Theories for laminated and sandwich plates

G. W. Ehrenstein, Faserverbund-Kunstoffe, Hanser, München (1992).

V. Dundrová, V. Kovarik, P. Šlapák, Biegetheorie der Sandwichplatten, Academia, Praha (1970).

K. Stamm K., H. Witte, Sandwichkonstruktionen, Springer, Wien-New York (1974).

A. K. Noor and W. S. Burton, “Assessment of computational models for multilayered anisotropic plates”, Compos. Structures,14, 233–265 (1990).

F. K. Noor and W. S. Burton, Assessment of computational models for multilayered anisotropic plates, Appl. Mech. Rev.,43, No. 4, 67–97 (1990).

F. K. Noor and W. S. Burton, and C. W. Bert, Computational models for sandwich panels and shells, Appl. Mech. Rev.,49, No. 3, 155–199 (1996).

A. Puck, Festigkeitsanalyse an Faser-Matrix-Laminaten: Realistische Bruchkriterien und Degrationsmodelle, Hanser, München (1996).

H. Altenbach, “Modelling of viscoelastic behaviour of plates”, in: M. Życzkowski (ed.), Creep in Structures, Springer, Berlin, (1990), pp. 531–537.

S. A. Ambartsumyan, Theory of Anisotropic Plates [in Russian], Nauka, Moscow (1987).

E. I. Grigolyuk and I. T. Seleznev, “Nonclassical theories of oscillations of rods, plates, and shells”, Itogi Nauki I Tekhniki. Ser. Mekh. Tverdogo Deformir. Tela, 5, Moscow (1973).

P. M. Naghdi, The Theory of Plates and Shells. Handbuch der Physik (S. Flügge, Hrsg.), Bd. VI a/2, Springer, Berlin (1972).

E. Reissner, “Reflections on the theory of elastic plates”, Appl. Mech. Rev.,38, No. 11, 1453–1464 (1985).

W. Wunderlich, Vergleich verschiedener Approximationen der Theorie dünner Schalen (mit numerischen Beispielen), Techn. Wiss. Mitt. der Instituts für Konstruktiven Ingenierbau der Ruhr-Universität Bochum, 73-1 (1973).

G. Kirchhoff, “Über das Gleichgewicht und die Bewegung einer elastischen Scheibe”, J. Reine Angew. Math.,40, 51–88 (1850).

E. Reissner, “On the theory of bending of elastic plates”, J. Math. Phys.,23, 184–191 (1944).

H. Hencky, “Über die Berücksichtigung der Schubverzerrung in ebenen Platten”, Ingenieur-Archiv,16, 72–76 (1947).

S. A. Ambartsumyan, “On the bending theory of anisotropic plates and shallow shells”, Izv. Akad. Nauk SSSR, No. 5, 69–77 (1958).

M. Levinson, “An accurate simple theory of the statics and dynamics of elastic plates”, Mech. Res. Comm.,7, No. 6, 343–350 (1980).

T. Lewinski, “On refined plate models based on kinematical assumptions”, Ingenieur-Archiv,57, 133–146 (1987).

K. H. Lo, R. M. Christensen, and E. M. Wu, “A high-order theory of plate deformation. Pt. I: Homogeneous plates”, Trans. ASME, J. Appl. Mech.,44, No. 4, 663–668 (1977).

I. N. Vekua, Some General Methods of Constructing Different Variants of the Theory of Shallow Shells [in Russian], Nauka, Moscow (1982).

M. Touratier, “An efficient standard plate theory”, Int. J. Eng. Sci.,29, No. 8, 901–916 (1991).

R. Kienzler, “Erweiterung der klassischen Schalentheorie; der Einfluß von Dickenverzerrung und Querschnittverwölbungen”, Ingenieur-Archiv,52, 311–322 (1982).

G. Preußer, “Eine Systematische Herleitung verbesserter Plattentheorien”, Ingenieur-Archiv,54, 51–61 (1984).

A. L. Gol'denveiser, “Construction of approximate theory of shells using asymptotic integration of equations of elasticity theories”, Prikl. Mat. Mekh.,26, No. 4, 668–686 (1962).

P. A. Zhilin, “Mechanics of deformable directed surfaces”, Int. J. Sol. Struct.,12, 635–648 (1976).

E. I. Grigolyuk and A. F. Kogan, “Current status in the theory of multilayered shells”, Prikl. Mekh.,8, No. 6, 3–17 (1972).

J. N. Reddy, “On the generalization of displacement-based laminate theories”, Appl. Mech. Rev.,42, No. 11, Pt. 2, S213-S222 (1993).

W. S. Burton and A. K. Noor, “Assessment of computational models for sandwich panels and shells”, Comput. Meth. Appl. Mech. Eng.,124, 125–151 (1995).

L. P. Khoroshun and B. V. Gerasimchuk, “Equations of bending of plates at nonlinear strains of transverse shear”, Prikl. Mekh.,18, No. 4, 64–70 (1982).

D. H. Hodges, B. W. Lee, and A. R. Atilgan, “Application of the variational-asymptotical method to laminated composite plates”, AIAA J.,31, No. 9, 1674–1683 (1993).

D. H. Robbins and J. N. Reddy, “Modelling of thick composites using a layerwise laminate theory”, Int. J. Numer. Meth. Eng.,36, 655–677 (1993).

E. I. Grigolyuk and G. M. Kulikov, “General direction of development of the theory of multilayered shells”, Mech. Compos. Mater.,24, No. 2, 231–241 (1988).

A. K. Noor and W. S. Burton, “Assessment of shear deformation theories for multilayered composite plates”, Appl. Mech. Rev.,42, No. 1, 1–13 (1989).

A. K. Noor and W. S. Burton, “Stress and free vibration analyses of multilayered composite plates”, Compos. Struct.,11, 183–204 (1989).

J. N. Reddy and D. H. Robbins, “Theories and computational models for composite laminates”, Appl. Mech. Rev.,47, No. 6, Pt. 1, 21–35 (1994).

H. Altenbach and P. A. Zhilin, “General theory of elastic simple shells” Usp. Mekh.,11, No. 4, 107–148 (1988).

T. Lewinski “On displacement-based theories of sandwich plates with soft core”, Mech. Res. Comm.,17, No. 6, 375–382 (1990).

E. Reissner, “The effect of transverse shear deformation on the bending of elastic plates”, J. Appl. Mech.,12, No. 11, 69–77 (1945).

E. Reissner, “On the bending of elastic plates” Quart. Appl. Math.,5, 55–68 (1947).

F. B. Hildebrand, E. Reissner, and G. B. Thomas, “Notes on the foundations of the theory of small displacements of orthotropic shells”, T. N. 1883, NACA (1949).

H. Altenbach, V. Matzdorf, “Zu einigen Anwendungen direkt formulierter Plattentheorien”, Wiss. Z. TU Magdeburg,32, No. 4, 95–99 (1988).

E. Reissner and Y. Stavsky, “Bending and stretching of certain types of heterogeneous aeolotropic elastic plates”, Trans ASME, J. Appl. Mech.,28, No. 3, 402–408 (1961).

J. M. Whitney, “The effect of transverse shear deformation on the bending of laminated plates”, J. Compos. Mater.,3, 534–547 (1969).

P. A. Zhilin, “On the Poisson and Kirchhoff theories of plates from the viewpoint of modern plate theory”, Izv. RAN. Mekh. Tverd. Tela, No. 3, 48–64 (1992).

J. N. Reddy, “An evaluation of equivalent-single-layer and layerwise theories of composite laminates”, Compos. Struct.,25, 21–35 (1993).

E. Bertóti, “Stress-based hierarchic models for laminated composites”, Computer. Meth. Appl. Mech. Eng.,123, 327–353 (1995).

K. Rohwer, “Application of higher order theories to the bending analysis of layered composite plates”, Int. J. Sol. Struct.,29, No. 1, 105–119 (1992).

K. Rohwer, “Computational models for laminated composites”, Z. Flugwiss. Weltraumforsch.,17, 323–330 (1993).

J. N. Reddy, “A generalization of two-dimensional theories of laminated composite plates” Comm. Appl. Num. Meth.,3, 173–180 (1987).

J. Altenbach, W. Kissing, H. Altenbach, Dünwandige Stab- und Stabschalentragwerke, Vieweg, Braunschweig, Wiesbaden (1994).

V. A. Ignat'ev, O. L. Sokolov, J. Altenbach, and W. Kissing, Calculation of Thin-Walled Spatial Designs of Plate and Plate-Rod Structures [in Russian], Stroyizdat, Moscow (1996).

E. J. Barbero, J. N. Reddy, and J. Teply, “An accurate determination of stresses in thick laminates using a generalized plate theory”, Int. J. Numer. Meth. Eng.,29, 1–14 (1990).

J. N. Reddy, E. J. Barbero, and J. Teply, “A plate bending element based on a generalized laminate plate theory”, Int. J. Numer. Meth. Eng.,28, 2275–2292 (1989).

X. Lu and D. Liu, “An interlaminar shear stress continuity theory for both thin and thick composite laminates”, Trans. ASME. J. Appl. Mech.,59, No. 3, 502–509 (1992).

J. Teply, E. J. Barbero, and J. N. Reddy, “Bending, vibration and stability of Arall laminates using generalized laminate plate theory”, Int. J. Sol. Struct.,27, No. 5, 585–599 (1991).

E. J. Barbero and J. N. Reddy, “Modelling of delamination in composite laminates using a layer-wise plate theory”, Int. J. Sol. Struct.,28, No. 3, 373–388 (1991).

K. Bhaskar and T. K. Varadan, “Refinement of higher-order laminated theories”, AIAA J.,27, No. 12, 1830–1831 (1989).

J. M. Whitney and A. W. Leissa, “Analysis of heterogeneous anisotropic plates”, Trans. ASME. J. Appl. Mech.,36, No. 2, 261–266 (1969).

H. Altenbach, J. Altenbach, R. Rikards, Einführung in die Mechanik der Laminat- und Sandwichtragwerke. Deutscher Verlag für Grundstoffindustrie, Stuttgart (1996).

T. S. Chow, “On the propagation of flexural waves in an orthotropic laminated plate and its response to an impulsive load”, J. Compos. Mater.,5, 306–319 (1971).

N. F. Knight, Jr. and Y. Oi, “Restatement of first-order shear-deformation theory for laminated plates”, Int. J. Sol. Struct.,34, No. 4, 481–492 (1997).

R. D. Mindlin, “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates”, Trans. ASME. J. Appl. Mech.,18, No. 2, 31–38 (1951).

Y. Oi Y. and N. F. Knight, Jr., “A refined first-order shear-deformation theory and its justification by plane-strain bending problem of laminated plates”, Int. J. Sol. Struct.,33, No. 1, 49–64 (1996).

E. Reissner, “A consistent treatment of transverse shear deformations in laminated anisotropic plates”, AIAA J.,10, No. 5, 716–718 (1972).

R. B. Rikards, A. K. Chate, and M. L. Kenzer, “Variants of averaging shear stiffness of laminated structures in calculation of natural frequencies according to the Timoshenko model”, Vopr. Dinam. Prochn.,52, 176–193 (1990).

S. Vlachoutsis, “Shear correction factors for plates and shells”, Int. J. Numer. Meth. Eng.,33, 1537–1552 (1992).

J. M. Whitney, “Shear correction factors for orthotropic laminates under static loads”, Trans. ASME. J. Appl. Mech.,37, No. 1, 302–304 (1970).

J. M. Whitney and C. T. Sun, “A higher order theory for extensional motion of laminated composites”, J. Sound Vibr.,30, No. 1, 85–97 (1973).

J. N. Reddy, “A refined nonlinear theory of plates with transverse shear deformation”, Int. J. Sol. Struct.,20, Nos. 9/10, 881–896 (1984).

J. N. Reddy and N. D. Phan, “Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory”, Int. J. Sol. Struct.,98, No. 2, 157–170 (1985).

Mallikarjuna and T. Kant, “A critical review and some results of recently developed refined theories of fibre-reinforced laminated composites and sandwiches”, Comp. Struct.,23, 293–312 (1993).

B. N. Phandya and T. Kant, “Higher-order shear deformable theories for flexure of sandwich plates—finite element evaluation”, Int. J. Sol. Struct.,24, No. 12, 1267–1286 (1988).

N. D. Phan and J. N. Reddy, “Analysis of laminated composite plates using higher-order shear deformation theory”, Int. J. Numer. Meth. Eng.,21, 2201–2219 (1985).

J. N. Reddy, “A simple higher-order theory for laminated composite plates”, Trans. ASME. J. Appl. Mech.,51, 745–752 (1984).

E. Reissner, “Note on the effect of transverse shear deformation in laminated anisotropic plates”, Comp. Meth. Appl. Mech. Eng.,20, 203–209 (1979).

H. Altenbach, “Eine nichlineare Theorie dünner Dreischichtschalen und ihre Anwendung auf die Stabilitätsuntersuchung eines dreischichtigen Streifens”, Techn. Mech.,3, No. 2, 23–30 (1982).

H. Altenbach, “Die Grundgleichungen einer linearen Theorie für dünne, elastische Platten und Scheiben mit inhomogenen Materialeigenschaften in Dickrichtung”, Techn. Mech.,5, No. 2, 51–58 (1984).

A. R. Atilgan and D. H. Hodges, “On the strain energy of laminated composite plates”, Int. J. Sol. Struct.,29, No. 20, 2527–2543 (1992).

V. G. Sutyrin and D. H. Hodges, “On asymptotically correct linear laminated plate theory”, Int. J. Sol. Struct.,33, No. 25, 3649–3671 (1996).

S. T. Mau, “A refined laminated plate theory”, Trans. ASME. J. Appl. Mech.,40, No. 2, 606–607 (1973).

K. H. Lee, N. R. Senthilnathan, S. P. Lim, and S. T. Chow, “An improved zig-zag model for the bending of laminated composite plates”, Compos. Struct.,15, 137–148 (1990).

K. H. Lee and L. A. Cao, “A predictor-corrector zig-zag model for the bending of laminated composite plates”, Int. J. Sol. Struct.,33, No. 6, 879–897 (1996).

M. Chow, “An efficient higher order composite plates theory for general lamination configurations”, AIAA J., 1496–1510 (1991).

K. H. Lee, W. Z. Lin, and Chow S. T., “Bidirectional bending of laminated composite plates using an improved zig-zag model”, Compos. Struct.,28, 283–294 (1994).

X. Li and D. Liu, “Zigzag theory for composite laminates”, AIAA J.,33, No. 6, 1163–1165 (1994).

H. Murakami, “Laminated composite plate theory with improved in-plane responses”, Trans. ASME. J. Appl. Mech.,53, No. 3, 661–666 (1986).

E. Nast, “Flächentragwerkstheorie höherer Ordnung mit speziellen Ansatzfunktionen”, Techn. Mech.,14, Nos. 3/4, 203–212 (1994).