Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin method

Engineering Analysis with Boundary Elements

Volumn 28, Issue 5, 2004, Pages 497-507

  Liew, K M ^a,b   Ren, J ^a,b   Kitipornchai, S ^c  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Element free Galerkin method; Martensitic transformation; Meshfree methods; Modeling and simulation; Shape memory alloy; Shape memory alloy beam

Indexed keywords

ELEMENT-FREE GALERKIN METHODS; MESHFREE METHODS; MODELING AND SIMULATION; SHAPE MEMORY ALLOY BEAM;

BOUNDARY CONDITIONS; COMPUTER SIMULATION; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; MARTENSITIC TRANSFORMATIONS; MATHEMATICAL MODELS; TENSORS;

SHAPE MEMORY EFFECT;

EID: 1842864918     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(03)00103-6     Document Type: Conference Paper

References (35)

1. Birman V. Review of mechanics of shape memory alloy structures. Appl Mech Rev. 50:(11):1997;629-645.
2. Brinson L.C., Lammering R. Finite element analysis of the behavior of shape memory alloys and their applications. Int J Solids Struct. 30:(23):1993;3261-3280.
3. Trochu F., Qian Y.Y. Nonlinear finite element simulation of superelastic shape-memory parts. Comput Struct. 62:1997;799-810.
4. Auricchio F., Taylor R.L., Lublinear J. Shape-memory alloys: macromodeling and numerical simulations of the superelastic behavior. Comput Meth Appl Mech Engng. 146:1997;281-312.
5. Lagoudas D.C., Bo Z., Qidwai M.A. A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composite. Mech Compos Mater Struct. 3:1996;153-179.
6. Qidwai M.A., Lagoudas D.C. Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms. Int J Numer Meth Engng. 47:2000;1123-1168.
7. Ren J., Liew K.M., Meguid S.A. Nonlinear FE analysis of the hysteresis behaviour of SMA. Int J Comput Engng Sci. 2:2001;621-632.
8. Liew K.M., Kitipornchai S., Ng T.Y., Zou G.P. Multi-dimensional superelastic behavior of shape memory alloys via nonlinear finite element method. Engng Struct. 24:2002;51-58.
9. Monaghan J.J. An introduction to SPH. Comput Phys Commun. 48:1988;89-96.
10. Nayroles B., Touzot G., Villon P. Generalizing the finite element method: difference approximation and diffuse elements. Comput Mech. 10:1992;583-594.
11. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. Meshfree methods: an overview and recent developments. Comput Meth Appl Mech Engng. 139:1996;3-47.
12. Belytschko T., Lu Y.Y., Gu L. Element-free Galerkin method. Int J Numer Meth Engng. 37:1994;229-256.
13. Durate C.A., Oden J.T. An h-p adaptive method using clouds. Comput Meth Appl Mech Engng. 139:1996;237-262.
14. Chen J.S., Pan C., Wu C.T. Application of reproducing kernel particle methods for large deformation and contact analysis of elastomers. Rubber Chem Technol. 7:1998;191-213.
15. Chen J.S., Pan C., Roque C., Wang H.P. A Lagrangian reproducing kernel particle method for metal forming analysis. Comput Mech. 22:1998;289-307.
16. Liu G.R. Meshfree methods, moving beyond the finite element method. 2002;CRC Press, Boca Raton, FL.
17. Atluri S.N., Kim H.G., Cho J.Y. A critical assessment of the truly meshless local Petrov-Galerkin (MLPG) and local boundary integral equation (LBIE) methods. Comput Mech. 24:1999;348-372.
18. Zhang X., Liu X., Lu M.W., Chen Y. Imposition of essential boundary conditions by displacement constraint equations in meshless methods. Commun Numer Meth Engng. 17:2001;165-178.
19. Liew K.M., Ng T.Y., Zhao X., Reddy J.N. Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells. Comput Meth Appl Mech Engng. 19:2002;4141-4157.
20. Liew KM, Zhao X, Ng TY. The element-free RKP-Ritz method for vibration of laminated rotating cylindrical panels. Int J Struct Stab Dyn; 2002;2:523-58.
21. Liew K.M., Huang Y.Q., Reddy J.N. A hybrid moving least squares and differential quadrature (MLSDQ) meshfree method. Int J Comput Engng Sci. 2:2002;1-12.
22. Liew K.M., Ng T.Y., Wu Y.C. Meshfree method for large deformation analysis: a reproducing kernel particle approach. Engng Struct. 24:2002;543-551.
23. Liew K.M., Wu H.Y., Ng T.Y. Meshless method for modeling of human proximal femur: treatment of nonconvex boundaries and stress analysis. Comput Mech. 28:2002;390-400.
24. Liew K.M., Wu Y.C., Zou G.P., Ng T.Y. Elasto-plasticity revisited: numerical analysis via reproducing kernel particle method and parametric quadratic programming. Int J Numer Meth Engng. 55:2002;669-683.
25. Wang J., Liew K.M., Tan M.J., Rajendran S. Analysis of rectangular laminated composite plates via FSDT meshless method. Int J Mech Sci. 44:2002;1275-1293.
26. Liew KM, Huang YQ, Reddy JN. Moving least square differential quadrature method and its application to the analysis of shear deformable plates. Int J Numer Meth Engng 2003;56:2331-51.
27. Boyd J.G., Lagoudas D.C. A thermodynamic constitutive model for shape memory alloy materials. Part I. The monolithic shape memory alloy. Int J Plast. 12:1996;805-842.
28. Tanaka K. A phenomenological description on thermomechanics behavior of shape memory alloys. ASME J Pressure Vessel Technol. 112:1990;158-163.
29. Liang C., Rogers C.A. A multi-dimensional constitutive model for shape memory alloys. J Engng Math. 26:1992;429-443.
30. Brinson L.C. One dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions. J Int Mater Sys Struct. 4:1995;229-242.
31. Lancaster P., Salkauskas K. Surfaces generated by moving least-squares method. Math Comput. 37:1981;141-158.
32. Reddy J.N. An introduction to the finite element method. 2nd ed:1993;McGraw-Hill, New York.
33. Reddy J.N. Energy principles and variational methods in applied mechanics. 2003;Wiley, New York.
34. Simo J.C., Oritz M. A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations. Comput Meth Appl Mech Engng. 49:1985;221-245.
35. Simo J.C., Taylor R.L. A return mapping algorithm for plane stress elastoplasticity. Int J Numer Meth Engng. 22:1986;649-670.