Meshless local petrov-galerkin method for linear coupled thermoelastic analysis

CMES - Computer Modeling in Engineering and Sciences

Volumn 16, Issue 1, 2006, Pages 57-68

  Sladek, J ^a   Sladek, V ^a   Zhang, Ch ^b   Tan, C L ^c  

^a INSTITUTE OF CONSTRUCTION AND ARCHITECTURE   (Slovakia)

^b UNIVERSITY OF SIEGEN   (Germany)

^c CARLETON UNIVERSITY   (Canada)

Author keywords

2 D problems; Laplace transform; Moving least squares interpolation; Orthotropic materials; Stehfest's inversion; Transient coupled thermoelasticity

Indexed keywords

BOUNDARY CONDITIONS; EQUATIONS OF MOTION; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; LEAST SQUARES APPROXIMATIONS; LINEAR SYSTEMS; PROBLEM SOLVING;

MOVING LEAST SQUARES INTERPOLATION; ORTHOTROPIC MATERIALS; STEHFEST'S INVERSION; TRANSIENT COUPLED THERMOELASTICITY;

THERMOELASTICITY;

EID: 33845442173     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. Atluri, S.N. (2004): The Meshless Method, (MLPG) For Domain & BIE Discretizations, Tech Science Press.
2. Atluri, S.N.; Sladek, J.; Sladek, V.; Zhu, T. (2000): The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity. Comput. Mech., 25: 180-198.
3. Atluri, S.N.; Han, Z.D.; Shen, S. (2003): Meshless local Petrov-Galerkin (MLPG) approaches for solving the weakly-singular traction & displacement boundary integral equations. CMES: Computer Modeling in Engineering & Sciences, 4: 507-516.
4. Batra, R.C.; Porfiri, M.; Spinello, D. (2004): Treatment of material discontinuity in two Meshless local Petrov-Galerkin (MLPG) formulations of axisymmetric transient heat conduction. Int. J. Num. Meth. Engn., 61: 2461-2479.
5. Belytschko, T.; Krogauz, Y.; Organ, D.; Fleming, M.; Krysl, P. (1996): Meshless methods; an overview and recent developments. Comp. Meth. Appl. Mech. Engn., 139: 3-47.
6. Bobaru, F.; Mukherjee, S. (2003): Meshless approach to shape optimization of linear thermoelastic solids. Int. J. Num. Meth. Engn., 53: 765-796.
7. Cannarozzi, A.A.; Ubertini, F. (2001): A mixed variational method for linear coupled thermoelastic analysis. Int. J. Solids and Structures, 38: 717-739.
8. Carslaw, H.S.; Jaeger, J.C. (1959): Conduction of Heat in Solids, Clarendon, Oxford.
9. Chen, J.; Dargush, G.F. (1995): Boundary element method for dynamic poroelastic and thermoelastic analyses. Int. J. Solids and Structures, 32: 2257-2278.
10. Dargush, G.F.; Banerjee, P.K. (1991): A new boundary element method for three-dimensional coupled problems of conduction and thermoelasticity. ASME J. Appl. Mech., 58: 28-36.
11. Gaul, L.; Kögl, M.; Wagner, M. (2003): Boundary Element Methods for Engineers and Scientists. Springer-Verlag, Berlin.
12. Han, Z.D.; Atluri, S.N. (2004a): Meshless local Petrov-Galerkin (MLPG) approaches for solving 3D problems in elasto-statics. CMES: Computer Modeling in Engineering & Sciences, 6: 169-188.
13. Han, Z.D.; Atluri, S.N. (2004b): A meshless local Petrov-Galerkin (MLPG) approach for 3-dimensional elasto-dynamics. CMC: Computers, Materials & Continua, 1: 129-140.
14. Hosseini-Tehrani, P.; Eslami, M.R. (2000): BEM analysis of thermal and mechanical shock in a two-dimensional finite domain considering coupled thermoelasticity. Engineering Analysis with Boundary Elements, 24: 249-257.
15. Keramidas, G.A.; Ting, E.C. (1976): A finite element formulation for thermal stress analysis. I. Variational formulation, II. Finite element formulation. Nuclear Engineering and Design, 39: 267-287.
16. Kögl, M.; Gaul, L. (2000): A dual reciprocity boundary element method for dynamic coupled anisotropic thermoelasticity. In: Boundary Elements XXII, pp. 565-577, WIT Press, Southampton, UK.
17. Kögl, M.; Gaul, L. (2003): A boundary element method for anisotropic coupled thermoelasticity. Arch. Appl. Mech., 73: 377-398.
18. Lekhnitskii, S.G. (1963): Theory of Elasticity of an Anisotropic Body, Holden Day, San Francisco.
19. Nowacki, W. (1986): Thermoelasticity, Pergamon, Oxford.
20. Park, K.H.; Banerjee, P.K. (2002): Two- and three-dimensional transient thermoelastic analysis by BEM via particular integrals. Int. J. Solids and Structures, 39: 2871-2892.
21. Prasad, N.N.V. (1998): Thermomechanical Crack Growth using Boundary Elements. WIT Press, Southampton, UK.
22. Prevost, J.H.; Tao, D. (1983): Finite element analysis of dynamic coupled thermoelasticity problems with relaxation times. Journal of Applied Mechanics, 50: 817-822.
23. Qian, L.F.; Batra, R.C. (2004): Transient thermoelastic deformations of thick functionally graded plate. Jour. Thermal Stresses, 27: 705-740.
24. Rizzo, F.J.; Shippy, DJ. (1977): An advanced boundary integral equation method for three-dimensional thermoelasticity. Int. J. Num. Meth. Engn., 11: 1753-1768.
25. Sellountos, E.J.; Polyzos, D. (2003): A MLPG (LBIE) method for solving frequency domain elastic problems. CMES: Computer Modeling in Engineering & Sciences, 4: 619-636.
26. Sellountos, E.J.; Vavourakis, V.; Polyzos, D. (2005): A new singular/hypersingular MLPG (LBIE) method for 2D elastostatics. CMES: Computer Modeling in Engineering & Sciences, 7: 35-48.
27. Shiah, Y.C.; Tan, C.L. (1999): Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity. Computational Mechanics, 23: 87-96.
28. Sladek, V.; Sladek, J. (1984): Boundary integral equation method in thermoelasticity. Part I: General analysis. Appl. Math. Modelling, 7: 241-253.
29. Sladek, J.; Sladek, V.; Atluri, S.N. (2001). A pure contour formulation for meshless local boundary integral equation method in thermoelasticity. CMES: Computer Modeling in Engineering & Sciences, 2: 423-434.
30. Sladek, J.; Sladek, V.; Zhang, Ch. (2003a): Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method. Computational Materials, 28: 494-504.
31. Sladek, J.; Sladek, V.; Krivacek, J.; Zhang, Ch. (2003b): Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids. Computational Mechanics, 32: 169-176.
32. Sladek, J.; Sladek, V.; Atluri, S.N. (2004a): Meshless local Petrov-Galerkin method for heat conduction problem in an anisotropic medium. CMES: Computer Modeling in Engineering & Sciences, 6: 309-318.
33. Sladek, J.; Sladek, V.; Atluri, S.N. (2004b): Meshless local Petrov-Galerkin method in anisotropic elastic ity. CMES: Computer Modeling in Engineering & Sciences, 6: 477-489.
34. Sladek, J.; Sladek, V.; Hellmich, Ch.; Eberhardsteiner, J. (2006): Heat conduction analysis of 3D axisymmetric and anisotropic FGM bodies by meshless local Petrov-Galerkin method. Computational Mechanics (in print).
35. Suh, I.G.; Tosaka, N. (1989): Application of the boundary element method to 3-D linear coupled thermoelasticity problems. Theor. Appl. Mech., 38: 169-175.
36. Stehfest, H.(1970): Algorithm 368: numerical inversion of Laplace transform. Comm. Assoc. Comput. Mach., 13: 47-49.
37. Timoshenko, S.P.; Goodier, J.N. (1951): Theory of Elasticity, McGraw-Hill, New York.
38. Wang, H.; Qin, Q.H.; Kang, Y.L. (2006): A meshless model for transient heat conduction in functionally graded materials. Computational Mechanics, 38: 51-60.
39. Zhu, T.; Zhang, J.D.; Atluri, S.N. (1998): A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approaches. Computational Mechanics, 21: 223-235.