Abstract
A two-way coupled statement of stability problem for shape memory alloy elements is given in the framework of the “fixed load” and “variable load” concepts. It is shown that the largest values of the critical parameters are obtained when solving the problem in the two-way coupled statement in the framework of the “fixed load” concept and the least values are obtained in the oneway coupled statement in the framework of the “variable load” concept.
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References
M. A. Rahman, J. Qui, and J. Tani, “Buckling and Postbuckling Characteristics of the Superelastic SMA Columns,” Int. J. Solids Struct. 38, 9253–9265 (2001).
M. A. Rahman, J. Qui, and J. Tani, “Buckling and Postbuckling Characteristics of the Superelastic SMA Columns – Numerical Simulation,” J. Intell. mater. Struct. 16, 691–702 (2005).
M. A. Rahman and J. Tani, “Postbuckling Characteristics of the Short Superelastic Shape Memory Alloy Columns – Experiment and Quantitative Analysis,” Int. J. Appl.Mech. Engng 11 (4), 941–955 (2006).
M. A. Rahman, S. R. Akanda, and M. A. Hossain, “Effect of Cross Section Geometry on the Response of an SMA Column,” J. Intell.Mater. Syst. Struct. 19 (2), 243–252 (2008).
S. Nemat-Nasser, J. Y. Choi, J. B. Isaacs, and D.W. Lisher, “ExperimentObservation ofHigh-Rate Buckling of Thin Cylindrical Shape Memory Shells,” in SPIE Proc.: Smart Structure and Materials 2005. Active Materials: Behavior and Mechanics, Ed. by W. D. Armstrong, Vol. 5761 (2005), pp. 347–354.
M. R. Amini and S. Nemat-Nasser, “Dynamic Buckling and Recovery of Thin Cylindrical Shells,” in SPIE Proc.: Smart Structure and Materials 2005. Active Materials: Behavior and Mechanics, Ed. by W. D. Armstrong, Vol. 5761 (2005), pp. 450–453.
S. Nemat-Nasser, J. Y. Choi, J. B. Isaacs, and D. W. Lisher, “Quasi-Static and Dynamic Buckling of Thin Cylindrical ShapeMemory Alloy Shells,” J. Appl.Mech. 73 (5), 825–833 (2006).
A. Tang and D. Li, “Quasi-Static Axial Buckling of TiNi Thin-Walled Cylindrical Shells,” Thin-Walled Struct. 51, 130–138 (2012).
A. Tang and D. Li, “Experimental Investigation of Axial Impact Buckling Response of Pseudo-Elastic NiTi Cylindrical Shells,” Int. J. Impact Engng 39, 28–41 (2012).
D. Jiang, N. Bechle, C. M. Landis, and S. Kyriakides, “Buckling and Recovery of NiTi Tubes under Axial Compression,” Int. J. Solids Struct. 80, 52–63 (2016).
P. A. Michailidis, N. Triantafyllidis, J. A. Shaw, and D. S. Grummon, “Superelasticity and Stability of a Shape Memory Alloy Hexagonal Honeycomb under In-Plane Compression,” Int. J. Solids Struct. 46, 2724–2738 (2009).
F. Richter, O. Kastner, and G. Eggeler, “Finite-Element Simulation of the Anti-Buckling-Effect of a Shape Memory Alloy Bar,” J.Mater. Engng Perform. 20 (4-5), 719–730 (2011).
J.Ocel,R.DesRoches,R. T. Leon, et al., “Steel Beam– Column Connections Using Shape Memory Alloys,” J. Struct. Engng 130 (5), 739–740 (2004).
R. T. Leon, R. DesRoches, J. Ocel, and G. Hess, “Innovative Beam Column Using Shape Memory Alloys,” in SPIE Proc.: Smart Structure and Materials 2001. Smart System for Bridges, Structures, and Highways, Ed. by S. C. Liu, Vol. 4330 (2001), pp. 227–237.
A. A. Movchan, L. G. Silchenko, S. A. Kazarina, et al., “Stability of Titanium Nickelide Rods Loaded in theMode ofMartensite Inelasticity,” Probl. Mashinostr. Nadezhn.Mashin, No. 3, 72–80 (2012) [J.Machin. Manufact. Reliabil. (Engl. Transl.) 41 (3), 245–251 (2012)].
Y. Urushiyama, D. Lewinnek, J. Qui, and J. Tani, “Buckling of Shape Memory Alloy Columns: Buckling of Curved Column and Twinning Deformation Effect,” JMSE Int. J. Ser. A Solid Mech. Mater. Engng 46 (1), 60–67 (2003).
J. Kunavar, F. Kosel, A. Pukšič, and T. Videnič, “GeometryOptimization in Buckling of ShapeMemory Alloy Column due to Constrained Recovery,” J. Intell.Mater. Syst. Struct. 23 (1), 65–76 (2012).
G. A. Malygin, “Euler Instability of Bidirectional Shape Memory Effect in a Titanium Nickelide Strip,” Fiz. Tverd. Tela 45 (12), 2233–2237 (2003) [Phys. Solid State (Engl. Transl.) 45 (12), 2342–2347 (2003)].
M. A. Savi, P.M. C. L. Pachco, and A.M. B. Braga, “Chaos in a Shape Memory Two-Bar Truss,” Int. J. Non-Lin.Mech. 37 (8), 1387–1395 (2002).
J. J. Lee and S. Choi, “Thermal Buckling and Postbuckling Analysis of a Laminated Composite Beam with Embedded SMA Actuators,” Compos. Struct. 47 (1-4), 695–703 (1999).
A. A. Movchan and S. A. Kazarina, “Experimental Study of Stability Loss Phenomenon due to Thermoelastic Phase Transformations under the Action of Compressing Stresses,” Probl. Mashinostr. Nadezhn. Mashin, No. 6, 82–89 (2002).
A. A. Movchan and L. G. Sil’chenko, “Buckling of a Rod Undergoing Direct or Inverse Martensite Transformation under Compressive Stresses,” Zh. Prikl.Mekh. Tekhn. Fiz. 44 (3), 169–178 (2003) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 44 (3), 442–449 (2003)].
A. A. Movchan and L. G. Sil’chenko, “Analysis of Buckling Induced by the Direct Thermoelastic Transformation under the Action of Compression Stresses,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 132–144 (2004) [Mech. Solids (Engl. Transl.) 39 (2), 104–114 (2004)].
A. A. Movchan and L. G. Sil’chenko, “The Stability of a Plate of Shape-Memory Alloy in a Direct Thermoelastic Phase Transition,” Prikl. Mat. Mekh. 68 (1), 60–72 (2004) [J. Appl. Math. Mech. (Engl. Transl.) 68 (1), 53–64 (2004)].
A. A. Movchan and L. G. Sil’chenko, “Analytical Solution of the Coupled Buckling Problem for a Plate From a Shape Memory Alloy Subjected to Inverse Martensite Transformation,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 164–178 (2004) [Mech. Solids (Engl. Transl.) 39 (5), 134–145 (2004)].
A. A. Movchan and L. G. Sil’chenko, “The Stability of a Circular Plate of Shape Memory Alloy during a Direct Martensite Transformation,” Prikl. Mat. Mekh. 70 (5), 871–883 (2006) [J. Appl.Math. Mech. (Engl. Transl.) 70 (5), 785–795 (2006)].
A. A. Movchan, “Selecting a Phase-DiagramApproximation and aModel of theDisappearance of Martensite Crystals for Shape Memory Alloys,” Zh. Prikl. Mekh. Tekhn. Fiz. 36 (2), 173–181 (1995) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 36 (2), 300–307 (1995)].
A. A. Movchan and L. G. Sil’chenko, “Buckling of a Circular Plate Made of a Shape Memory Alloy due to a Inverse Thermoelastic Martensite Transformation,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 117–130 (2008) [Mech. Solids (Engl. Transl.) 43 (1), 100–111 (2008)].
A. A. Movchan, I. A. Movchan, and L. G. Sil’chenko, “Stability of an Annular Plate of a Shape Memory Alloy,” Zh. Prikl. Mekh. Tekhn. Fiz. 52 (2), 144–155 (2011) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 52 (2), 279–287 (2011)].
L. I. Shkutin, “Analysis of Plane Phase Strains of Rods and Plates,” Zh. Prikl. Mekh. Tekhn. Fiz. 47 (2), 156–164 (2006) [J. Appl.Mech. Tech. Phys. (Engl. Transl.) 47 (2), 282–288 (2006)].
L. I. Shkutin, “Analysis of Axisymmetric Phase Strains in Plates and Shells,” Zh. Prikl. Mekh. Tekhn. Fiz. 48 (2), 163–171 (2007) [J. Appl.Mech. Tech. Phys. (Engl. Transl.) 48 (2), 285–291 (2007)].
A. A. Movchan, I. A. Movchan, and L. G. Sil’chenko, “Effect of Structural Transformation and Deformation Nonlinearity on the Stability of a Shape Memory Alloy Rod,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 137–147 (2010) [Mech. Solids (Engl. Transl.) 45 (6), 876–884 (2010)].
L.G. Sil’chenko, A. A. Movchan, and I.A. Movchan, “Structural Transformation Taken into Account during the Analysis of the Stability of a Round Plate with Shape Memory,” Probl. Mashinostr. Nadezhn. Mashin, No. 5, 57–65 (2010) [J. Machin.Manufact. Reliabil. (Engl. Transl.) 39 (5), 452–458 (2010)].
I. V. Mishustin and A. A. Movchan, “Modeling of Phase and Structure Transformations Occurring in Shape MemoryAlloys under NonmonotonicallyVarying Stresses,” Izv. Ross. Akad.Nauk.Mekh. Tverd. Tela, No. 1, 37–53 (2014) [Mech. Solids (Engl. Transl.) 49 (1), 27–39 (2014)].
I. V. Mishustin and A. A. Movchan, “Analog of the Plastic Flow Theory for DescribingMartensitic Inelastic Strains in Shape Memory Alloys,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 78–95 (2015) [Mech. Solids (Engl. Transl.) 50 (2), 176–190 (2015)].
F. Shanley, “Column Theory beyond the Elastic Limit,” Mekh., No. 2, 88–98 (1951).
Ya. G. Panovko and I. I. Gubanova, Stability and Vibrations of Elastic Systems (Nauka, Moscow, 1987) [in Russian].
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Original Russian Text © S.A. Dumanskii, A.A. Movchan, 2017, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2017, No. 5, pp. 37–48.
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Dumanskii, S.A., Movchan, A.A. Two-Way Coupled Statement of the Problem of Loss of Stability due to Inverse Thermoelastic Phase Transition in a Shape Memory Alloy. Mech. Solids 52, 501–510 (2017). https://doi.org/10.3103/S0025654417050053
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DOI: https://doi.org/10.3103/S0025654417050053