Abstract
A refined high-order global-local laminated/sandwich beam theory is developed that satisfies all the kinematic and stress continuity conditions at the layer interfaces and considers effects of the transverse normal stress and transverse flexibility, e.g. for beams with soft cores or drastic material properties changes. The global displacement components, described by polynomial or combinations of polynomial and exponential expressions, are superposed on local ones chosen based on the layerwise or discrete-layer concepts. Furthermore, the non-zero conditions of the shear and normal tractions of the upper and lower surfaces of the beam may also be enforced. In the present C1-continuous shear locking-free finite element model, the number of unknowns is independent of the number of layers. Comparison of present bending and vibration results for thin and thick beams with results of the three-dimensional theory of elasticity reveals efficiency of the present method. Moreover, the proposed model is computationally economic and has a high convergence rate.
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References
Carrera E., Brischetto S.A.: Survey with numerical assessment of classical and refined theories for the analysis of sandwich plates. Appl. Mech. Rev. 62(010803), 1–17 (2009)
Zhang Y.X., Yang C.H.: Recent developments in finite element analysis for laminated composite plates. Compos. Struct. 88, 147–157 (2009)
Hu H., Belouettar S., Potier-Ferry M., Daya E.M.: Review and assessment of various theories for modeling sandwich composites. Compos. Struct. 84, 282–292 (2008)
Pagano N.J.: Exact solutions for composite laminates in cylindrical bending. J. Compos. Mater. 3, 398–411 (1969)
Pagano N.J.: Exact solutions for rectangular bi-direction composites and sandwich plates. J. Compos. Mater. 4, 20–34 (1970)
Pagano N.J., Hatfield S.J.: Elastic behavior of multilayered bidirectional composites. AIAA J. 10, 931–9331 (1972)
Stavsky Y., Loewy R.: On vibrations of heterogeneous orthotropic shells. J. Sound Vibr. 15, 235–236 (1971)
Reissner E.: The effects of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12, 69–76 (1945)
Mindlin R.D.: Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates. ASME J. Appl. Mech. 18, 1031–1036 (1951)
Whitney J.M.: The effects of transverse shear deformation on the bending of laminated plates. J. Compos. Mater. 3, 534–547 (1969)
Reddy J.N.: Mechanics of laminated composite plates and shells: Theory and analysis. 2nd edn. CRC Press, Boca Raton (2004)
Reddy J.N.: A generalization of two-dimensional theories of laminated composite plates. Commun. Appl. Numer. Meth. 3, 173–180 (1987)
Reddy J.N., Barbero E.J., Teply J.: A plate bending element based on a generalized laminate plate theory. Int. J. Numer. Meth. Eng. 28, 2275–2292 (1989)
Barbero E.J., Reddy J.N., Teply J.: An accurate determination of stresses in thick laminates using a generalized plate theory. Int. J. Numer. Meth. Eng. 29, 1–14 (1990)
Robbins D.H. Jr, Reddy J.N.: Modeling of thick composites using a layerwise laminate theory. Int. J. Numer. Meth. Eng. 36, 655–677 (1993)
Heuer R.: Static and dynamic analysis of transversely isotropic, moderately thick sandwich beams by analogy. Acta Mech. 91, 1–9 (1992)
Adam C., Ziegler F.: Forced flexural vibrations of elastic-plastic composite beams with thick layers. Compos. Part B 28, 201–213 (1997)
Adam C.: Moderately large vibrations of imperfect elastic-plastic composite beams with thick layers. Int. J. Acoustics Vib. 7, 11–20 (2002)
Adam C.: Nonlinear flexural vibrations of layered panels with initial imperfections. Acta Mech. 181, 91–104 (2006)
Lekhnitskii, S.G.: Strength calculation of composite beams. Vestnik inzhen i tekhnikov, No 9 (1935)
Ren J.G.: Bending theory of laminated plates. Compos. Sci. Tech. 27, 225–248 (1986)
Ren J.G., Owen D.R.J.: Vibration and buckling of laminated plates. Int. J. Solids Struct. 25, 95–106 (1989)
Ambartsumian, S.A.: Theory of anisotropic plates. Translated from Russian by Cheron T and Edited by Ashton JE., Tech. Pub. Co. (1969)
Whitney J.M.: The effects of transverse shear deformation on the bending of laminated plates. J. Compos. Mater. 3, 534–547 (1969)
Icardi U.: Eight-noded zig-zag element for deflection and stress analysis of plates with general lay-up. Compos. Part B 29, 425–441 (1998)
Icardi U.: Higher-order zig-zag model for analysis of thick composite beams with inclusion of transverse normal stress and sublaminates approximations. Compos. Part B 32, 343–354 (2001)
Icardi U.: A three-dimensional zig-zag theory for analysis of thick laminated beams. Compos. Struct. 52, 123–135 (2001)
Reissner E.: On a mixed variational theorem and on a shear deformable plate theory. Int. J. Numer. Meth. Eng. 23, 193–198 (1986)
Murakami H.: A laminated beam theory with interlayer slip. J. Appl. Mech. 51, 551–559 (1984)
Murakami H.: Laminated composite plate theory with improved in-plane responses. J. Appl. Mech. 53, 661–666 (1986)
Carrera E.: A study of transverse normal stress effects on vibration of multilayered plates and shells. J. Sound Vibr. 225, 803–829 (1999)
Carrera E.: Single-layer vs multi-layers plate modeling on the basis of Reissner’s mixed theorem. AIAA J. 38, 342–343 (2000)
Vidal P., Polit O.: A family of sinus finite elements for the analysis of rectangular laminated beams. Compos. Struct. 84, 56–72 (2008)
Beheshti-Aval S.B., Lezgy-Nazargah M.: A finite element model for composite beams with piezoelectric layers using a sinus model. J. Mech. 26, 249–258 (2010)
Carrera E.: Historical review of Zig-Zag theories for multilayered plates and shells. Appl. Mech. Rev. 56, 287–308 (2003)
Li X., Liu D.: Generalized laminate theories based on double superposition hypothesis. Int. J. Numer. Meth. Eng. 40, 1197–1212 (1997)
Shariyat M.: Non-linear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global–local plate theory. Compos. Struct. 92, 72–85 (2010)
Shariyat M.: A generalized high-order global–local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads. Compos. Struct. 92, 130–143 (2010)
Shariyat M.: A generalized global–local high-order theory for bending and vibration analyses of sandwich plates subjected to thermo-mechanical loads. Int. J. Mech. Sci. 52, 495–514 (2010)
Carrera E., Brischetto S.: Analysis of thickness locking in classical, refined and mixed multilayered plate theories. Compos. Struct. 82, 549–562 (2008)
Lo K.H., Christensen R.M., Wu E.M.: A high-order theory of plate deformation, Part II: Laminated plates. J. Appl. Mech. 44, 663–676 (1977)
Manjunatha B.S., Kant T.: New theories for symmetric/unsymmetric composite and sandwich beams with C0 finite elements. Compos. Struct. 23, 61–73 (1993)
Reddy J.N.: Theory and Analysis of Elastic Plates and Shells, 2nd ed. CRC/Taylor & Francis, London (2007)
Shariyat M.: Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells, under combined axial compression and external pressure. Int. J. Solids Struct. 45, 2598–2612 (2008)
Shariyat M.: Dynamic buckling of suddenly loaded imperfect hybrid FGM cylindrical shells with temperature-dependent material properties under thermo-electro-mechanical loads. Int. J. Mech. Sci. 50, 1561–1571 (2008)
Shariyat M.: Dynamic buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo-electro-mechanical loadings, considering the temperature-dependency of the material properties. Compos. Struct. 88, 228–239 (2009)
Shariyat M.: Vibration and dynamic buckling control of imperfect hybrid FGM plates with temperature-dependent material properties subjected to thermo-electro-mechanical loading conditions. Compos. Struct. 88, 240–252 (2009)
Polit O., Touratier M., Lory P.: A new eight-node quadrilateral shear bending plate finite element. Int. J. Numer. Meth. Eng. 37, 387–411 (1994)
Bekuit J.-J.R.B., Oguamanam D.C.D., Damisa O.: A quasi-2D finite element formulation for the analysis of sandwich beams. Finite Elem. Anal. Des. 43, 1099–1107 (2007)
Kapuria S., Dumir P.C., Jain N.K.: Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams. Compos. Struct. 64, 317–327 (2004)
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Lezgy-Nazargah, M., Shariyat, M. & Beheshti-Aval, S.B. A refined high-order global-local theory for finite element bending and vibration analyses of laminated composite beams. Acta Mech 217, 219–242 (2011). https://doi.org/10.1007/s00707-010-0391-9
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DOI: https://doi.org/10.1007/s00707-010-0391-9