On the basis of a semi-analytical finite element method, an effective approach has been developed for studying transient processes of dynamic deformation of three-dimensional heterogeneous bodies of revolution and prismatic bodies of complex shape and structure by the action of time-and space-varying pulsed stressing with allowance for the plastic properties of the material and time-varying contact interaction conditions. New types of finite elements have been created, on the basis of which computational relationships of the semi-analytical finite element method (SAFEM) for problems of dynamics have been constructed. Modified relationships of the Newmark method have been obtained, which have been formulated for the amplitude subsystems of SAFEM. Effective block iteration algorithms for the solution of large systems of nonlinear equations of SAFEM have been developed and realized.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
V. A. Bazhenov, A. I. Gulyar, A. S. Sakharov, and A. G. Topor, Semi-Analytical Finite Element Method in Deformable Body Mechanics [in Russian], Vipol, Kiev (1993).
V. A. Bazhenov, A. I. Gulyar, A. G. Topor, and I. I. Solodei, “Development of SAFEM as applied to problems of statics and dynamics of bodies of revolution under nonaxisymmetric loads,” Prikl. Mekh., 34, No. 1, 31–38 (1998).
G. D. Gavrilenko and O. A. Trubitsina, Vibration and Stability of Ribbed Shells of Revolution [in Russian], Barviks, Dnepropetrovsk (2008).
A. N. Guz’ (Ed.), Mechanics of Composites [in Russian], in 12 volumes, Naukova Dumka, Kiev (1993).
P. P. Lepikhin and V. A. Romashchenko, Strength of Thick-Walled Shells of Revolution under Pulsed Loading [in Russian], Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev (2010).
V. V. Kharchenko, Simulation of Processes of High-Rate Deformation of Materials with Allowance for Viscoplastic Effects [in Russian], LOGOS, Kiev (1999).
A. Yu. Chirkov, “Application of mixed variational formulations based on the finite element method to the solution of problems on natural vibrations of elastic bodies,” Strength Mater., 40, No. 2, 253–268 (2008).
L. M. Kachanov, Fundamentals of the Plasticity Theory [in Russian], Gos. Izd. Tekh.-Teoret. Lit., Moscow (1963).
B. I. Koval’chuk, A. A. Lebedev, and S. É. Umanskii, Mechanics of Inelastic Deformation of Materials and Structural Members [in Russian], Naukova Dumka, Kiev (1987).
V. A. Pal’mov, Vibration of Elastoplastic Bodies [in Russian], Nauka, Moscow (1976).
Yu. N. Shevchenko and I. V. Prokhorenko, Methods of Shell Design [in Russian], Vol. 3: Theory of Elastoplastic Shells in Nonisothermal Loading Processes, Naukova Dumka, Kiev (1981).
B. A. Gorlach, Finite Inelastic Strains of Solids under Thermomechanical Actions [in Russian], in 2 parts, Moscow (1985).
V. M. Segal, Technological Problems of the Plasticity Theory [in Russian], Nauka i Tekhnika, Minsk (1977).
K.-J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs (1982).
O. C. Zienkiewicz, The Finite Element Method in Engineering Science, McGraw-Hill, London (1971).
O. C. Zienkiewicz and K. Morgan, Finite Elements and Approximations, Wiley & Sons, London (1983)
V. A. Bazhenov, A. I. Gulyar, A. L. Kozak, et al., Numerical Finite Element Simulation of the Fracture of Concrete-Steel Constructions [in Russian], Naukova Dumka, Kiev (1996).
V. A. Bazhenov, O. I. Gulyar, S. O. Piskunov, and O. S. Sakharov, Semi-Analytical Finite Element Method in Problems of Fracture of Three-Dimensional Bodies [in Ukrainian], KNUBA, Kiev (2005).
A. B. Zolotov and P. A. Akimov, Some Analytical Numerical Methods for the Solution of Boundary Problems of Structural Mechanics [in Russian], ASV, Moscow (2004).
A. B. Zolotov and P. A. Akimov, Practical Methods for the Design of Building Structures. Numerical Analytical Methods [in Russian], ASV, Moscow (2006).
A. B. Zolotov, P. A. Akimov, V. N. Sidorov, and M. L. Mozgaleva, Numerical and Analytical Methods for the Design of Building Structures [in Russian], ASV, Moscow (2009).
V. A. Bazhenov, O. I. Gulyar, O. G. Topor, and I. I. Solodei, “SAFEM analysis of the dynamic elastoplastic interaction of heterogeneous bodies,” in: Strength of Materials and Theory of Structures [in Ukrainian], Issue 67, KNUBA, Kiev (2000), pp. 3–17.
O. I. Gulyar, O. G. Topor, and I. I. Solodei, “Three-dimensional problem of dynamics for elastoplastic heterogeneous bodies of revolution in the semi-analytical finite element method,” in: Strength of Materials and Theory of Structures [in Ukrainian], Issue 66, KNUBA, Kiev (1999), pp. 56–57.
A. I. Gulyar, I. V. Polovets, and A. S. Sakharov, Numerical Finite Element Simulation of Processes of Plastic Forming of Bodies of Revolution in the Presence of Friction Forces [in Russian], Kiev (1984). Deposited in UkrNIINTI, No. 1788.
V. A. Bazhenov, O. I. Gulyar, O. G. Topor, and I. I. Solodei, “Efficiency of algorithms for the solution of elastic and elastoplastic problems of dynamics by the semi-analytical finite element method,” in: Strength of Materials and Theory of Structures [in Ukrainian], Issue 64, KNUBA, Kiev (1998), pp. 99–115.
K.-J. Bathe, E. Ramm, and E. L. Wilson, “Finite element formulation for large deformation dynamic analysis,” Int. J. Numer. Meth. Eng., 5, No. 2, 353–386 (1975).
Translated from Problemy Prochnosti, No. 5, pp. 13 – 27, September – October, 2013.
About this article
Cite this article
Bazhenov, V.A., Gulyar, A.I. & Solodei, I.I. Numerical Simulation of Dynamic Processes of Elastoplastic Interaction between Three-Dimensional Heterogeneous Bodies on the basis of Semi-Analytical Finite Element Method. Part 1. Computational Relationships of the Semi-Analytical Finite Element Method and Algorithms for the Study of Transient Processes of Dynamic Deformation of Heterogeneous Prismatic Bodies and Bodies of Revolution. Strength Mater 45, 523–533 (2013). https://doi.org/10.1007/s11223-013-9489-3
- plastic strains
- contact surface
- heterogeneous prismatic bodies and bodies of revolution
- semi-analytical finite element method