2-D transient dynamic analysis of cracked piezoelectric solids by a time-domain BEM

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 33-40, 2008, Pages 3108-3121

  García Sánchez, Felipe ^a   Zhang, Chuanzeng ^b   Sáez, Andrés ^c  

^a UNIVERSITY OF MÁLAGA   (Spain)

^b UNIVERSITY OF SIEGEN   (Germany)

^c UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Convolution quadrature; Dynamic crack analysis; Dynamic intensity factors; Piezoelectric solids; Time domain BEM

Indexed keywords

BOUNDARY ELEMENT METHOD; CRACKS; DYNAMIC ANALYSIS; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; TIME DOMAIN ANALYSIS;

COLLOCATION METHOD; CONVOLUTION QUADRATURE; DYNAMIC INTENSITY FACTORS; PIEZOELECTRIC SOLIDS;

PIEZOELECTRIC MATERIALS;

BOUNDARY ELEMENT METHOD; CRACKS; DYNAMIC ANALYSIS; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; PIEZOELECTRIC MATERIALS; TIME DOMAIN ANALYSIS;

EID: 44749087590     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.02.013     Document Type: Article

References (44)

1. Barnett D.M., and Lothe J. Dislocations and line charges in anisotropic piezoelectric insulators. Phys. Stat. Sol. (b) 76 (1975) 105-111
2. Cady W.G. Piezoelectricity (1964), Dover Publishers, New York
3. Daros H. Wave propagation in unbounded piezoelectric media of transversely isotropic symmetry. Braunschweig Series on Mechanics vol. 39 (1999), TU Braunschweig, Germany
4. Daros H., and Antes H. Dynamic fundamental solutions for transversely isotropic piezoelectric materials of crystal class 6 mm. Int. J. Solids Struct. 37 (2000) 1639-1658
5. Daros H. A fundamental solutions for transversely isotropic piezoelectric solids under electrically irrotational approximation. Mech. Res. Commun. 29 (2002) 61-71
6. Daros H. The elastic motion of a transversely isotropic piezoelectric solid caused by impulsive loading. Z. Angew. Math. Phys. (ZAMP) 51 (2002) 397-418
7. Denda M., and Araki Y. Eigenvalue analysis by time-harmonic BEM for 2-D piezoelectricity: comparison of eigensolvers. In: Yao Z., and Aliabadi M.H. (Eds). Boundary Element Techniques (2002), Tsinghua University Press, Beijing, China 71-76
8. Denda M., Araki Y., and Yong Y.K. Time-harmonic BEM for 2-D piezoelectricity applied to eigenvalue problems. Int. J. Solids Struct. 41 (2004) 7241-7265
9. Dineva P., Gross D., and Rangelov T. Dynamic interaction of cracks in piezoelectric materials. In: Hwangm I.S., Schanz M., Steinbach O., Beer G., and Langer U. (Eds). Book of Abstracts: IABEM 2006 Conference Graz Austria, July 10-12, 2006 (2006), Verlag der TU Graz, Austria 221-224
10. J. Domínguez, A. Sáez, F. García-Sánchez, Numerical approach for dynamic fracture in piezoelectric solids, in: Proceedings of the XXI International Congress of Theoretical and Applied Mechanics (XXI ICTAM), Warsaw, Poland, 2004.
11. G. Dziatkiewicz, P. Fedelinski, Dynamic analysis of piezoelectric structures by the dual reciprocity boundary element method, in: B. Gatmiri, A. Sellier, M.H. Aliabadi, (Eds.), Advances in Boundary Element Techniques VII. EC Ltd., UK, 2006, pp. 121-126.
12. Enderlein M. FEM-analysis of cracks in piezoelectric structures under dynamic electromechanical loading. In: Nilsson F. (Ed). Proceedings of the 15th European Conference on Fracture (2004), Stockholm, Sweden
13. Enderlein M., Ricoeur A., and Kuna M. Finite element techniques for dynamic crack analysis in piezoelectrics. Int. J. Fract. 134 (2005) 191-208
14. García-Sánchez F., Sáez A., and Domínguez J. Dynamic crack interaction in 2-D piezoelectrics. In: Atluri S.N., and Tadeu S.N. (Eds). Advance in Computational & Experimental Engineering & Sciences (2004), Tech Science Press 218-223
15. García-Sánchez F., Sáez A., and Domínguez J. Anisotropic and piezoelectric materials fracture analysis by BEM. Comput. Struct. 83 (2005) 804-820
16. F. García-Sánchez, Numerical Study of Fracture Problems in Anisotropic Elastic and Piezoelectric Solids, Ph.D. Thesis, University of Sevilla, Spain, 2005 (in Spanish).
17. F. García-Sánchez, Ch. Zhang, A. Saez, A 2-D time-domain BEM for dynamic analysis of cracked piezoelectric solids, in: B. Gatmiri, A. Sellier, M.H. Aliabadi (Eds.), Advances in Boundary Element Techniques VII. EC Ltd., UK, 2006, pp. 165-171.
18. García-Sánchez F., Zhang Ch., Sládek J., and Sládek V. 2-D transient dynamic crack analysis in piezoelectric solids by BEM. Comput. Mater. Sci. 39 (2007) 179-186
19. Gradshteyn I.S., and Ryzhik I.M. Table of Integrals Series and Products. sixth ed. (2000), Academic Press
20. Gaul L., Kögl M., and Wagner M. Boundary Element Methods for Engineers and Scientists (2003), Springer, Berlin
21. Gaul L., Kögl M., Moser F., and Schanz M. Boundary element methods for the dynamic analysis of elastic viscoelastic and piezoelectric solids. In: Stein E., de Borst R., and Hughes T.J.R. (Eds). Encyclopedia of Computational Mechanics (2004), John Wiley & Sons
22. D. Gross, P. Dineva, T. Rangelov, Dynamic fracture behaviour of a multilayered piezoelectric solid, DFG Research Report Institute of Mechanics, TU Darmstadt, Germany, 2002.
23. Gross D., Dineva P., and Rangelov T. BIEM for cracked piezoelectric solids under dynamic load. In: Yao Z.H., Yuan M.W., and Zhong W.X. (Eds). Proceedings of the WCCM VI in conjuction with APCOM'04 (2004), Tsinghua University Press & Springer-Verlag, Beijing, China September 5-10
24. Gross D., Dineva P., and Rangelov T. 2D wave scattering by a crack in a piezoelectric plane using traction BIEM. Struct. Integr. Dur. 1 (2005) 35-47
25. Gross D., Dineva P., and Rangelov T. BIEM solution of piezoelectric cracked finite solids under time-harmonic loading. Engng. Anal. Bound. Elem. 31 (2007) 152-162
26. Kögl M., and Gaul L. Dual reciprocity boundary element method for three-dimensional problems of dynamic piezoelectricity. Boundary Elements XXI (1999), WIT Press, Southampton, UK 537-548
27. Kögl M., and Gaul L. A boundary element method for transient piezoelectric analysis. Engng. Anal. Bound. Elem. 24 (2000) 591-598
28. Kögl M., and Gaul L. Piezoelectric analysis with FEM and BEM. In: Suleman A. (Ed). Smart Structures: Applications and Related Technologies. CISM Courses and Lectures vol. 429 (2001), Springer-Verlag, Wien 120-130
29. Khutoryansky N., and Sosa H. Dynamic representation formulas and fundamental solutions for piezoelectricity. Int. J. Solids Struct. 32 (1995) 3307-3325
30. Khutoryansky N.M., and Sosa H. Construction of dynamic fundamental solutions for piezoelectric solids. Appl. Mech. Rev. 48 (1995) 222-229
31. 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. Comput. Mech. 29 (2002) 510-519
32. Lubich C. Convolution quadrature and discretized operational calculus. Part I. Numer. Math. 52 (1988) 129-145
33. Lubich C. Convolution quadrature and discretized operational calculus. Part II. Numer. Math. 52 (1988) 413-425
34. Norris N. Dynamic Green's functions in anisotropic piezoelectric, thermoelastic and poroelastic solids. Proc. R. Soc. London A 447 (1994) 175-188
35. Pan E. A BEM analysis of fracture mechanics in 2-D anisotropic piezoelectric solids. Engng. Anal. Bound. Elem. 23 (1999) 67-76
36. Parton V.Z., and Kudryavtsev B.A. Electromagnetoelasticity (1988), Gordon and Breach Science Publishers
37. Sáez A., Domínguez J., and García-Sánchez F. BEM for cracked piezoelectric solids. In: Yao Z.H., Yuan M.W., and Zhong W.X. (Eds). Proceedings of the WCCM VI in Conjuction with APCOM'04 September 5-10 (2004), Tsinghua University Press & Springer Verlag, Beijing, China
38. Sáez A., García-Sánchez F., and Domínguez J. Hypersingular BEM for dynamic fracture in 2-D piezoelectric solids. Comput. Meth. Appl. Mech. Engng. 196 (2006) 235-246
39. Sladek J., Sladek V., Zhang Ch., García-Sánchez F., and Wüunche M. Meshless local Petrov-Galerkin method for plane piezoelectricity. Comput. Mater. Continua. 4 (2006) 109-118
40. Wang C.-Y., Zhang Ch., and Hirose S. Dynamic fundamental solutions and time domain BIE formulations for piezoelectric solids. In: Gallego R., and Aliabadi M.H. (Eds). Advance in Boundary Element Techniques, IV (2003), Queen Mary and Westfield College, University of London, UK 215-225
41. Wang C.-Y., and Zhang Ch. 2D and 3D dynamic Green's functions and time-domain BIE formulations for piezoelectric solids. In: Yao Z.H., Yuan M.W., and Zhong W.X. (Eds). Proceedings of the WCCM VI in Conjuction with APCOM'04, September 5-10, 2004 (2004), Tsinghua University Press & Springer Verlag, Beijing, China
42. Wang C.Y., and Zhang Ch. 3-D and 2-D dynamic Green's functions and time-domain BIEs for piezoelectric solids. Engng. Anal. Bound. Elem. 29 (2005) 454-465
43. Ch. Zhang, Transient dynamic analysis of cracked piezoelectric solids by a time-domain BIEM, in: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner (Eds.), Proceedings of the Fifth World Congress on Computational Mechanics (WCCMV), July 7-12, 2002. Vienna University of Technology, Vienna, Austria-ISBN 3-9501554-0-6.
44. Zhang Ch., Wang C.-Y., and Hirose S. A time-domain BIEM for dynamic crack analysis of a piezoelectric solid. In: Yao Z., and Aliabadi M.H. (Eds). Boundary Element Techniques (2002), Tsinghua University Press, Beijing, China 119-126