TECHNICAL MECHANICS
ISSN (Print): 1561-9184, ISSN (Online): 2616-6380
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UDC 539.3:519.6
Technical mechanics, 2014, 2, 12 - 23
SIMULATION OF STRAINING THE PLATE WITH ELASTIC EXTENDED INCLUSIONS BASED ON FINITE ELEMENT METHOD
Gudramovich V. S., Gart E. L., Strunin K. A.
| ABSTRACT |
The research aim is to study numerically the stressed-strained state of rectangular plates with arbitrarilyoriented
extended
inclusions
(strip
ones
with
and
without
twists
at
ends)
depending
on
the
combination
of
rigidities
of inclusions, theirs sizes and orientations, relations of rigidities of inclusions and the plate. The research
method is the finite-element method in the form of the ANSYS standard licensed package. The following results
are obtained: the effects of the relation of rigidities of inclusions and the plate (matrix), their sizes, mutual orientations
of inclusions on distribution of stresses and strains over a wide range of materials (the paper deals with
aluminium and its alloys, steel, copper as examples) are analyzed. Plots of distributions of stresses intensities are
built. Two inclusions in the form of strips and ones with rounding at ends are examined. Algorithms for calculating
allow
consideration
of
the
stressed-strained
state
with
variations
in
characteristics
of
extended
inclusions,
their
forms,
quantities as well as relations of rigidities of inclusions and the matrix over wide range of rigidities. The
analysis made is of scientific and practical use for modelling processes in powder metallurgy and ceramics production,
deforming
the
media
with
discrete
variations
in
the
structure
and
structural
members
with
thin
straps
and
inclusions.
| KEYWORDS |
numerical simulation, stressed-strained state, inclusions, finite-element method, ANSYS standard licensed package
| FULL TEXT: |
| REFERENCES |
1. Benerji P. Method of Finite Elements for Applied Sciences: Translated from English / P. Benerji, R. Batterfield.
– Moscow: Mir, 1984. – 496 p.
2. Vasidzu K. Variation Methods for the Theory of Elasticity and Plasticity (in Russian) / K. Vasidzu. – Moscow: Mir,
1987. – 544 p.
3. Hallaher R. Finite Elements Method. Fundamentals: Translated from English. / R. Hallaher. – Moscow: Mir,
1984. – 428 p.
4. Gart E. L. Numerical analysis of elastic and plastic straining structured media (in Russian) / E. L. Gart, V. S.
Gudramovich // Dopovidi NANU. – 2012. – No 5. – P. 49 – 56.
5. Gart E. L. Finite-element analysis of plane-strained media with inclusions (in Russian) / E. L. Gart // Visnyk
Dnipropetrovskogo Universitetu. Seriya: Mekhanika. – 2011. – Is. 15, Vol. 2. – P. 39 – 47.
6. Gart E. L. Projection and iteration schemes of realization of finite-element method for problems straining
plates with holes and inclusions (in Ukrainian) / E. L. Hart, V. S. Hudramovych // Matematychni Metody i
Fiziko-Mekhanichni Polya. – 2013. Vol. 56, No 2. – P. 48 – 59.
7. Gudramovich V. S. Simulation of stressed-strained state of shell structures of rocket technology and power
engineering (in Russian) / V. S. Gudramovich // Tekhnicheskaya Mekhanika. – 2013. – P. 97 – 104.
8. Gudramovich V. S. Projection and iteration schemes of finite-elements method for problems of straining structured
media (in Russian) / V. S. Gudramovich, E. L. Gart // Suchasni Problemy Mekhaniki ta Matematiki: Proceedings of
the International Conference dedicated to 85
th
anniversary of Academician Ya. S. Pidstrygach (21 – 25 May, 2013,
Lviv): in three volumes. – Lviv: IPPMM named after Ya. S. Pidstrygach, NASU, 2013. – Vol. 1. – P. 32 – 33.
9. Gultyaev V. I. Regularities of Plastic Deformation of Structural Materials in Complex Loading (in Russian) / V. I.
Gultyaev: author’s abstract of Doctor’s Thesis. – Tver: Publishing House of TGTU, 2012. – 44p.
10. Zenkevich O. Finite Elements and Approximation. Translated from English / O. Zenkevich, K. Morgan. –
Moscow: Mir, 1986. – 318 p.
11. Koval Yu. N. Deformation and Relaxation Phenomena in Transformations of Martensite Type (in Russian) /
Yu. N. Koval, V. A. Lobodyuk. – Kiev: Naukova Dumka, 2010. – 288 p.
12. Lyashenko B. A. Hardening metal surface by coating with discrete structure having improved adhesion and
cohesion resistance (in Russian) / B. A. Lyashenko, Yu. A. Kuzema, M. S. Digam. – Kiev: Institute for Problems
in Strength named after G. S. Pisarenko, NASU. – 1984. – 57 p.
13. Lyashenko B. A. Hardening discrete-structure coatings (in Russian) / B. A. Lyashenko, A. Ya. Movshovich, A.
I. Dolmatov // Tekhnologicheskii Sistemy. – 2001. – No 4. – P. 17 – 25.
14. Maksymenko A. L. Full-scale simulation of effect hard inclusions on sintering (in Ukrainian) / A. L. Maksymenko,
A. V. Kuzmov // Naukovi Notatky. Collected Papers. – Is. 25, Part II. – Lutsk: Publishing House
LNTU, 2009. – P. 143 – 146.
15. Podgaysky M. S. Thermic reinforcement of rolled stock (in Russian) / M. S. Podgaysky // Metallovedenie i
Termicheskaya Obrabotka Metallov. – 1992. – No 10. – P. 20 – 23.
16. Samarsky A. A. Methods of Solutions of Precise Equations (in Russian) / A. A. Samarsky, Ye. S. Nikolaev. Moscow:
Nauka,
1972.
– 592 p.
17. Skorokhod V. V. Reologic Fundamentals of Sintering Theory (in Russian) / V. V. Skorokhod. – Kiev: Naukova
Dumka, 1972. – 152 p.
18. Sulym G. T. Fundamentals of Mathematical Theory of Thermal and Elastic Equilibrium of Strained Solids
with Thin Inclusions (in Ukrainian) / G. T. Sulym. – Lviv, 2007. – 716 p.
19. ANSYS release 11.0. Documentation for ANSYS WORKBENCH [Ýëåêòðîííûé ðåñóðñ], 2007.
20. Barrallier L. Residual stress analysis in nitrided layers. A comparison between the X-ray diffraction tech-
nique and a thin plate deflection method / L. Barrallier, J. Barralis, J. Frey // Bull. Cercleetud. metaux. –
1993. – Vol. 16, ¹ 7. – Ð. 4.1 – 4.12.
21. Honein T. On bonded inclusions with circular or straight boundaries in plain elastostatics / T. Honein,
G. Herrmann // Trans. ASME. Journ. of Applied Mechanics. – 1990. – Vol. 57. – P. 850 – 856.
22. Olevsky E. A. On line sintering strength of ceramic composites / E. A. Olevsky, A. Maximenko, O. Van Der
Biest // Intern. Journ. of Mechanical Sciences. – 2002. – Vol. 44. – P. 756 – 770.
23. Olevsky E. A. Theory of sintering: from discrete to continuum / E. A. Olevsky // Material Science and Engineering,
Reports:
A
Review
Journal,
R23.
– 1998. – P. 41 – 100.
24. Rose L. R. F. An application of the inclusion analogy for banded reinforcements / L. R. F. Rose // Intern/
Journ. of Solids and Structures. – 1981. – Vol. 17, ¹ 8. – P. 827 – 838.
Copyright (©) 2014 Gudramovich V. S., Gart E. L., Strunin K. A.
Copyright © 2014-2018 Technical mechanics
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