A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) piezoelectric and magneto-electric-elastic solids with continuously varying material properties. Stationary and transient dynamic problems are considered in this paper. The local weak formulation is employed on circular subdomains where surrounding nodes randomly spread over the analyzed domain. The test functions are taken as unit step functions in derivation of the local integral equations (LIEs). The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Atluri, S.N.: The Meshless Method (MLPG) For Domain & BIE Discretizations. Tech Science Press, Forsyth, GA (2004)
Belytschko, T., Krogauz, Y., Organ, D., Fleming, M., Krysl, P.: Meshless methods; an overview and recent developments. Comp. Meth. Appl. Mech. Eng. 139, 3–47 (1996)
Berlingcourt, D.A., Curran, D.R., Jaffe, H.: Piezoelectric and piezomagnetic materials and their function in transducers. Phys. Acoustics 1, 169–270 (1964)
Enderlein, M., Ricoeur, A., Kuna, M.: Finite element techniques for dynamic crack analysis in piezoelectrics. Int. J. Fract. 134, 191–208 (2005)
Eringen, C.E., Maugin, M.A.: Electrodynamics of Continua. Springer, Berlin (1990)
Feng, W.J., Su, R.K.L.: Dynamic internal crack problem of a functionally graded magneto-electro-elastic strip. Int. J. Solid. Struct. 43, 5196–5216 (2006)
Fleming, M., Chu, Y.A., Moran, B., Belytschko, T.: Enriched element-free Galerkin methods for crack tip fields. Int. J. Numer. Meth. Eng. 40, 1483–1504 (1997)
Garcia-Sanchez, F., Rojas-Diaz, R., Saez, A., Zhang, Ch.: Fracture of magnetoelectroelastic composite materials using boundary element method (BEM). Theor. Appl. Fract. Mech. 47, 192–204 (2007)
Garcia-Sanchez, F., Saez, A., Dominguez, J.: Anisotropic and piezoelectric materials fracture analysis by BEM. Comput. Struct. 83: 804–820 (2005)
Hu, K.Q., Li, G.Q., Zhong, Z.: Fracture of a rectangular piezoelectromagnetic body. Mech. Res. Commun. 33, 482–492 (2006)
Kuna. M.: Finite element analyses of cracks in piezoelectric structures — a survey. Arch. Appl. Mech. 76, 725–745 (2006)
Landau, L.D., Lifshitz, E.M.: Electrodynamics of Continuous Media (second edition). Perga-mon Press, New York (1984)
Li, J.Y.: Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. Int. J. Eng. Sci. 38, 1993–2011 (2000)
Liu, G.R., Dai, K.Y., Lim, K.M., Gu, Y.T.: A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures. Comput. Mech. 29, 510– 519 (2002)
Nan, C.W.: Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B 50, 6082–6088 (1994)
Ohs, R.R., Aluru, N.R.: Meshless analysis of piezoelectric devices. Comput. Mech. 27, 23–36 (2001)
Pan, E.: A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids. Eng. Anal. Bound. Elem. 23, 67–76 (1999)
Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity, Piezoelectrics and Electrically Conductive Solids. Gordon and Breach, New York (1988)
Sladek, J., Sladek, V., Atluri, S.N.: Meshless local Petrov-Galerkin method in anisotropic elasticity. CMES Comput. Model. Eng. Sci. 6, 477–489 (2004)
Sladek, J., Sladek, V., Zhang, Ch., Garcia-Sanchez, F., Wünsche, M.: Meshless Local Petrov-Galerkin method for plane iezoelectricity. CMC: Comput. Mater. Continua 4, 109–118 (2006)
Song, Z.F., Sih, G.C.: Crack initiation behavior in magnetoelectroelastic composite under in-plane deformation. Theor. Appl. Fract. Mech. 39, 189–207 (2003)
Stehfest, H.: Algorithm 368: numerical inversion of Laplace transform. Commun. Assoc. Comput. Mach. 13, 47–49 (1970)
Suresh, S., Mortensen, A.: Fundamentals of Functionally Graded Materials. Institute of Materials, London (1998)
Tian, W.Y., Gabbert, U.: Macro-crack-micro-crack problem interaction problem in magneto-electroelastic solids. Mech. Mater. 37, 565–592 (2005)
Tian, W.Y., Rajapakse, R.K.N.D.: Fracture analysis of magnetoelectroelastic solids by using path independent integrals. Int. J. Fract. 131, 311–335 (2005)
Wang, B.L., Mai, Y.W.: Crack tip field in piezoelectric/piezomagnetic media. Eur. J. Mech. A-Solid. 22, 591–602 (2003)
Wang, B.L., Mai, Y.W.: Applicability of the crack-face electromagnetic boundary conditions for fracture of magnetoelectroelastic materials. Int. J. Solid. Struct. 44, 387–398 (2007)
Zhu, X., Wang, Z., Meng, A.: A functionally gradient piezoelectric actuator prepared by metallurgical process in PMN-PZ-PT system. J. Mater. Sci. Lett. 14, 516–518 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science + Business Media B.V
About this chapter
Cite this chapter
Sladek, J., Sladek, V., Wen, P.H. (2009). Modeling of Smart Structures by Meshless Local Integral Equation Method. In: Eberhardsteiner, J., Hellmich, C., Mang, H.A., Périaux, J. (eds) ECCOMAS Multidisciplinary Jubilee Symposium. Computational Methods in Applied Sciences, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9231-2_18
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9231-2_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9230-5
Online ISBN: 978-1-4020-9231-2
eBook Packages: EngineeringEngineering (R0)