Wanji C.: Refined triangular element for laminated elastic–piezoelectric plates. Compos. Struct. 78, 129–139 (2007a) · doi:10.1016/j.compstruct.2005.08.018
[187] Zhen W., Wanji C.: A study of global–local higher-order theories for laminated composite plates. Compos. Struct. 79, 44–54 (2007b) · doi:10.1016/j.compstruct.2005.11.027
[188] Zhou X., Chattopadhyay A., Gu H.: Dynamic responses of smart composite using a coupled thermo-piezoelectric-mechanical model. AIAA J. 38, 1939–1948 (2000) · doi:10.2514/2.848
[189] Zhu C., Lam Y.C.: A Rayleigh-Ritz solution for local stresses in composite laminates. Composit. Sci. Technol. 58, 447–461 (1998) · doi:10.1016/S0266-3538(97)00168-1
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.