A model of dynamic bending of rigid-plastic hybrid composite elliptical plates with a rigid center and simply supported or clamped contour, subjected to a uniformly distributed short-time intense dynamic load of explosive type is developed. The plates are multilayered and fibrous, with a symmetric distribution of layers with respect to the middle surface. The reinforcing fibers, made of different materials, are located in directions parallel or normal to the plate contour. Various mechanisms of dynamic deformation of the plates are considered. For each mechanism, equations of their dynamic behavior are obtained. Operating conditions of these mechanisms are analyzed. Analytical expressions for evaluating the limit loads, deformation time, and residual deflections are obtained. It is shown that a change in reinforcement parameters significantly affects the bearing capacity and residual deflection of the plates. The solutions proposed can be used in the design of reinforced metal-composite elliptical plates. Numerical examples are given for different reinforcement structures.
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References
A. P. Yankovskii, “Viscoplastic dynamics of metal-composite layered-fibrous shells at the action of loads of explosive type. I. Statement of the problem and a solution method,” Маtemat. Metodi Fiz.-Mekh. Polya, 55, No. 2, 119-130 (2012).
O. N. Popov, A. P. Malinovskii, M. O. Moiseenko, and T. A. Тreputneeva, “Calculation of heterogeneous structural beyond the limit of elasticity,” Vestnik TGASU, No. 4, 127-142 (2013).
N. A. Abrosimov, A. V. Elesin, and N. A. Novoseltseva, “Numerical analysis of the effect of reinforcement structure on the dynamic behavior and ultimate deformability of composite shells of revolution,” Mech. Compos. Mater., 50, No. 2, 313-326 (2014). DOI: 10.1007/s11029-014-9409-z.
M. S. Qatu, R.W. Sullivan, and W. Wang, “Recent research advances on the dynamic analysis of composite shells: 2000-2009,” Compos. Struct., 93, 14-31 (2010). DOI:https://doi.org/10.1016/j.compstruct.2010.05.014.
Z. K. Awad, T. Aravinthan, Y. Zhuge, and F. Gonzalez, “A review of optimization techniques used in the design of fibre composite structures for civil engineering applications,” Materials and Des., 33, 534-544 (2012). DOI:https://doi.org/10.1016/j.matdes.2011.04.061.
M. F. Jr. Caliri, A. J. M. Ferreira, and V. Tita, “A review on plate and shell theories for laminated and sandwich structures highlighting the finite element method,” Compos. Struct. (2016). DOI: https://doi.org/10.1016/j.compstruct.2016.02.036.
N. A. Abrosimov and V. G. Bazhenov, Nonlinear Problems of Dynamics of Composite Structures [in Russian], Nizhni Novgorod, Izd. NNGU, 391 p. (2002).
Yu. V. Nemirovskii and T. P. Romanova, “Dynamic plastic damageability of simply and doubly connected elliptic plates,” Prikl. Mekh. Tekhn. Fiz., 43, No. 2, 142-154 (2002).
Yu. V. Nemirovskii and T. P. Romanova, “Deformation of protective planar barriers with technological hatches,” Probl. Prochn., 39, No. 1, 22-38 (2007).
Yu. V. Nemirovskii and T. P. Romanova, “Dynamic deformation of a curvilinear plate with a rigid insert,” Prikl. Mekh. Tekhn. Fiz., 47, No. 2, 126-138 (2006).
T. P. Romanova and Yu. V. Nemirovskii, “Dynamic rigid-plastic deformation of arbitrarily shaped plates,” J. Mech. Mater. Struct., 3, No. 2, 313-334 (2008). DOI: https://doi.org/10.2140/jomms.2008.3.313.
Yu. V. Nemirovskii, “On a condition of plasticity (strength) for a reinforced layer,” Prikl. Mekh. Tekhn. Fiz.,. No. 5, 81-88 (1969).
Yu. V. Nemirovsky and B. S. Resnikoff, “On limit equilibrium of reinforced slabs and effectiveness of their reinforcement,” Archiwum Inzynierii Ladowej, XXI, No. 1, 57-67 (1975).
Yu. V. Nemirovskii and A. P. Yankovskii, “Pecurliarities of viscoplastic deformation of reinforced plates of variable thickness at the action of loads of explosive type,” Prikl. Mekh., 44, No. 2, 85-98 (2008).
Yu. V. Nemirovskii and A. P. Yankovskii, “Viscoplastic dynamics of layered-fibrous plates of variable thickness at the action of loadings of explosive type,” Mekh. Kompoz. Mater. Konstr. 12, No. 4, 484-501 (2006).
Yu. V. Nemirovskii and N. A. Fedorova, Mathematical Modeling of Planar Structures of Reinforced Fibrous Materials [in Russian], Krasnoyarsk, Izd. SFU, 136 p. (2010).
A. A. Savelov, Plane Curves [in Russian], M., Gos. Izd. Fiz. Mat. Liter., 293 p. (1960).
Yu.V. Nemirovskii and T. P. Romanova, “Dynamics of damage of plastic reinforced metal-composite annular plates,” Fundament. Prikl. Sovr. Mekh., Sb. Mater. Konf. Tomsk, April, 12-14, 2011, Tomsk, Tomsk Gos. Univ., 253 - 254 (2011).
Yu.V. Nemirovskii and T. P. Romanova, “Dynamic bending of reinforced regular polygonal plates with a rigid washer under the action of explosive loads,” Sb. Тr. Меzhd. Коnf. Akt. Probl. Prikl. Mat..Inform., Mekh., Voronezh, September, 20-22, 2010, Voronezh. Gos..Univ., 255-269 (2010).
M. I. Erkhov, “Theory of Perfectly Plastic Bodies and Structures [in Russuan], M., Nauka, 1978, 352.
G. Almkvist and B. Berndt, “Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π, and the Ladies diary,” Am. Math. Monthly., 95, 585-608 (1988).
H. G. Hopkins, “Some remarks concerning the solution of plastic plate problems upon the yield criterion,” Proc. 9th Int. Cong. Appl. Mech., 6, 448-457 (1957).
Т. P. Romanova, “Load-carrying ability and optimization of three-layer reinforced round plates from different-resistance materials supported along the internal contour,” Probl. Prochn. Plast., 77, No. 3, 286-300 (2015).
A. P. Yankovskii, “Elastic-plastic deformation of the bent reinforced plates with a weakened resistance to transverse shear,” Prikl. Mat. Mekh., 77, iss. 6, 853-876 (2013).
E. Carrera and S. Brischetto, “A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates,” Appl. Mech. Rev., Trans. ASME, 62, No. 1, 010803-1-010803-17 (2009).
V. F. Panin, and Yu. A. Gladkov, “Structures with a Filler [in Russian], - M.: Mekh. Eng., 272 p. (1991).
M. Rezaeifard, S. J. Salami, M. B. Dehkordi, and M. Sadighi, “A new nonlinear model for studying a sandwich panel with thin composite faces and elastic-plastic core,” Thin-Walled Structures, 107, 119-137 (2016). DOI: https://doi.org/10.1016/j.tws.2016.06.012.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 53, No. 5, pp. 809-828 , September-October, 2017.
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Romanova, T.P. Modeling the Dynamic Bending of Rigid-Plastic Hybrid Composite Elliptical Plates with a Rigid Insert. Mech Compos Mater 53, 565–578 (2017). https://doi.org/10.1007/s11029-017-9687-3
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DOI: https://doi.org/10.1007/s11029-017-9687-3