General theory of thin plates on the basis of nonsymmetric theory of elasticity

Mechanics of Solids - Tập 47 - Trang 119-136 - 2012
S. O. Sargsyan1
1Nalbandian Gyumri State Pedagogical Institute, Gyumri, Armenia

Tóm tắt

The paper uses the asymptotically justified hypothesis method to construct three different general refined theories of micropolar thin elastic plates, depending on the values of physical dimensionless material parameters, involving: (i) independent displacement and rotation fields, (ii) constrained rotation, and (iii) low shear stiffness. All angular shear deformations are taken into account.

Tài liệu tham khảo

V. E. Panin (Editor), Physical Mesomechanics and Computer Simulation of Materials, Vol. 1 (Nauka, Novosibirsk, 1995) [in Russian]. N. F. Morozov, “Structure Mechanics of Materials and Structural Elements. Interaction between Nano-Micro-Meso- and Macro-Scales in Deformation and Fracture,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 188–189 (2005). R. V. Goldstein and N. F. Morozov, “Mechanics of Deformation and Fracture of Nanomaterials and Nanotechnology,” Fiz. Mezomekh. 10(5), 17–30 (2007) [Phys. Mesomech. (Engl. Transl.) 10 (5–6), 235–246 (2007)]. E. A. Ivanova, A. M. Krivtsov, and N. F. Morozov, “Derivation of Macroscopic Relations of the Elasticity of Complex Crystal Lattices Taking into Account the Moment Interactions at the Microlevel,” Prikl. Mat. Mekh. 71(4), 595–615 (2007) [J. Appl. Math. Mech. (Engl. Transl.) 71 (4), 543–561 (2007)]. A. S. J. Suiker, A. V. Metrikine, and R. De Borst, “Comparison of Wave Propagation Characteristics of the Cosserat Continuum Model and Corresponding Discrete Lattice Models,” Int. J. Solids Struct. 38(9), 1563–1583 (2001). V. I. Erofeev,Wave Processes in Solids with Microstructure (Izd-vo MGU, Moscow, 1999) [in Russian]. I. S. Pavlov and A. I. Potapov, “Two-Dimensional Model of a Granular Medium,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 98–109 (2007) [Mech. Solids (Engl. Transl.) 42 (2), 250–259 (2007)]. S. A. Lisina and A. I. Potapov, “Generalized Continuum Models in Nanomechanics,” Dokl. Ross. Akad. Nauk 420(3), 328–330 (2008) [Dokl. Phys. (Engl. Transl.) 53 (5), 275–277 (2008)]. V. V. Korepanov, M. A. Kulish, V. P. Matveenko, and I. N. Shardakov, “Analytical and Numerical Solutions for Static and Dynamic Problems of the Asymmetric Theory of Elasticity,” Fiz. Mezomekh. 10(5), 77–90 (2007) [Phys. Mesomech. (Engl. Transl.) 10 (5–6), 281–293 (2007)]. I. Yu. Smolin, “Using Micropolar Models to Describe Plastic Deformation at Mesolevel,” in Mathematical Modeling of Systems and Processes, No. 14 (Izdat. PGTU, Perm, 2006), pp. 189–205 [in Russian]. A. I. Lur’e and P. A. Belov, “Variational Statement of Mathematical Models of Media with Microstructures,” in Mathematical Modeling of Systems and Processes, No. 14 (Izd-vo PGTU, Perm, 2006), pp. 114–132 [in Russian]. A. C. Eringen, Microcontinuum Field Theories. Vol.1: Foundation and Solids (Springer, New York, 1999). M. Onami (Editor), Introduction to Micromechanics, (Metallurgiya, Moscow, 1987) [in Russian]. R. D. Gauthier and W. E. Jahsman, “A Quest for Micropolar Elastic Constants. Part II,” Arch. Mech. 33(5), 717–737 (1981). R. Lakes, “Experimental Methods for Study of Cosserat Elastic Solids and Other Generalized Elastic Continua,” in Continuum Models for Materials with Micro-Structure, Ed. by H. Muhlhaus (Wiley, New York, 1995), No. 1, pp. 1–22. A.E. Green and P. M. Naghdi, “The Linear Elastic Cosserat Surface and Shell Theory,” Int. J. Solids Struct. 4(6), 585–592 (1968). V. A. Palmov and H. Altenbach, “Über eine Cosseratsche Theorie für Elastische Platen,” Thechn. Mech. 3(3), 3–9 (1982). V. A. Palmov, “Simplest Noncontradictory System of Equations of the Theory of Thin Elastic Shells,” in Mechanics of Solids (Nauka, Moscow, 1986), pp. 106–112 [in Russian]. P. A. Zhilin, “Basic Equations of Nonclassical Theory of Shells,” in Dynamics and Strength of Machines. Proc. Leningrad Polytech. Inst., No. 386 (1982), pp. 29–46 [in Russian]. L. I. Shkutin, Mechanics of Deformation of Flexible Bodies (Nauka, Novosibirsk, 1988) [in Russian]. V. A. Eremeev and L.M. Zubov, Mechanics of Elastic Shells (Nauka, Moscow, 2008) [in Russian]. G. A. Vanin, “Couple-Stress Mechanics of Thin Shells,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 116–128 (2004) [Mech. Solids (Engl. Transl.) 39 (4), 92–101 (2004)]. M. Birsan, “The Solution of Saint-Venant’s Problem in the Theory of Cosserat Shells,” J. Elasticity 74, 185–214 (2004). S. A. Ambartsumyan, Micropolar Theory of Shells and Plates (Izd-vo NAN Armeii, Erevan, 1999) [in Russian]. S. O. Sargsyan, “Applied One-Dimensional Theories of Beams Based on Nonsymmetric Theory of Elasticity,” Fiz. Mezomekh. 11(5), 41–54 (2009). S. O. Sargsyan, “Boundary-Value Problems of the Asymmetric Theory of Elasticity for Thin Plates,” Prikl. Mat. Mekh. 72(1), 129–147 (2008) [J. Appl. Math. Mech. (Engl. Transl.) 72 (1), 77–86 (2008)]. S. O. Sargsyan, “The General Theory of Micropolar Thin Elastic Shells,” Dokl. NAN RA 108(4), 309–319 (2008). S. H. Sargsyan, “Analytic Mechanics of Bars, Plates, and Shells on Asymmetrical Theory of Elasticity,” in Abstracts Book. 22nd Int. Cong. Theor. and Appl. Mech. ICTAM2008. Adelaide, Australia, 2008 (2008), p. 228. B. L. Pelekh, Stress Concentration near Holes in Bending of Transversely Isotropic Plates (Naukova Dumka, Kiev, 1977) [in Russian]. Ch. Decolon, Analysis of Composite Structures (Taylor and Frances Books, New York, 2002). S. A. Ambartsumyan, Theory of Anisotropic Plates (Nauka, Moscow, 1987) [in Russian]. V. A. Pal’mov, “Basic Equations of the Theory of Nonsymmetric Elasticity,” Prikl. Mat. Mekh. 28(3), 401–408 (1964) [J. Appl. Math. Mech. (Engl. Transl.) 28 (3), 496–505 (1964)]. E. V. Kuvshinskii and E. L. Aero, “Continuum Theory of Asymmetric Elasticity,” Fiz. Tverd. Tela 5(9), 2591–2598 (1969) [Sov. Phys. Solid State (Engl. Transl.)]. W. Nowacki, Theory of Elasticity (PWN, Warsaw, 1970; Mir, Moscow, 1975).