APPLICATION OF KIRCHHOFF-LOVE HYPOTHESES FOR NON-LINEAR PLATE BENDING

Виталий Борисович Минтюк

Abstract


Two plates were considered that follow the Kirchhoff-Love hypotheses and have John’s material formulation and the standard second order material formulation. A comparative analysis of actual strain and stress distributions was carried for the inverse problem of plate non-linear bending. It was shown that through-thickness variation of the components of plate Bio symmetric stress tensor was much closer to linear distribution than the distribution law for the components of second Piola-Kirchhoff stress tensor. Linearization of stresses with respect to the degenerated coordinate leads to practically similar values of internal moments and significantly different membrane forces.


Keywords


non-linear plate bending; Kirchhoff-Love hypotheses; energy-conjugated tensors

References


Khalilov, S. A., Mintyuk, V. B. Ploskii nelineinyi izgib balki. Vyvod zamknutoi sistemy uravnenii [Simple non-linear bending of beam. Derivation of closed equations set]. Aviatsionno-kosmicheskaya tekhnika i tekhnologiya [Aerospace Engineering and Technology]. Kharkiv, «KhAI» Publ., 2011, no. 1, vol. 78, pp. 39 – 45.

Mintyuk, V. B. Issledovanie ploskogo nelineinogo izgiba balki [Researching nonlinear plane bending of a beam]. Aviatsionno-kosmicheskaya tekhnika i tekhnologiya [Aerospace Engineering and Technology]. Kharkiv, «KhAI» Publ., 2011, no. 3, vol. 80, pp. 43 – 52.

Mintyuk, V. B. Issledovanie geometricheski i fizicheski nelineinogo obobshchennogo ploskogo napryazhennogo sostoyaniya [Research of geometrically and physically nonlinear generalized plane stress]. Aviatsionno-kosmicheskaya tekhnika i tekhnologiya [Aerospace Engineering and Technology]. Kharkiv, «KhAI» Publ., 2012, no. 4, vol. 91, pp. 38 – 44.

Ambartsumyan, S. A. Teoriya anizotropnykh plastin: prochnost', ustoichivost' i kolebaniya [The theory of anisotropic plates: strength, buckling and oscillations]. Moskow, «Nauka» Publ., 1987. 360 р.

Antman, St. S. Nonlinear Problems of Elasticity. NY, Springer Publ., 1995. 835 p.

Ciarlet, Ph. G. Mathematical Elasticity. Volume II:Theory of Plates. Amsterdam, Elsevier Publ., 1997. 498 p.

Chernykh, K. F. Nelineinaya teoriya uprugosti v mashinostroitel'nykh raschetakh [Nonlinear theory of elasticity in engineering calculations]. Leningrad, «Mashinostroenie» Publ., 1986. 336 р.

Panovko, Ya. G. Ustoichivost' i kolebaniya uprugikh sistem [Buckling and oscillations of elastic systems]. Moskow, «Nauka» Publ., 1979. 384 р.

Ciarlet, P. G. Mathematical Elasticity. Vol. I. Three-dimensional elasticity. Elsevier Science Publishers, 1988. 451 p.




DOI: https://doi.org/10.32620/aktt.2017.4.02