Dynamic 3D axisymmetric problems in continuously non-homogeneous piezoelectric solids

International Journal of Solids and Structures

Volumn 45, Issue 16, 2008, Pages 4523-4542

  Sladek, Jan ^a   Sladek, Vladimir ^a   Solek, Peter ^b   Saez, Andres ^c  

^a INSTITUTE OF CONSTRUCTION AND ARCHITECTURE   (Slovakia)

^b SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^c UNIVERSIDAD DE SEVILLA   (Spain)

Author keywords

Anisotropic functionally graded materials; Laplace transform; Meshless approximation; Stehfest algorithm; Thermal load; Time difference form; Transient problems

Indexed keywords

BOUNDARY CONDITIONS; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; THERMAL LOAD; THREE DIMENSIONAL;

ANISOTROPIC FUNCTIONALLY GRADED MATERIALS; MESHLESS APPROXIMATION; STEHFEST ALGORITHMS; TIME-DIFFERENCE FORMS; TRANSIENT PROBLEMS;

PIEZOELECTRIC MATERIALS;

EID: 44549083540     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.03.027     Document Type: Article

References (64)

1. Ashida F., Tauchert T.R., and Noda N. Potential function method for piezothermoelastic problems of solids of crystal class 6 mm in cylindrical coordinates. Journal of Thermal Stresses 17 (1994) 361-375
2. Aouadi M. Generalized thermo-piezoelectric problems with temperature-dependent properties. International Journal of Solids and Structures 43 (2006) 6347-6358
3. Atluri S.N. The Meshless Method, (MLPG) for Domain & BIE Discretizations (2004), Tech Science Press
4. Atluri S.N., Han Z.D., and Shen S. Meshless local Petrov-Galerkin (MLPG) approaches for solving the weakly-singular traction & displacement boundary integral equations. CMES: Computer Modeling in Engineering & Sciences 4 (2003) 507-516
5. Atluri S.N., Liu H.T., and Han Z.D. Meshless local Petrov-Galerkin (MLPG) mixed finite difference method for solid mechanics. CMES: Computer Modeling in Engineering & Sciences 15 (2006) 1-16
6. Belytschko T., Krogauz Y., Organ D., Fleming M., and Krysl P. Meshless methods; an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 139 (1996) 3-47
7. Carslaw H.S., and Jaeger J.C. Conduction of Heat in Solids (1959), Clarendon, Oxford
8. Chen W.Q., Lu Y., Ye R., and Cai J.B. 3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings. Archives of Applied Mechanics 72 (2002) 39-51
9. Curran D.A., Cross M., and Lewis B.A. Solution of parabolic differential equations by the boundary element method using discretization in time. Applied Mathematical Modelling 4 (1980) 398-400
10. Davi G., and Milazzo A. Multidomain boundary integral formulation for piezoelectric materials fracture mechanics. International Journal of Solids and Structures 38 (2001) 2557-2574
11. Davies B., and Martin B. Numerical inversion of the Laplace transform: a survey and comparison of methods. Journal of Computational Physics 33 (1979) 1-32
12. Ding H., and Liang J. The fundamental solutions for transversally isotropic piezoelectricity and boundary element method. Computers & Structures 71 (1999) 447-455
13. Ding H.J., Wang H.M., and Chen W.Q. Analytical solution for the electroelastic dynamics of a nonhomogeneous spherically isotropic piezoelectric hollow sphere. Archives of Applied Mechanics 73 (2003) 49-62
14. Dunn M.L. Micromechanics of coupled electroelastic composites: effective thermal expansion and pyroelectric coefficients. Journal of Applied Physics 73 (1993) 5131-5140
15. Enderlein M., Ricoeur A., and Kuna M. Finite element techniques for dynamic crack analysis in piezoelectrics. International Journal of Fracture 134 (2005) 191-208
16. Garcia-Sanchez F., Saez A., and Dominguez J. Anisotropic and piezoelectric materials fracture analysis by BEM. Computers & Structures 83 (2005) 804-820
17. Garcia-Sanchez F., Zhang Ch., Sladek J., and Sladek V. 2-D transient dynamic crack analysis in piezoelectric solids by BEM. Computational Materials Science 39 (2007) 179-186
18. Gornandt A., and Gabbert U. Finite element analysis of thermopiezoelectric smart structures. Acta Mechanica 154 (2002) 129-140
19. Govorukha V., and Kamlah M. Asymptotic fields in the finite element analysis of electrically permeable interfacial cracks in piezoelectric bimaterials. Archives Applied Mechanics 74 (2004) 92-101
20. Gruebner O., Kamlah M., and Munz D. Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium. Engineering Fracture Mechanics 70 (2003) 1399-1413
21. Gross D., Rangelov T., and Dineva P. 2D wave scattering by a crack in a piezoelectric plane using traction BIEM. SID: Structural Integrity & Durability 1 (2005) 35-47
22. Gross D., Dineva P., and Rangelov T. BIEM solution for piezoelectric cracked finite solids under time-harmonic loading. Engineering Analysis with Boundary Elements 31 (2007) 152-162
23. Han F., Pan E., Roy A.K., and Yue Z.Q. Responses of piezoelectric, transversally isotropic, functionally graded and multilayered half spaces to uniform circular surface loading. CMES: Computer Modeling in Engineering & Sciences 14 (2006) 15-30
24. Houbolt J.C. A recurrence matrix solution for the dynamic response of elastic aircraft. Journal of Aeronautical Science 17 (1950) 540-550
25. Kuna M. Finite element analyses of crack problems in piezoelectric structures. Computational Materials Science 13 (1998) 67-80
26. Kuna M. FEM-techniques for thermo-electro-mechanical crack analyses in smart structures. In: Wei Y. (Ed). IUTAM Symposium on Mechanics and Reliability of Actuating Materials (2006), Springer, Beijing 131-143
27. Lancaster P., and Salkauskas K. Curves and Surface Fitting: An Introduction (1986), Academic Press, London
28. Liew K.M., He X.Q., Ng T.Y., and Sivashanker S. Active control of FGM plates subjected to a temperature gradient: modelling via finite element method based on FSDT. International Journal for Numerical Methods in Engineering 52 (2001) 1253-1271
29. Liu G.R., Dai K.Y., Lim K.M., and Gu Y.T. A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures. Computational Mechanics 29 (2002) 510-519
30. Loza I.A., and Shulga N.A. Axisymmetric vibrations of a hollow piezoceramic sphere with radial polarization. Soviet Applied Mechanics 20 (1984) 113-117
31. Loza I.A., and Shulga N.A. Forced axisymmetric vibrations of a hollow piezoceramic sphere with an electrical method of excitation. Soviet Applied Mechanics 26 (1990) 818-822
32. Mindlin R.D. On the equations of motion of piezoelectric crystals, problems of continuum. In: Muskelishvili N.I. (Ed). Mechanics 70th Birthday Volume (1961), SIAM, Philadelpia 282-290
33. Mindlin R.D. Equations of high frequency vibrations of thermopiezoelasticity problems. International Journal of Solids and Structures 10 (1974) 625-637
34. Nowacki W. Some general theorems of thermo-piezoelectricity. Journal of Thermal Stresses 1 (1978) 171-182
35. Nayroles B., Touzot G., and Villon P. Generalizing the finite element method. Computational Mechanics 10 (1992) 307-318
36. Ohs R.R., and Aluru N.R. Meshless analysis of piezoelectric devices. Computational Mechanics 27 (2001) 23-36
37. Ootao Y., and Tanigawa Y. Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere. Composite Structures 81 (2007) 540-549
38. Pan E. A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids. Engineering Analysis with Boundary Elements 23 (1999) 67-76
39. Paulino G.H., Jin Z.H., and Dodds R.H. Failure of functionally graded materials. In: Karihaloo B., and Knauss W.G. (Eds). Comprehensive Structural Integrity vol. 2 (2003), Elsevier Science 607-644
40. Qin Q.H. Fracture Mechanics of Piezoelectric Materials (2001), WIT Press, Southampton
41. Qin Q.H., and Mai Y.M. Crack growth prediction of an inclined crack in a half-plane thermopiezoelectric solid. Theoretical and Applied Fracture Mechanics 26 (1997) 185-191
42. Rajapakse R.K.N.D., and Xu X.L. Boundary element modeling of cracks in piezoelectric solids. Engineering Analysis with Boundary Elements 25 (2001) 771-781
43. Rao S.S., and Sunar M. Analysis of distributed thermopiezoelectric sensors and actuators in advanced intelligent structures. AIAA Journal 31 (1993) 1280-1286
44. Saez A., Garcia-Sanchez F., and Dominguez J. Hypersingular BEM for dynamic fracture in 2-D piezoelectric solids. Computer Methods in Applied Mechanics and Engineering 196 (2006) 235-246
45. Shang F., Wang Z., and Li Z. Thermal stress analysis of a three-dimensional crack in a thermopiezoelectric solid. Engineering Fracture Mechanics 55 (1996) 737-750
46. Shang F., Kuna M., and Scherzer M. Analytical solutions for two penny-shaped crack problems in thermo-piezoelectric materials and their finite element comparisons. International Journal of Fracture 117 (2002) 113-128
47. Shang F., Kuna M., and Kitamura T. Theoretical investigation of an elliptical crack in thermopiezoelectric material. Part I: Analytical development. Theoretical Applied Fracture Mechanics 40 (2003) 237-246
48. Shang F., Kitamura T., and Kuna M. Theoretical investigation of an elliptical crack in thermopiezoelectric material. Part II: Crack propagation. Theoretical Applied Fracture Mechanics 40 (2003) 247-253
49. Sheng N., and Sze K.Y. Multi-region Trefftz boundary element method for fracture analysis in plane piezoelectricity. Computational Mechanics 37 (2006) 381-393
50. Sladek J., Sladek V., and Atluri S.N. Meshless local Petrov-Galerkin method in anisotropic elasticity. CMES: Computer Modeling in Engineering & Sciences 6 (2004) 477-489
51. Sladek J., Sladek V., Zhang Ch., Garcia-Sanchez F., and Wunsche M. Meshless Local Petrov-Galerkin Method for Plane Piezoelectricity. CMC: Computers, Materials & Continua 4 (2006) 109-118
52. Sladek J., Sladek V., Zhang Ch., and Tan C.L. Meshless local Petrov-Galerkin Method for linear coupled thermoelastic analysis. CMES: Computer Modeling in Engineering & Sciences 16 (2006) 57-68
53. Sladek J., Sladek V., Zhang Ch., Solek P., and Starek L. Fracture analyses in continuously nonhomogeneous piezoelectric solids by the MLPG. CMES: Computer Modeling in Engineering & Sciences 19 (2007) 247-262
54. Sladek J., Sladek V., Zhang Ch., and Solek P. Application of the MLPG to thermo-piezoelectricity. CMES: Computer Modeling in Engineering & Sciences 22 (2007) 217-233
55. Stehfest H. Algorithm 368: numerical inversion of Laplace transform. Communication of the Association for Computing Machinery 13 (1970) 47-49
56. Suresh S., and Mortensen A. Fundamentals of Functionally Graded Materials (1998), Institute of Materials, London
57. Timoshenko S.P., and Goodier J.N. Theory of Elasticity (1951), McGraw-Hill, New York
58. Tsamasphyros G., and Song Z.F. Analysis of a crack in a finite thermopiezoelectric plate under heat flux. International Journal of Fracture 136 (2005) 143-166
59. Tzou H.S., and Ye R. Piezothermoelasticity and precision control of piezoelectric systems: theory and finite element analysis. Journal of Vibration and Acoustics 116 (1994) 489-495
60. Ueda S. Crack in functionally graded piezoelectric strip bonded to elastic surface layers under electromechanical loading. Theoretical Applied Fracture Mechanics 40 (2003) 225-236
61. Yu S.W., and Qin Q.H. Damage analysis of thermopiezoelectric properties: Part I - Crack tip singularities. Theoretical Applied Fracture Mechanics 25 (1996) 263-277
62. Yu S.W., and Qin Q.H. Damage analysis of thermopiezoelectric properties: Part II - Effective crack model. Theoretical Applied Fracture Mechanics 25 (1996) 279-288
63. Zhu X., Wang Z., and Meng A. A functionally gradient piezoelectric actuator prepared by metallurgical process in PMN-PZ-PT system. Journal of Material Science Letter 14 (1995) 516-518
64. Zhu X., Zhu J., Zhou S., Li Q., and Liu Z. Microstructures of the monomorph piezoelectric ceramic actuators with functionally gradient. Sensors Actuators A 74 (1999) 198-202