 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 51, Issue 3 / 2016 | Next article >> |
| S.S. Gavryushin and A.S. Nikolaeva, "Method of Change of the Subspace of Control Parameters and Its Application to Problems of Synthesis of Nonlinearly Deformable Axisymmetric Thin-Walled Structures," Mech. Solids. 51 (3), 339-348 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
3 |
Pages |
339-348 |
| DOI |
10.3103/S0025654416030110 |
| Title |
Method of Change of the Subspace of Control Parameters and Its Application to Problems of Synthesis of Nonlinearly Deformable Axisymmetric Thin-Walled Structures |
| Author(s) |
S.S. Gavryushin (Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5, Moscow, 105005 Russia, gss@bmstu.ru)
A.S. Nikolaeva (Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5, Moscow, 105005 Russia) |
| Abstract |
The theoretical foundations, methods, and algorithms developed to analyze the stability and postbuckling behavior of thin elastic axisymmetric shells are discussed. The algorithm for numerically studying the processes of nonlinear deformation of thin-walled axisymmetric shells by the solution parametric continuation method is generalized to solving the practical problem of design of mechanical actuators of discrete action. The synthesis algorithm is based on the method of changing the subspace of control parameters, which is supplemented with the procedure of smooth transition in changing the subspaces. The efficiency of the proposed algorithm is illustrated by an example of synthesis of a thermobimetallic actuator of discrete action. The procedure of determining an isolated solution, whose existence was predicted by V. I. Feodosiev, is considered in the framework of studying the process of nonlinear deformation of a corrugated membrane loaded by an external pressure. |
| Keywords |
nonlinear deformation, synthesis problem, thin-walled axisymmetric shell, actuator, postbuckling behavior, discrete switching, numerical algorithm, parametric continuation, changing the subspace of parameters, smooth transition procedure |
| References |
| 1. | D. H. Bich and H. V. Tung,
"Nonlinear Axisymmetric Response of Functionally Graded Shallow Spherical Shells
under Uniform External Pressure Including Temperature Effects,"
Int. J. Nonlin. Mech.
46 (9), 1195-1204 (2011). |
| 2. | H. Y. Chan and W. J. Li,
"A Thermally Actuated Polymer Micro Robotic Gripper for Manipulation of Biological Cells,"
in Proc. IEEE Int. Conf. Robotics and Automation (ICRA 2003), No. 9 (2003),
pp. 288-293. |
| 3. | J. Kusterer, F. J. Hernandez, S. Haroon, and E. Kohn,
"Bi-Stable Micro Actuator Based on Stress Engineered Nano-Diamond,"
Diamond Related Mater.
15 (4), 773-776 (2006). |
| 4. | J. J. Lee, J. K. Oh, I. Lee, J. J. Rhiu,
"Nonlinear Static and Dynamic Instability of Complete Spherical Shells
Using Mixed Finite Element Formulation,"
Int. J. Nonlin. Mech.
38 (6), 923-934 (2003). |
| 5. | L. A. Liew, A. Tuantranont, V. M. Bright,
"Modeling of Thermal Actuation in a Bulk-Micro-Machined CMOS Micromirror,"
Microelectron
31, 791-801 (2000). |
| 6. | O. C. Zienkiewicz,
The Finite Element Method, 3rd. ed.
(McGraw-Hill, New York, 1977). |
| 7. | E. I. Grigolyuk and E. A. Lopanitsyn,
Finite Deflections, Stability, and Postbuckling Behavior of Thin Shallow Shells
(MGTU "MAMI", Moscow, 2004)
[in Russian]. |
| 8. | K. Marguerre,
"Zur Theorie der gekrümmten Platter grosser Formándering,"
in Proc. 5th Intern, Congr. Appl. Mech. Cambridge, Massachusetts, 1938
(Wiley, New York, 1939),
pp. 93-101. |
| 9. | V. I. Feodosiev,
Elastic Elements of Precision Instrument Engineering
(Oborongiz, Moscow, 1949)
[in Russian]. |
| 10. | E. Reissner,
"On Axisymmetrical Deformation of Thin Shells of Revolution,"
in Proc. 3rd Sympos. Appl. Math., Vol. 3
(McGraw-Hill, New York, 1950),
pp. 27-52. |
| 11. | J. Mescall,
"Numerical Solution of Nonlinear Equations for Shell of Revolution,"
AIAA J.
4 (11), 2041-2043 (1966). |
| 12. | E. I. Grigolyuk and V. I. Shalashilin,
Problems of Nonlinear Deformation:
The Continuation Method Applied to Nonlinear Problems in Solid Mechanics
(Nauka, Moscow, 1988; Kluwer, Dordrecht, 1991; Springer, New York, 1991). |
| 13. | N. V. Valishvili,
"An Algorithm of the Solution of Nonlinear Boundary Value Problems,"
Prikl. Mat. Mekh.
32 (6), 1089-1096 (1968)
[J. Appl. Math. Mech. (Engl. Transl.)
32 (6), 1107-1110 (1968)]. |
| 14. | N. V. Valishvili,
Computer Methods for Analysis of Shells
of Revolution
(Mashinostroenie, Moscow, 1976)
[in Russian]. |
| 15. | E. Riks,
"The Application of Newton's Method to the Problem of Elastic Stability,"
J. Appl. Mech.
39, 1060-1065 (1972). |
| 16. | M. A. Crisfield,
"A Fast Incremental/Iterative Solution Procedure that Handles `Snap-Through',"
Comput. Struct.
13 (1), 55-62 (1981). |
| 17. | V. I. Shalashilin and E. B. Kuznetsov,
Solution Parametric Continuation Method and the Best Parametrization
(Editorial URSS, Moscow, 1999)
[in Russian]. |
| 18. | E. B. Kuznetsov,
Several Applications of the Solution Best Parametric Continuation Method
(Izdat. MAI, Moscow, 2013)
[in Russian]. |
| 19. | P. Deufhard,
Newton Method for Nonlinear Problems.
Affine Invariance and Adaptive Algorithms
(Springer, 2000). |
| 20. | M. Prashanth and D. K. Gupta,
"Convergence of a Parametric Continuation Method,"
Kodai Math. J.
37 (1), 212-234 (2014). |
| 21. | Y. Yan, Y. Bo, and D. Bo,
"Robust Continuation Method for Tracking Solution Curves of Parametrized Systems,"
Num. Alg.
65 (4), 825-841 (2014). |
| 22. | A. N. Bonini, E. M. Magalhaes, and D. A. Alves,
"Development and Assessment of Nonlinear Predictors for Continuation Method,"
Int. J. Engng Appl. Sci.
5 (1), 1-9 (2014). |
| 23. | V. I. Arnold,
Catastrophe Theory
(Nauka, Moscow, 1990)
[in Russian]. |
| 24. | M. M. Vainberg and V. A. Trenogin,
Theory of Branching of Solutions of Non-Linear Equations
(Nauka, Moscow, 1969; Noordhoff, Leyden, 1974). |
| 25. | S. S. Gavryushin,
"Numerical Simulation and Analysis of Processes of Nonlinear Deformation of Flexible Shells,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 109-119 (1994)
[Mech. Solids (Engl. Transl.)]. |
| 26. | S. S. Gavryushin,
Development of Methods for Computation and Design of Elastic Shell Structures of Device Facilities,
Doctoral Dissertation in Technical Sciences
(Moscow, 1994)
[in Russian]. |
| 27. | A. A. Karim and S. S. Gavryushin, "Numerical Analysis of
Thermobimetallic Elements of High-Speed Electrotechnical Units,"
Izv. Vyssh. Uchebn. Zaved. Mashinostr., No. 8, 17-23 (2005). |
| 28. | V. I. Feodosiev, "On Large Deflections and Stability of Circular
Membrane with Small Corrugation," Prikl. Mat. Mekh., No. 9,
389-412 (1945). |
| 29. | S. S. Gavryushin, "Analysis and Synthesis of Function Elements of
Robotic Devices with Prescribed Law of Motion," Izv. Vyssh.
Uchebn. Zaved. Mashinostr., No. 12, 23-32 (2011). |
| 30. | S. S. Gavryushin, O. O. Baryshnikova, and O. F. Boriskin,
Numerical Analysis of Machine and Device Structure Elements
(Izdat. Bauman MGTU, Moscow, 2014)
[in Russian]. |
| 31. | S. S. Gavryushin, "Numerical Simulation of Processes of Nonlinear
Deformation of Thin Elastic Shells," Vestnik MGTU im. Baumana.
Ser. Mat. Mod. Chisl. Met., No. 1, 151-166 (2014). |
| 32. | S. S. Gavryushin, A. Macmillan, A. S. Nikolaeva, and
T. B. Podkopaeva, "Computation of Perspective Structures of
Actuators," Izv. Vyssh. Uchebn. Zaved. Mashinostr., No. 8, 73-78
(2015). |
|
| Received |
05 February 2016 |
| Link to Fulltext |
|
| << Previous article | Volume 51, Issue 3 / 2016 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English