On the nonlinear behaviour of bimodular multilayer ed plates.
Porco, Giacinto ; Spandea, Giuseppe ; Zinno, Raffaele
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 2 (1991), p. 317-337 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

In an earlier study [16] the nonlinear behaviour of unimodular laminated plates was studied. This paper, following the previous study, concerns a large deflection analysis of moderately thick rectangular plates having arbitrary boundary conditions and finite thickness shear moduli. The plates are manufactured in bimodular materials and constructed in a cross-ply fashion or in a single layer with arbitrary fibre direction angle. Numerical results are obtained by a finite element technique in which are specified five degrees of freedom, three displacements and two bending slopes per node. Furthermore, the effects of plate aspect ratio, bimodularity ratio and fibre orientation are studied; finally, comparisons with some results available in literature are also given.

In una precedente Nota [16] è stato studiato il comportamento nonlineare di piastre laminate composite realizzate in materiale unimodulare. In questo lavoro, proseguendo lo studio precedente, viene analizzato il comportamento non lineare di piastre rettangolari moderatamente spesse arbitrariamente vincolate. Le piastre sono realizzate in materiale bimodulare e modellate secondo lo schema cross-ply ovvero in una singola lamina avente una arbitraria orientazione della direzione delle fibre. I risultati sono ottenuti adottando una tecnica computazionale agli elementi finiti considerando, per ogni nodo, cinque gradi di libertà: tre componenti di spostamento e due rotazioni flessionali. Inoltre vengono studiati gli effetti del rapporto di forma, del rapporto di bimodularità e della direzione delle fibre; vengono, infine, riportati alcuni confronti con risultati reperibili in letteratura.

Publié le : 1991-12-01
@article{RLIN_1991_9_2_4_317_0,
     author = {Giacinto Porco and Giuseppe Spandea and Raffaele Zinno},
     title = {On the nonlinear behaviour of bimodular multilayer ed plates.},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {2},
     year = {1991},
     pages = {317-337},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1991_9_2_4_317_0}
}

Porco, Giacinto; Spandea, Giuseppe; Zinno, Raffaele. On the nonlinear behaviour of bimodular multilayer ed plates.. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 2 (1991) pp. 317-337. http://gdmltest.u-ga.fr/item/RLIN_1991_9_2_4_317_0/

[1] Ashton, J. E. - Whitney, J. M., Theory of laminated plates. Technomic Publishing Co. Inc., 1970.

[2] Saint Venant, B., Notes to the 3rd ed. of Navier's, Résumé des leçons de la résistance des corps solides. Paris1864, 175.

[3] Timoshenko, S., Strength of materials. In: Advanced Theory and Problems 2nd éd., Van Nostrand, Princeton, New Jersey 1941, part 2, 362-369. | JFM 67.0794.03

[4] Ambartsumyan, S. A., The axisymmetric problem of a circular cylindrical shell made of material with different stiffnesses in tension and compression. Izvestiya Akademiya Nauk SSSR, Mekhanika, n. 4, 77-85 (Engl, trans. National Tech. Information Center Document AD. 675312, 1967).

[5] Jones, R. M. - Morgan, H. S., Bending and extension of cross-ply laminates with different moduli in tension and compression. Computers & Structures, vol. 11, 1980, 181-190. | Zbl 0467.73094

[6] Bert, C. W., Models for fibrous composites with different properties in tension and in compression. J. of Engng. Mat. Tech., Trans. of ASME 99H(4), 1977, 344-349.

[7] Ambartsumyan, S. A. - Khachatryan, A. A., Basic equations in the theory of elasticity for materials with different stiffness in tension and compression. Inzh. Zhur. MTT2, 1966, 44-53 (in Russian).

[8] Ambartsumyan, S. A., Basic equations and relations in the theory of anisotropic bodies with different moduli in tension and compression. Inzh. Zhur. MTT3, 1969, 51-61 (in Russian).

[9] Tabaddor, F., Constitutive different equations for bimodulus elastic materials. AIAA J., vol. 10(4), 1972, 516-518.

[10] Bert, C. W. - Reddy, J. N. - Sudhakar Reddy, V. - Chao, W. C., Bending of thick rectangular plates laminated of bimodulus composite materials. AIAA J., vol. 19(10), 1981, 1342-1349. | Zbl 0464.73083

[11] Mindlin, R. D., Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates. J. of Appl. Mech., 1951, 31-38. | Zbl 0044.40101

[12] Von Karman, T., Festigkeitsprobleme in Maschinenbau. Encycl. Math. Wiss., vol. 4, 1910, 348-351.

[13] Von Karman, T. - Sechler, E. E. - Donnell, L. H., The strength of thin plates in compression. Trans. ASME, vol. 54, 1932, 53-57. | Zbl 0004.07802

[14] Gordaninejad, F., Nonlinear bending of anisotropic bimodular composite plates. Computers & Structures, vol. 33, 1989, 615-620.

[15] Gordaninejad, F., A finite element model for the analysis of thick, anisotropic, bimodular, fibrous-composite plates. Computers & Structures, vol. 31, 1989, 907-912. | Zbl 0705.73231

[16] Porco, G. - Spadea, G. - Zinno, R., A geometrically nonlinear analysis of laminated composite plates using a shear deformation theory. Atti Acc. Lincei Rend. fis., s. 8, vol. 83, 1989, 159-176. | MR 1142455 | Zbl 0732.73027

[17] Bruno, D. - Porco, G. - Zinno, R., Finite element analysis of nonlinear laminated composite plates. Proceedings of International Meeting UPSA IV (Capri, June 14-16, 1989). | Zbl 0761.73106

[18] Reddy, J. N. - Chao, W. C., Nonlinear bending of bimodular-material plates. Int. J. Solids Structures, vol. 19, n. 3 , 1983, 229-237. | Zbl 0502.73059

[19] Reddy, J. N. - Chao, W. C., Finite-element analysis of laminated bimodulus composite material plates. Computers & Structures, vol. 12, 1980, 245-251. | Zbl 0449.73079