Open Access

ARTICLE

Dynamic Anti-plane Crack Analysis in Functional Graded Piezoelectric Semiconductor Crystals

by J. Sladek¹, V. Sladek¹, E. Pan³, D.L. Young⁴

1 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia.
2 Corresponding author.
3 Computer Modeling and Simulation Group, Department of Civil Engineering, University of Akron, Akron, OH 44325-3905, USA.
4 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan.

Computer Modeling in Engineering & Sciences 2014, 99(4), 273-296. https://doi.org/10.3970/cmes.2014.099.273

Abstract

This paper presents a dynamic analysis of an anti-plane crack in functionally graded piezoelectric semiconductors. General boundary conditions and sample geometry are allowed in the proposed formulation. The coupled governing partial differential equations (PDEs) for shear stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. The derived local integral equations involve one order lower derivatives than the original PDEs. All field quantities are approximated by the moving least-squares (MLS) scheme. After performing spatial integrations, we obtain a system of ordinary differential equations for the involved nodal unknowns. It is noted that the stresses and electric displacement field in functionally graded piezoelectric semiconductors exhibit the same singularities at crack tips as in a homogeneous piezoelectric solid. The influence of the initial electron density on the intensity factors and energy release rate is also investigated.

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Keywords

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